Problem SolvingProcess Improvement Tools &Techniques Guide book.pdf

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Problem Solving and ProcessImprovement

Tools and Techniques Guide Book

© Max Zornada, Henley Management Group Pty Ltd, A.C.N. 054 337 101

61 Carrington Street, Adelaide 5000 South Australia,

Tel (08) 8237 0586, Fax (08) 8237 0555, Email:[email protected] Web: www.hmg.com.au



Problem Solving and Process Improvement Tools and Techniques Page 2




Contents

1. Introduction ......................................................................................................................................... 5

2. Problem Solving and Decision Making in Organisations ................................................................... 6

Conventional Approaches to Problem Solving .................................................................................................. 6

Problem Solving and Improvement in Six Sigma Organisations ................................................................. ...... 8

Root Cause Analysis ....................................................... .................................................................... ............. 10

The Problem Solving Tools and Techniques ................................................................ .................................... 13

3. Process Mapping ............................................................................................................................... 15

What is Process Mapping? .......................................................................................... .................................... 15

When to use Process Mapping ............................................................................................................ ............. 16

How to Build a Process Map ................................................................ ........................................................... 17

Issues to consider when developing Process Maps ................................................................. ......................... 18

Variations on Basic Process Mapping ............................................................... .............................................. 19

4. Problem Identification Tools and Techniques .................................................................................. 22

Brainstorming ................................................................. ................................................................. ................ 23

List Reduction ................................................................. ................................................................. ................ 27

Nominal Group Technique .......................................................... ................................................................... .. 28

Multivoting ........................................................... ................................................................... ......................... 31

5. The Seven Tools of Quality .............................................................................................................. 32

Cause and Effect Analysis (Fishbone Diagram) .......................................................... .................................... 33

Check Sheets ........................................................ ................................................................... ......................... 38

Pareto Analysis ............................................................... ................................................................. ................ 40

Histograms ........................................................... ................................................................... ......................... 46

The Scatter Diagram ................................................................ ................................................................... .... 51

Run Charts ........................................................... ................................................................... ......................... 57

Control Charts ................................................................ ................................................................. ................ 60

The X Chart .......................................................... ................................................................... ......................... 65

The X-bar and R Chart .................................................................................................................................... 68

The i and mr Chart........................................................................................................................................... 73

The np Chart. .......................................................................................................................... ......................... 79

The p Chart .......................................................... ................................................................... ......................... 84

The c Chart ...................................................................................................................................................... 88




The u Chart .......................................................... ................................................................... ......................... 92

Interpreting Control Charts .................................................................. ........................................................... 97

Process Capability .......................................................... .................................................................... ........... 100

6. Extensions to the Seven Tools of Quality....................................................................................... 102

Interviews ............................................................. ................................................................... ....................... 103

Questionnaires ................................................................ ................................................................. .............. 106

Dot Plots .............................................................. ................................................................... ....................... 109

Box Plots .............................................................. ................................................................... ....................... 111

Force Field Analysis ....................................................... .................................................................... ........... 121

7. The Seven Quality Management and Planning Tools .................................................................... 124

The Affinity Diagram ....................................................................................... .............................................. 126

Relations Diagram .......................................................... .................................................................... ........... 132

The Systematic Diagram (Tree Diagram) ........................................................ .............................................. 138

The Matrix Diagram ....................................................... .................................................................... ........... 142

The Decision Matrix ...................................................................................................................................... 145

The Prioritisation Matrix ............................................................ ................................................................... 149

The Allocation Matrix ................................................................ .................................................................. .. 152

The Process Decision Program Chart ......................................................................................................... .. 155

The Network Diagram (Critical Path) ......................................................................... .................................. 158

Appendix: Understanding Data and Variation ................................................................................... 159

1. Introduction to Variation .................................................................................................... ....................... 160

2. Observing Variation .................................................................................................................................. 160

3. Characterising Data ................................................................................................ .................................. 160

4. Understanding Variation ................................................................................................................ ........... 170




1. Introduction

This “Tools and Techniques” guidebook is intended to act as a reference source

for problem solving and process improvement practitioners, facilitators, team

leaders and team members. In this guidebook, you will find a comprehensivecoverage of all the major tools and techniques that have been found to be useful

in problem solving and process improvement applications. This includes the

original seven tools proposed by Dr. Kaoru Ishikawa as well as many others used

in support of these.

Before looking at each tool or technique in detail, the early part of this handbook

addresses the context in which the tools are used, by considering the issue of

problem solving and decision making in organisations, and contrasting

conventional approaches to structured quality based approaches.

In particular, we will look at the DMAIC problem solving process and processimprovement framework that is part of the Six Sigma philosophy.




2. Problem Solving and Decision Making in

Organisations

Convent ional Approaches to Problem Solv ing

Being regularly confronted with problems to be solved, issues to be resolved and

decisions to be made is and has always been a major part of the day-to-day work

routine for all employees, regardless of the type and size of organisation, or the

level at which they work.

The only apparent difference as one moves through the organisational levels

from shopfloor to boardroom, is the type and scope of problems, issues,

decisions and the individual’s power to address them.

Individual experts and expertise, “troubleshooters” and “gut feel”, usually in themanagement and executive levels have dominated problem solving and decision

making approaches in most organisations.

The result of such approaches have been knee-jerk reactions to symptoms,

temporary “fixes” that fail to address the true causes of a problem and lack of

commitment by the those affected to implement the solution.

Hierarchical organisational structures and lengthy internal lines of

communication means that only a small proportion of all problems and issues

are ever known about by the management levels who have the authority to

address them.

Therefore, not only is problem solving and decision making overly dependent on

a few key individuals, but even where the individuals are effective problem

solvers, they rarely find out about more than a relatively small proportion of the

problems.

The consequences of such approaches are that most of the organisation’s

employees work in an environment where they have to put up with a whole host

of unresolved issues and problems, which they know about but are helpless to

act upon, as part of their day-to-day work life. This leads to frustration anddemotivation.

A more dangerous consequence is that when particular unresolved issues and

problems persist over a long period of time, they gradually become accepted as

part of the organisation’s “business as usual” paradigm. Both management and

workforce become blind to the problem or issues, accepting them as a natural

part of the way things are.




A common response to any “outsider” or newcomer challenging or highlighting

such a problem or issue is often - “that’s the way we do thing’s around here!”.

In this manner, problems, inefficiencies and bad practices become

institutionalised. Attempts to address them are met with resistance, often coming

from those who would benefit most from the change.

Such organisations are easy prey for quality driven competitors. When faced

with the need to improve, they are usually blind to the opportunities within their

organisation and so focus their energies blaming external factors.




Problem Solv ing and Improvement in Six Sigma

Organisat ions

Problem solving in Six Sigma organisations follows a structured process that

provides the discipline to ensure problem solvers do not jump to solutions beforethey have analysed the causes and that the solutions when implemented, really

do address and eliminate the root causes of problems.

In particular, there is a strong focus on reducing variation and the cost of poor

quality.

The core of the Six Sigma approach is the Define, Measure, Analyse, Improve,

Control cycle or DMAIC.

This is illustrated in Figure 2.1 below.

Figure 2.1. The DMAIC Cycle

When applying the DMAIC cycle, problem solving and process improvement

teams work through each stage in turn, where by they are required to:

Define – the problem/opportunity, customer and customer requirements and

the process that will be affected;

Measure – Determine and implement the required process measured to

monitor and establish the current performance baseline for the process and

the problem impact.

Analyse – Analyse the problem and the process by conducting a root cause

analysis until the potential root cause(s) is found.

Define

Measure

Analyse

Improve

Control

6




Improve – Generate potential solutions and assess them suitability, before

selecting the preferred solution and implementing it.

Control – institutionalise the change by embedding it into the process

through procedures, systems and standards. Implementing appropriate

performance measures for ongoing monitoring of the process.The basic DMAIC process can be further expanded to provide detailed

guidance for problem solving and process improvement teams by presenting

the key stages with their detailed steps in the form of a story board the team

work their way through, as shown in Figure 2.2.

Figure 2.2: DMAIC Problem Solving – Process Improvement Storyboard






Quality based problem solving focuses on identifying and eliminating root

causes. It does this by providing a structured process through the DMAIC

cycle, whereby causes can be tested to determine whether or not they are root

causes, as they are found.

Root causes can be further assessed to determine whether they are the correctroot cause for the problem at hand. ie. we may find a root cause, but it may not

be the root cause of our problem.

Identifying Root Causes

An overview of the root cause analysis process can be presented as follows.

Observedsymptom

"TheProblem"

Applyproblemsolvingprocess

Causefound?

Iscauseactionable? Not aroot cause

Causefound?

Doesaction(s)fixproblem?

Not therightcause

Problem Sol

YES

YES

NO

NO

Figure 2.4 Finding the Root Cause

A key feature of non-root causes, is that they are rarely directly actionable.

Problem solvers may often derive an action by jumping to conclusions and

acting on these.




If cycling through the root cause analysis process identifies a cause that is not

directly actionable, it is unlikely to be a root cause. This cause then becomes the

focus of the next cycle of analysis.

The process is repeated until an actionable cause is found.

An actionable cause will be a root cause, but it may be the wrong root cause.

Therefore, the process requires problem solving teams to check whether or not

actioning the root cause actually solves the problem. If it doesn’t, the process is

repeated until the right root cause is found.

Using the tools and techniques

Although there are many tools and techniques available, in practice, one finds

that a few tend to be used time and time again. The common cycle of events,

linked to the specific tools used most of the time is illustrated in Figure 2.5.

Cause & Effect Analysis

(Fishbone diagram) used to

brainstorm possible causes.

Vote on most likely and

develop data collection

approach and instrument.

This will usually be some sort

of checksheet.

Collect data using thechecksheet or other

appropriate data gathering

proforma.

Analyse Data using a Pareto

chart , determine most likely

cause.

If cause not actionable,

redefine problem to

determine causes of thiscause and repeat the process.

Figure 2.5 Using the Problem Solving Tools

No

Yes

Is cause

actionable?

Define the problem




The Problem Solv ing Tools and Techniques

There are now a wide range of tools and techniques available to the quality

practitioner.

The problem solving and continuous improvement processes previously

described all call for the use of specific tools at the various stages of the process.

A key technique is the use of flow charting or process mapping as a tool for

understanding business and work processes.

By far the most common tools and techniques used to supplement process

mapping are the original seven tools of quality put forward by Dr. Kaoru

Ishikawa. These are:

Check sheets;

Cause-and-Effect diagrams;

Pareto Charts;

Histograms;

Scatter Diagrams;

Run Charts;

Control Charts.

Since then, many more tools and techniques have been added to the growing

arsenal that is now available to the quality practitioner. Most of the tools andtechniques have been developed for use at both the individual level or as part of

a group or team process.

In addition, their use has been extended well beyond their initial manufacturing

application as the quality philosophy has spread to the broader business

community.

This booklet introduces the reader to:

Process Mapping using the flowcharting technique;

Tools used to support initial problem identification. This includes:

Brain Storming

Nominal Group Technique

Multivoting




The original seven tools of Quality. Namely:

Histograms;


Check sheets; Pareto Charts;

Scatter Diagrams;

Run Charts;

Control Charts.

Tools that have been added and accepted as supplements to the seven tools.

Including:

Interviews;

Opinion Questionnaires;

Dot Plots;

Box Plots;

Force Field Analysis;

Process Capability Study;

The seven quality management and planning tools developed to support and

guide managerial problem solving and decision making. These include:

Affinity Diagram;

Interrelationship Diagram;

Systematic Diagram;

Matrix Diagram;

Matrix-Data Analysis;

Process Decision Program Chart;

Activity Network Diagram.




3. Process Mapping

What is Process Mapping?

Process mapping is a technique used to analyse business and work processes.

Process mapping or flow charting as it is sometimes called, allows users to

build a picture or map of a process - a process map, using easy-to-understand

visual symbols. A process map reveals what a process actually looks like, its

shape and the flow of work through it.

The symbols most often used in process mapping/flow charting are given in

Figure 3.1.

Figure 3.1 Process Mapping Symbols

Figure 3.2 illustrates part of a typical process map.

The process mapping technique, when properly applied, is particularly good at

illustrating the structure and logic behind the process flow and highlighting key

decision points.

Symbol Name Brief Definition

Operation or

process step

Decision Point

Document

Generated

Continuation

Point

Input/Output

Block

Flow lines

Depending on the level of detail being developed, can be

used to denote anything from a simple task, major activity

or a whole sub-processes.

Used to indicate the process is continued elsewhere on

the flow diagram or on another sheet.

Point at which a form or report is generated by the

process.

Point where a decision must be made before any

further action can be taken.

Optionally used to describe an input or output from a

processing block.

Use to connect all blocks to display the sequence in

which operations are performed.

Termination

point

Used to indicate the start and end of a process.




IsAccount Mgr in?

Raiseofficial order

IsOrderOK?

ProvideAdditional Info

2

Yes

No

No

Yes

SendtoDataProcessing

Call Account Manager

SendtoAccount Mgr.

ProvideAdditional Info

ReturntoDataProc

Start

Document

generated

Processstep

Decisionpoint

Continuation

point

Figure 3.2. A Process Map - this example shows the order entry part of an

order fulfilment process

When to use Process Mapping

Process mapping is used whenever there is a need to understand the process.

This is usually the first step in problem solving and process improvement

situations. Process maps will readily highlight:

inherent structural inefficiencies built into a process;

areas offering the greatest potential for improvement;

what sensible measures of performance are likely to be.

Process mapping is the key tool to used gain an understanding of business or

work processes as a prerequisite to any process improvement or process re-

engineering activities.




How to Bui ld a Process Map

1. Select the process . Determine which process you wish to study.

2. Defi ne the boundar ies . Define the boundaries to your process. Will you be

looking at a small work process that is part of a much larger business process

or will you be looking at a major process that connects with external suppliers

at one end and external customers at the other? Define where you process

begins and where it finishes.

3. Identi fy the start and end poin ts . Identify where the process starts and

where it ends, identify the inputs to and outputs from the process. In particular,

identify what it is that causes the process to operate or triggers the start of the

process and what is it that determines when the process has concluded. ie.

what event, occurrence or condition.

4. Start drawing the process map . To do this:

Identify all the process steps that must occur between the beginning and end

points of the process. ie. identify each activity, task, decision point, inspection,

check point etc. that occurs;

Lay them out in the sequence in which they occur in practice. Use the standard

symbols to depict the different types of activities that may occur;

Connect the various steps with flow lines to show how the process flows

through the steps.

5. Check accur acy and completeness.Ensure all the team members involved

in developing the process map agree on what the process looks like.

If not already represented on the team, ensure people involved with each

aspect of the process are given the opportunity to comment. In particular,

check that every step and decision point has been included and that the chart

depicts what actually happens and not what team members think should

happen.(a common trap).

6. Prepare the final process map

7. Repeat step 5 . If necessary, make final adjustments.




Issues to c onsider when developing Process Maps

Level of Detail

The level of detail required for a process map will be dependent on the use theteam wish to make of the map. Is a simple overview all that is required or do

you need a detailed flowchart to identify areas of waste and inefficiency.

Typically, when looking for opportunities to change fundamental process

structures, an overview which illustrates the existing structure may be all that

is required.

Where a team is scrutinising a process to:

identify opportunities to reduce waste, complexity and inefficiency;

identify key control points;

develop meaningful performance measures;

a much more higher level of detail will need to be developed.

Who should be involved?

Ideally, the process map should be constructed by a team, whose membership

includes individuals from each part of the organisation involved with the

process.

When process mapping is left to management, staff experts or outside

consultants, the end result rarely provides a true reflection of what actually

happens. Rather, it is often the individual’s perceptions of the process or the

way it should operate.

It is essential to get the input of the people that have to work in the process day

in-day out to get the true picture of the way the process actually works.




Var iations on Basic Process Mapping

Process Blocking

In some situations it may not be necessary to document a process in detail.

All that may be required is a basic understanding of the process structure. In

the case of large business wide processes, management may need to get an

understanding of the overall process shape, before deciding to allocate teams

to examine the various subsections in detail - ie. develop detailed process

maps.

Process blocking is a tool that can be used to do this. In process blocking, we

represent major “chunks” of the process as blocks without detailed

flowcharting of what goes on inside the block.

An example of a company’s order fulfilment process, depicted using the

process blocking technique is shown in Figure 3.3.

RaiseOfficialOrder

DataProcessing

ReceiveOrder

Rejection

process

PurchasingProcess

Dispatch

&Deliver

Start

Install

Commissi

Finish

Account

Payable

Credit Check

Warehouse picking process

Figure 3.3. Order Fulfilment Process - Process Blocks




Organisational/Functional Process Maps

An example of this variation of a process map is illustrated in Figure 3.4.

The Organisational/Functional Process Map, which I refer to as a “Zig-Zag”

chart because of the way process flows often zig-zag across the chart, requiresthe team to identify all the functional positions in the organisation which are

involved in a process.

All the people involved in a process, commencing with the customer at the far

left, all internal positions and any external suppliers, usually placed at the far

right are placed horizontally across the top of the chart.

The process map is then drawn so as to depict which parts of the process are

performed by whom.

Customer Front Line

Assessm't Stamp Settlem't Manager Valuation Document'n Broker

Figure 3.4. A Zig-Zag Chart of a Bank Lending Process




Depending on the size of the process and the level of detail required, this type

of chart may be developed for the detail process map, for process or for some

combination of the two which gives an appropriate level of detail.

The advantages of this technique are that it:

Highlights how the people in the organisation work together, or are

required to work together to make the process work;

Highlights where activities happen, are required to happen or may be

organised to be done in parallel;

Readily highlights inefficiency and opportunities for inefficiencies to arise

which manifests itself in the form of zig-zagging and handovers of between

positions.

The other major advantage of this approach, in the cases of service processes

which interface with external customers, is that it allows the team to understand

how the customer sees the process.

The interaction between the customer and the organisation occurs every time a

process flow line crosses the boundary between the customer column and the

organisation.

Regardless of what the process does inside the organisation, these will be the

parts of the process the customer sees and will form the basis of their view of

how the organisation delivers its service.




4. Problem Identification Tools and Techniques

In many cases, the problem to be addressed is obvious. At other times, the

problem may not be all that apparent or well defined.

The problem identification tools and techniques are all aimed at improving the

process by which team members identify and define the specific problem, to

which they will apply the problem solving process.

The tools and techniques presented in this section include:

Brainstorming;

Nominal Group Technique;

Multivoting;




Brainstorming

What is Brainstorming?

Brainstorming is a technique for generating a large number of ideas in a short period of time.

It is a group activity in which all members try to think of as many ideas as

possible on a given topic as possible. The focus is on the quantity of ideas

generated, not on the quality, as all ideas are evaluated later.

Brainstorming assumes that no matter how crazy or irrelevant an idea may

seem at first, it may spark an original and worthwhile idea that no one would

have thought of otherwise.

Brainstorming can serve to:

document what the team already collectively knows;

stimulate creative thinking;

get everyone involved;

bring the group closer together to work and think as a team.

When to use Brainstorming

Brainstorming is a particulary valuable tool to help teams identify problems towork on. It can also be used for identifying:

possible causes;

identify possible solutions;

identify ways to implement solutions.




How do you use Brainstorming?

Although the term "brainstorming" is often use generically to describe any idea

generating activity involving a group of people, the formal brainstorming

technique follows some specific rules.

The brainstorming process is usually progressed in stages, these are:

Preparation;

Idea generation;

Review;

Evaluation;

Follow-up.

Preparation

1. Determine the purpose and establish some guidelines. Determine the

purpose of the brainstorming exercise. Make it clear to the group the type of

ideas that are being sought and establish guidelines with respect to any areas to

emphasise or ignore.

2. Set a time limit. Allow enough time for people to contribute their own

ideas and to build on the ideas of others. Do not make the time too short.

People often contribute their most valuable ideas towards the end of a session,

when they have run out of ideas and have to force themselves to come up withmore.

3. Distribute all data relevant to the purpose of the meeting before the

meeting, to avoid wasting meeting time briefing members on the purpose.

Idea Generatio n Stage

1. Encourage contributions from everyone. Encourage group members to

contribute any idea no matter how improbable. Keep the pace reasonably quick

so that group members do not have time to self-censor their contributions.

2. List all of the contributions as they are offered. This ensures that ideas do

not get lost, it avoids duplication and enables other group members to build on

other people's ideas. Often a completely impractical idea from one person will

spark another member to think of a creative and practical idea.

3. Don't evaluate. Criticism or comments about someone's idea may slow

down or even kill off further contribution. The purpose of brainstorming is to

generate as many ideas as possible, so encourage all contributions.




Some typical idea spurring questions to assist group members with building on

each others ideas include:

What else is like this ?

What other ideas does this suggest ?

Greater frequency ?

Review

Review the list of idea, to ensure all team members understand what has been

written down. This review is done purely as an aid to understanding and

clarification. There is no discussion or criticism at this stage.

Evaluation

Evaluate all the contributions, to:

combine or consolidate duplicate and related items;

exclude items irrelevant to the topic;

exclude personnel related items - we are focussing on the problem with the

process;

Discuss and evaluate each item, if discussion generate new items, add these to

the list.

Conclude the session. Distribute copies of all the ideas generated to the teammembers after the session, for individual reflection.

Follow -up Stage

A follow-up team meeting is held to prioritise and reduce this list of ideas.

This is usually done using the list reduction, multi-voting or nominal group

techniques.




Leading a Brainstorming Session

There are two general methods for leading a brainstorming session. The most

familiar is the fr ee wheel ing method, where:

Group members call out their ideas spontaneously A scribe records the ideas as they are offered

A variation on this is round-robin brainstorming, where:

The leader asks each member in turn, for an idea

Members may pass on any round

The session continues until all members have passed during the round

Ideas are recorded as in free wheeling




List Reduct ion

What is List Reduction?

List reduction is a technique that can be used to evaluate and assess the resultsof a brainstorming or other session that has generated an extensive list of

ideas, so as to reduce it to a significant few that can be investigated in detail.

How to use List Reduction

The group identifies some criteria or "filters" that should be satisfied for an

item to remain on the list. Some typical criteria might be:

Is this item likely to improve the situation ?

Is this feasible ?

Is the cost excessive ?

Keeping the agreed upon criteria in mind, group members review or in

appropriate cases vote on each item. Any borderline items should be bracketed

or underlined rather than crossed, out so that group members may return to

them later if necessary.

In general, the group focuses on and continues to evaluate the items that

remain on the list.

The process may be repeated with different or more stringent criteria, until the

list is reduced to a manageable number of options for applying some of the

other analytical tools.






Idea Presentatio n

The idea presentation stage is progressed as follows:

The facilitator asks each team member in turn to volunteer one idea. The

ideas are written up on a flip-chart or white board, visible to the teammembers as they are offered.

Members are encouraged to “feed” off each other’s ideas ie. if some one

thinks of a new idea after hearing some one else’s idea, they add it to their

list and offer it when it is their turn next.

This process continues until everyone has offered all their ideas.

No discussion or criticism is allowed at this stage.

Idea Discus sion

Review the list of ideas, to ensure all team members understand what has been

written down. This review is done purely as an aid to understanding and

clarification. Again, no discussion or criticism at this stage.

Evaluation

Evaluate all the contributions, to:

combine or consolidate duplicate and related items;

exclude items irrelevant to the topic;

exclude personnel related items - we are focussing on the problem with the

process;

Discuss and evaluate each item, if discussion generate new items, add these to

the list.

Priorit ise

An approach to prioritisation used during NGT is as follows:

Each member writes out their own copy of all the ideas left over from the

previous stage;

They individually rate their idea ie. give each idea a score out of ten, or

allocate 100 points between the ideas etc.;

The team leader or facilitator asks each member to call out their score each

idea;

The scores are totalled to give the overall rankings ie. the highest score

being the highest ranked.




Make a decision

Where a decision needs to be made, so as to arrive at a decision on a single

idea or option, the following extension to the above process can be applied.

Take the ranked ideas which resulted from the prioritisation step andeliminate the lowest ranked item from the list;

Reprioritise the items on the list using the prioritisation process previously

described;

Eliminate the lowest ranked idea;

Repeat the process until only one item remains.

Alternately:

Select the highest ranked item.

Variat ion

A variation to the basic ranking and decision making technique presented here

is to:

Define several relevant criteria against which to rate the ideas;

Apply a rating for each criteria to each idea;

Develop a consolidated score that encompasses all the criteria.






5. The Seven Tools of Quality

This section presents the seven basic tools of Quality. These are the original

seven tools put forward by Dr. Kaoru Ishikawa. They are:

Check sheets;

Histograms;


Pareto Charts;

Scatter Diagrams;

Run Charts;

Control Charts.

The use of each of these tools shall now be discussed in detail.




Cause and Effect Analys is (Fishb one Diagram)

What is a Cause and Effect Analysis?

Cause and Effect analysis is a technique for identifying the possible causes of aknow effect, usually the problem to be solved.

The Cause and Effect diagram is also known as a "Fishbone diagram" or an

Ishikawa diagram, after the Japanese Quality Management statistician Dr.

Kaoru Ishikawa who developed the technique in 1943.

The Cause-and-Effect diagram is a visually effective method of recording the

possible causes of a problem being analysed as they are suggested, organised

into the major categories that potentially contribute to a problem.

It is effectively a structured form of brainstorming. The use of the fishbonediagram to provide structure to brainstorming activity provides a degree of

focus on the problem at hand and more clearly allows team members to see or

establish the link between the observed effect and possible causes.

When do you use Cause and Effect Analysis?

The fishbone diagram is usually used after the problem identification/selection

stage of the problem solving process but before the data collection stage.

Once a problem has been identified using one the techniques identied earlier,the fishbone diagram is used to focuss the team thinking on possible causes.

The fishbone diagram will assist team members to determine what issues they

should be collecting data on, during the data collection stage of the problem

solving process.

Another advantage of cause-and-effect diagrams is that one can tell at a glance

how thoroughly a problem has been investigated. A diagram which contains a

lot of detail would suggest that a group has delved deeply into a problem.

At a more macro level, a fishbbone diagram can be used as an overall problem

identification tool, by deliberately using a broad or vague problem statement to

start the process eg. “improve business performance”, “improve quality”. The

outcomes of the fishbone exercise will be some more specific problems on

which improvement teams may focus.




How do you build a Cause and Effect Diagram?

Constructing a Cause and Effect diagram is a four step process. This is

illustrated on the following page in Figures 5.1.a to 5.1.d.

1. Describe the problem or "effect". Write a summary statement of the problem in a box on the right of the chart, with an line across the chart

representing the “backbone” See Figure 5.1.a.

Installation

Delays

Figure 5.1.a. Starting the Fishbone

2. Decide on cause categories, add these to the diagram. These major

categories of causes are placed parallel to and some distance from the main process arrow. The major categories are then connected by arrows slanting

towards the main arrow. The diagram will resemble a fishbone from which it

gets its name. See Figure 5.1.b.

Figure 5.1.b. Adding the Problem Category Spines

What constitute meaningful categories may vary, depending on the nature of the

problem.

Unfortunately, when commencing a cause and effects analysis, we will often not

be able to anticipate the problem categories which may emerge as we progress

with the exercise.

Therefore, we usually use some common “generic” categories to get the

process started eg. common “starters” used in service businesses include:

People Procedures

Equipment Environment

Installation

Delays




people;

procedures;

environment;

equipment.

In manufacturing businesses, common starters are:

people;

methods;

machines;

materials.

After conducting our initial cause and effect analysis, we may find that the

results obtained are good enough to proceed with data collection.

Alternately, our first attempt at cause and effect analysis may reveal that the

potential causes naturally fall into certain categories. At this point we may

wish to redraw the fishbone diagram using categories that we now know are

specific to the particular problem being analysed and continue the analysis in

greater depth using these categories.

3. Brainstorm for possible causes. Write these on the chart clustered around

the major category of causes they most influence. Causes should be divided

and subdivided to show, as accurately as possible the various elements of each

and how they interact. See Figure 5.1.c.

Figure 5.1.c. Building the Fishbone Diagram

People Procedures


InstallationDelays

Sales people

Truck availability

Computer problems

Poor inventory control

Poor sales notification

Bad weather

Heavy traffic

Technician

Heavy workloads




Where team members identify causes related to causes that have already been

added to the fishbone diagram, these subsequent causes are shown as

extensions to the ones already identified, as illustrated in Figure 5.1.d.

Figure 5.1.d. Continuing to build the Fishbone

4. Evaluate the possible causes. Look at each item on the fishbone and ask how

it could contribute to the problem. Either list the responses next to the item or

draw them as extensions to the fishbones as shown is Figure 5.1.d.

This analysis should also reveal how the causes provoke the effects and assist in

developing appropriate solutions.

Variations and Ideas

There are several methods for available for developing Cause and Effect or

"fishbone" diagrams.

The random method requires group members to suggest causes which apply

to any of the major sub-divisions of the diagram. As in brainstorming, the

session has a leader and a scribe to record the contributions of the group.

People Procedures


InstallationDelays

Sales people

Truck availability

Computer problems

Poor inventory control

Poor sales notification

Bad weather

Heavy traffic

Technician

Heavy workloads

C o m p u t e r d

o w n

Back ups

C o m p

u t e r c

r a s h

Not availabletoo busy

Wrong skills

No stock on hand

Order not insystem

Notenough trucks

Truck breakdowns




The systematic method requires the leader to choose one of the major sub-

divisions on which to focus the group's attention. The brainstorming process

looks at each sub-division in turn until the diagram has been completed.

When constructing the fishbone diagram, attention to a few facilitation

pointers will add value to the exercise:

Use large charts and use large printing - ensure everyone can see what is

going on;.

To encourage a free flow of ideas, follow the usual brainstorming rules;

Do not overload the diagram. If a group of causes begins to dominate,

develop a separate diagram to explore this group in more detail;

Construct a separate diagram for each problem. Where a problem

definition is not specific enough, some major categories of the diagram

may become overloaded and it will become necessary to redefine the

problem;

Look out for and examine closely the relationships between causes. This is

where unexpected solutions are likely to turn up;

Circle the most likely causes. This is usually done after all possible ideas

have been posted on the fishbone diagram and each has been critically

examined.

Preparing to Collect Data

In rare situations, an obvious implementable solution, which all team membersagree on will emerge as a result of the cause and effect analsysis.

However, the usual result of such a session is to go and collect further

information in order to evaluate the key causes that emerged from the fishbone

diagram.

The results of the cause and effect analysis can be used to guide the data

collection exercise and form the basis of the check sheet design.

Developing the Check sh eet

To derive the required check sheet format from the fishbone analysis, the

following steps can be followed:

Evaluate the identified causes to identify potential “root” causes;

Apply prioritisation, ranking and list reduction techniques to reduce the list

and identify the most likely or key causes;

Develop a checksheet which includes the reduced list of causes.




Check Sheets

What is a Check Sheet ?

A check sheet or tallysheet is a form that allows you to systematically collectdata. You enter the data as check marks, ticks or measurements and analyse

them later. Checksheets are usually used for recording numerical data.

There is no standard form for checksheets. They should be set up to whatever

form is easiest to record and analyse the information.

When to use a Checksheet

One type of checksheet is needed when you are recording data that you are

counting, such as how often something happens over a given period of time, a

different type is used for recording measurements.

Checksheets are particularly useful when several people are collecting data.

They ensure that everyone will collect comparable data in the same format,

and they also provide a clear record of gathered data.

How to use a Checksheet

1. Determine the type of data that you need to collect. This should guide the

user to the type of check sheet required. You will be trying to answer the

questions:

Will the data gathered reveal facts ?

Can the data be analysed in such a way so as to reveal facts ?

Therefore, decide initially all the factors which might affect a situation and

how you might analyse the information when you collect it.

2. Determine the categories or types of data possible. It will not be

necessary to define all the categories at the start. The check sheet can be

expanded in light of actual experience.

3. Design the checksheet form for people to use as they record the data.

The sheet must reflect the type of data collected and reflect the categories of

data that are likely to be expected.

4. Test the checksheet Get someone who didn't help design it to use it. Make

any revisions that are necessary.




Design a master checksheet if required to combine the results of numerous

individual forms where several people will be involved in collecting the data.

5. Proceed to gather data. Sample checksheet for a counting example is

shown in Table 5.1.

Table 5.1 Causes of Lost Time Injuries

Table 5.2 illustrates a measuring example.

Table 5.2 Box Weight Sampling

Weights in Grams

Batch

Number Sample 1 Sample 2 Sample 3 Sample 4 Average

R1-710-4 502 509 499 501 503

R1-710-5 497 501 505 502 501

R1-710-6 501 500 502 499 501

R2-710-1 500 507 504 503 504R2-710-2 502 508 498 499 502

Category Tally Frequency

Total

Allergy

Broken limb

Back/Neck

Concussion

Contusion

Heart Attack

Other

1

2

3

4

5

6

7

8

8

12

6

14

7

1

23

3

78

Sprains




Pareto Analysis

What is Pareto Analysis?

Pareto analysis is a technique for recording and analysing information relatingto a problem or a cause, which readily enables the most significant

contributors to be identified.

The resulting display, referred to as a Pareto Chart is a special form of

histogram which allows the information to be visually displayed.

A pattern will usually emerge when we look at the relationship between the

numbers of items/occurrences of any situation and their relationship to the

cause under consideration. This pattern has been referred as the "80/20" rule.

The Pareto Principle

This form of analysis and the resulting chart is named after an Italian

economist Vilfredo Pareto, who studied the distribution of wealth in Europe in

the late 18th and early 19th centuries. He concluded that 80% of the wealth

was held be 20% of the population. Thus the Pareto Principle or 80/20 rule

was born.

During the 20th century Dr. J. Juran was able to show that this was a much

more general principle as a result of his studies into business activities. For

example: 80% of a company's waste are as a result of 20% of the causes;

The bulk of a company's business comes from relatively few customers;

80% of your phone calls come from 20% of your friends and colleagues.

Although the exact ratio is not critical, the principle that problems can be

classified as either being one of the vital f ew or the tri vial many is important,

as it provides considerably more focus to our problem solving efforts and

yields disproportionately beneficial results.

Pareto analysis shows at a glance which problems can be treated as the vital

few, which are the trivial many and assists which the allocation of priorities.

Although this technique will confirm many known notorious problems as

belonging to the vital few, one of its major benefits is in being able to flush out

problems not previously thought of as significant, identifying these as also

belonging to the vital few.




When do you use Pareto Analysis?

Pareto analysis can be used for several purposes. Namely, to:

define where to concentrate problem solving efforts to get the most impact;

display the relative importance of the various components of a problem;

narrow a list of possible causes to identify the most likely cause;

to identify root causes.

How to Construct a Pareto Chart

1. Determine the categories to be plotted on the chart. Typically you will

want to categorise the data to be analysed. These categories will most likely be

those against which data was collected on the check sheet used during the data

collection stage.

2. Determine the measurement scale to use. The most common are cost,

frequency of occurrence and percentage.

3. Collect and tabulate the information required. See the previous section

on check sheets for more information. The following is an example of a record

of machine stoppages recorded for a wrapping machine.

Table 5.3. Machine Stoppages

Causes Number of

Occurences

Percentage

Machine breakdown 9 6%

Operators Error 14 9%

Wrapping Jam 62 41%

Mechanical Jam 18 12%

Product Jam 38 25%

Foreign Object 3 2%

Other 8 5%

Total 152 100%




4. List the categories along the bottom of the chart, starting with the

largest one on the left. If there are many very small categories, group these

together into a single group called "other". See Figure 5.2.a.

Wrapping

Jam

Product

JamMech.

Jam

Operator

Error Machine

B/downOther Forei

bjt

Figure 5.2.a. Categories Layout for Pareto Chart

5. On the left side, mark off the vertical axis representing the measure

that was used. Mark off the units of measure up to or slightly more than the

maximum occurrences measured for any one category.

WrappingJam

Product Jam

Mech.Jam

Operator Error

MachineB/down

Other ForeiObjet

0

10

20

30

40

50

60

70

Figure 5.2.b Mark up the Vertical Axis




6. Draw a bar above each category to represent its size in terms of the

measurement which was used. From Table 5.3, draw a bar respresenting the

nubmer of occurences for each catergory of cause. This is illustrated in Figure

5.2.c.

Wrapping

Jam

Product

JamMech.

Jam

Operator

Error Machine

B/downOther Forei

Objet

0

10

20

30

40

50

60

70

62

38

1814

9 8

3

Figure 5.2.c. The completed Pareto Chart

7. Interpret the Pareto Chart From Figure 5.2 we can see that wrapping jam is the

major cause, followed by product jam. The remainder of the causes are relatively

insignificant at this stage when compared to the first two.

The Pareto chart suggests, that to eliminate the problem of wrapping machine

stoppages, focussing our efforts initially on resolving the reasons why wrapping

jams occur and then on product jams will give a disproportionately high

improvement in performance, when compared to putting effort into the other

causes. ie. These are the “Pareto” causes, accounting for some 66% of the

problem.

A word of caution! This is not to say that the other causes are not important and

should be ignored. Improvement teams should work to eventually eliminate or

minimise all the causes identified.






0

20

40

60

80

100

41

25

129

6 5 2

Wrapp'gJam

Mech.Jam

Mach.B/down

Other ForeiObje

Product Jam

Op.Error

Figure 5.2.e. A Percentage Pareto with Cumulative Line




Histograms

What is a Histogram?

A histogram is a chart using bars of varying heights that illustrates the shape of a data distribution from which data has been collected.

When to Use a Histogram

Use a histogram when you need to obtain an understanding of the degree and

nature of variations that are occurring in a given process, where they are

occurring and to what extent.

How to Construct a Histogram

1. Define what you are going to measure

Example: Age at failure of washing machines in customers homes.

2. Collect the data.

The following represents data collected over a one month period.

Age in months, of washing machines at fail ure

56 46 48 50 42 43 5212 49 44 50 32 60 74

1 72 60 57 40 49 49

80 63 49 45 57 23 61

41 34 54 68 37 67 78

15 68 56 47 63 59 72

68 71 63 68 29 51 53

70

3. Determine the number of classes into which to divide the data. When

looking at a large group of figures, they can more easily be displayed andunderstood if they are grouped for convenience.

The intervals that define the groupings are usually called “classes" or "class

intervals" and the number of data readings falling into each of the classes are

called the "frequencies".

The following table provides a good "rule of thumb" for determining the

number of classes or intervals to use.




Table 5.4 Determining the number of Class Intervals

Number of Data Values (N) Number of Classes (K)

Under 50 5 to 7

50 to 100 6 to 10

100 to 250 7 to 12

Over 250 10 to 20

In our example, the number of data values is 50 ie. N = 50. Therefore, from the

above table, we shall select the number of class intervals as 7. ie. K = 7.

4. Determine the class interval size.

By examining our original data, we can observe that the largest value (which

we shall arbitrarily call L) is 80. ie. L = 80. Similarly, the smallest value

present is 1 (which we shall arbitrarily call S) ie. S = 1.

The class sizes can now be calculated as:

L - S = 80 - 1 = 79 = 11.28

K 7 7

Which we shall round off to 12.

5. Construct a Tally Sheet with the appropriate class boundaries defined.

With reference to our previous calculations, we can construct a Tally Sheet

(also referred to as a frequency diagram) and analyse our data in preparation

for plotting a histogram. This is shown in Table 5.5.

Table 5.5 Tally Chart of washing machine failures

Class No Class

Boundaries

Frequency Tally Frequency

or Count

1 1 to 12II

22 13 to 24 II 2

3 25 to 36 III 3

4 37 to 48 10

5 49 to 60 II 17

6 61 to 72 III 13

7 73 to 84 III 3

Total = 50




As a crosscheck that you have constructed the tally chart correctly, the

frequency column should total up the number of values in the original data. In

the example given here, N = 50.

6. Construct the Histogram. Write the class interval values at the bottom of

the graph. Write the frequency measures along the vertical axis.

1-1213-2425-3637-4849-6061-7273-0

5

10

15

20

Figure 5.3.a. Laying out the axes for a Histogram

7. Draw in bars representing number of items counted in each of the class

intervals. The completed histogram is show in Figure 5.3.b.

1-1213-2425-3637-4849-6061-7273-80

5

10

15

20

2 23

10

17

13

3

Figure 5.3.b. Completed Histogram






A "comb like" histogram suggests poor measurement method, faulty or

incorrectly set instrumentation or similar recording problem.

Figure 5.3.d Bi-modal distribution

This histogram is "bimodal" ie. it has two data peaks. Bi or multi-modal

histograms suggest that data from two or more populations has been mixed

together, as is the case when there are two or more different processes at work,

which the observer may have confused or assumed to be as one.

Figure 5.3.e. Outlying peak

An outlying peak such as on this histogram like this is suspicious. Investigate the

cause(s) of the peak on the far right as it appears to be an unusual occurrence

when compared to the remainder of the distribution.




The Scatter Diagram

What is a Scatter Diagram?

Scatter diagrams, often called a scattergrams, show whether there is arelationship between two different characteristics of some process, operation

or other phenomenon.

Measurements are plotted as dots on a graph and the resulting pattern should

indicate whether or not there is a relationship. eg. an increase in one element

corresponds to an increase in the other etc.

When to Use Scatter Diagrams

Scatter diagrams are used to uncover relationships that could indicate possible

causes. In particular, scatter diagrams can help establish whether an effect isrelated to a particular cause.

Some examples could include, does working more overtime hours affect the

numbers of work related injuries? Does high customer satisfaction lead to

increased sales?

How to Construct a Scatter Diagram

1. Determine which two characteristics are to be studied

Example: the amount of business generated is related to the number of calls

made by sales representatives?

2. Collect the data. Collect paired samples of data. Typically at least 50 to

100 should be collected to ensure sufficient accuracy. For the purposes of this

example, as lesser number shall be used. The data is shown in Table 5.6.




Table 5.6 Sales data for last calendar year

Month Sales Calls Sales ($’000)

January 7 300

February 8 350

March 18 1100

April 44 2000

May 20 1250

June 24 1300

July 30 1600

August 32 1650

September 12 800

October 18 900

November 12 750

December 4 200

3. In preparation for graphing, mark off measures for one characteristic on

the horizontal axis and measures for the second on the vertical axis. Ensure the

low end of both scales is in the lower left hand corner. This is illustrated in

Figure 5.4.a.

0 10 20 30 400

500

1,000

1,500

2,000

2,500

Numberof SalesCalls

Figure 5.4.a. Laying out the axes for a Scatter Diagram

4. Plot the information on the graph. For the example given, for each month

of the year, plot a dot, cross or other marker on the graph paper, positioning it

in relation to both the horizontal and vertical axes. This is illustrated in Figure

5.4.b.






0 10 20 30 40 50 600

20

40

60

80

100

120

Figure 5.4.e. A weak negative correlation

0 10 20 30 40 50 600

20

40

60

80

100

Figure 5.4.f. Weak positive correlation

0 1020304050600

20

40

60

80

100

120

Figure 5.4.g. No correlation




0 1020304050600

20

40

60

80

100

Figure 5.4.h. Non-linear (hyperbolic) correlation

0 10 20 30 400

500

1,000

1,500

2,000

2,500

Figure 5.4.i. Stratification

01020304050600

20

40

60

80

100

Figure 5.4.j. Non-linear (Inverse Hyperbolic) correlation




Some Notes about using Scatter Diagrams

When using the scatter diagram, note the following important points:

Correlation does not mean that a cause and effect relationship exists

between the two characteristics being plotted. It only means the two arerelated is some way, maybe through a third characteristic we are yet to test,

it does not mean that one causes the other;

If you are putting data from different sources onto a scatter diagram. it is

possible that differences between the sources will interfere with the whole

picture. Overcome this by using separate diagrams or by using different

colours for data from different sources;

Correlation may only exist over part of the range over which the data has

been collected. Be aware so as not to misread a diagram and assume that

correlation exists over the entire range;

Negative relationships can be just as important as positive relationships.




Run Charts

What is a Run Chart ?

A Run chart is a graph in which a line is used to sequentially connect the data

points. It gives a pictorial representation of what is happening to the process or system being measured, over time.

It can also be used to show the relationship between two variables in which

case it is referred to as a Line Graph.

A Run Chart is easy to look at and any patterns in the data become readily

apparent.

When to Use a Run Chart

Run charts are used when there is a need to monitor trends over time, or whenthe team suspects the cause of a problem is due to changes in a process or

system occurring over a period of time.

How to Construct a Run Chart

1. Determine the process/system characteristic or measure to monitor.

Example: A courier firm promising overnight parcel delivery has been

experiencing increasing customer complaints about late deliveries. A run

chart will be developed to monitor the number overnight delivery parcels

delivered late each month.

2. Collect the required data.

The number of late deliveries during the past year were extracted from the

computerised logistics management system. These are given in Table 5.7.

Table 5.7. Overnight parcel deliveries delivered late during past 12 months

Month Number Month Number

January 160 July 133February 157 August 125

March 169 September 151

April 131 October 169

May 145 November 163

June 120 December 165




3. Layout the axes for your chart. Draw the horizontal axis (x-axis) scaled

by the appropriate time interval, in our example this will be months. Draw the

vertical axis (y-axis) scaled by the frequency measure used. This is shown in

Figure 5.5.a.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec110

120

130

140

150

160

170

180

Month

N u m b e r o f L a t e D e l i v e r i e s

Figure 5.5.a. Laying out the axes for a Run chart

4. Plot the data point for each month. Plot each individual data point and

connect them up with a line. This is shown in Figure 5.5.b.


120

130

140

150

160

170

180

N u m b e r o f L a t e D e i v e r i e

s

Month

Figure 5.5.b. Plotting the points on a Run chart

5. Calculate and plot the average (mean) of the data. From the data given in

Table 5.7, calculate the mean or average number of late deliveries per month for

the whole year. This has been calculated as 149.




Draw a line representing the average on the run chart. This is also shown on

Figure 5.5.c.


120

130

140

150

160

170

180

N u m b e r o f L a t e

e i v e r e s

Month

149

Figure 5.5.c The completed Run chart

A Note on Interpreting Run Charts

A "normal" Run Chart should show a relatively equal distribution of points

above and below the average line.

Patterns which shown wide variations may indicate problems with an

unstable process, a "slack" process or merely indicate time related cycles present in the system such as seasonal variations.

Run charts may be used to show several groups of data simultaneously.

Each group may be plotted as a separate line on the same graph using

different symbols to mark the points. This may allow relationships between

data to become apparent where they are present, eg. trends in one measure

are reflected by a trend in the other measure, and reflect correlations

between measures.




Contro l Charts

What are Control Charts?

A Control Chart is a graphic comparison of how a process is performing withhow the process should perform.

It is basically a run chart with some additional information added, in the form

of lines representing control limits for the process being monitored. Control

limits are statistically determined upper and lower boundaries that define the

range of measurements that would be considered to be normal for a given

process.

A Control Chart enables you to distinguish between variation that is a natural

part of a process, and that caused by something outside the process that could

indicate a problem.

The Control Chart Principle

The principles on which control charts are based are discussed in more detail

in Appendix 1 - Understanding Variation and Data. To briefly summarise

some of the key points:

Control charts use the knowledge of the standard deviation of data around

its mean, which has been collected about a process, to determine what the

natural limits of performance for that process are;

The standard deviation and mean can be calculated for any set of data;

For data which follows the “Normal” distribution, the range defined

between the mean minus three times the standard deviation (called the

lower control limit) and the mean plus three times the standard deviation

(called the upper control limit), will enclose 99.73% of all possible data

points that can be obtained from such a process;

The upper and lower control limits will therefore indicate the natuaral

limits of variation of a process. ie. 99.73% of the time, the process will

yield a data point within these limits;

Although not all data follows the Normal distribition, most data collected

from “real” processes are close to normally distributed, and where they are

not, the sampling plan used to collect the data can yield normally

distributed points.




When to use Control Charts

Control Charts can be used to address two broad categories of problems:

Process anal ysis involves understanding the nature of variation in

processes by looking at the effect of different process factors, so as toidentify potential problems;

Process control involves monitoring a process for which has been

standardised, for which control limits have been set, to determine if the

standardisation was correct and if it is being maintained.

Process control and process analysis charts are made in the same way, except

their purposes are different.

Types of Data and Types of Charts

The form of Control Chart used will depend on the type of data that is to be

plotted.

Data will be of two basic types:

things that you measure, or;

things that you count.

For things that you measure , such as measurements of some physical

dimension (eg. length in millimetres), time (eg. waiting time in minutes),

weight (eg. weight in kilograms) or other unit of measurement, data can take

any value depending on its measure.

Such data can take on what are known to as "indiscrete" values or variables. ie.

they can be anything and they can vary from item to item.

Measured or variable data is referred to as Continuous data.

For things that you count , for example, the number of defective items in a

sample, or the number of errors per form, the data can only take on certain or

"discrete" values. This type of data is called Attr ibutes data .

For attributes data, their can be two types - categorical data and occurrence

data.

The first type of attributes data is where we decide that we only want to know

whether an "attribute" is present or not.

For example, we may be monitoring the number of claim forms that have been

incorrectly filled out. Any error present on the form qualifies the form as




"incorrectly filled out" irrespective of how many errors have been made on any

particular form. It is either correct or not correct.

Other examples of this type of data is typically of the form OK or Not OK,

Pass or Fail, True or False etc. This type of data is called Categori cal Data .

The other type of "attribute" data is where we can have a count of more than

one attribute per unit examined.

For example, we may be interested in how many errors were made per claim

form, not just whether the form was correct or incorrect. In this case we count

the number of errors per form and can end up with a data count that is greater

than the number of items examined. eg. if we examine 10 forms and find that

there are an average of 3 errors per form, we can end up with 30 total errors for

10 forms. Such data is referred to as Occur rence Data .

Different Control Charts are used for each of these different types of data, and

in the case of attributes data depending on whether the sample size, also

referred to as subgroup size, can be kept constant from measurement to

measurement. This is summarised in Table 5.8.

Table 5.8. Summary of Control Chart Types.

Continous

Data

Categorical

Data

Occurrence

Data

Lots of data

available chart

Sample size

constant

np chart

(pn chart)

c chart

Limited data

available

i and mr

chart

Sample size

not constant

p chart u chart

How to Construct a Control Chart

The following is a general procedure for constructing a Control chart.

The specific steps to be used in constructing the various charts given in Table

5.8. will be presented in subsequent sections.

1. Select the process is to be monitored and determine what data will be

collected for it.

2. Determine which type of chart is suitable. Once the data to be collected,

or characteristic to be monitored has been established, determine which chart

is applicable to that type of data.




Refer to Table 5.8. or refer to the decision tree given in Figure 5.6 to decide

which chart is appropriate.

3. Decide how often data is to be collected. The more frequently the event

you wish to monitor occurs, the more frequently you will need to take

measurements.

For example: Measure queue outpatient waiting times at 10:00am and 2:00pm,

measure manufactured pin diameters every hour. etc.

The time interval between successive measurements or data collection is

referred to as the sampling in terval.

4. Decide how many data points to record each time. That is, how many

measurements will you take or how much data will you collect each time

measurements are take or data collected. This is the sample or subgroup size . eg. measure waiting times for first five customers, measure first 10 pins

manufactured each hour.

5. Collect the data. Implement you sampling/data collection plan. During

each sampling interval or at the predetermined time, collect one sample of data

values.

6. Calculate the statistics of interest. Use the prescribed statistical formulas

for the particular chart you have chosen to calculate the position of the:

Centre Line or Mean (CL) Upper Control Limit (UCL)

Lower Control Limit (LCL)




Areyoucountingor measuring?

Counting

Measuring

ContinuousData

Canyouhavemorethanone

count per unit

Lotsof data

available

Not muchdataavailable

X-bar ( X)

andRCharts

i andmr Charts

No

CategoricalData

OccurenceData

ConstantSampleSize

Samplesizenotconstant

npChart

pChart

ConstantSampleSize

Samplesizenotconstant

cChart

uChart

Yes

Figure 5.6 Control chart selection logic tree

7. Draw the control chart

This involves laying out the chart format, and then plotting the data points.

To lay out the chart format:

Draw and scale the vertical and horizontal axes;

Draw the Centre Line, Upper and Lower Control Limits.

Then plot the data values collected on the Control Chart

8. Analyse the Control Chart.

In general, if all the points plotted fall within the control limits, the process can

be said to be in control and operating normally. The existence of points outside

the control limits or the existed or certain characteristic trends would suggest

that the process is not in control and that special causes are present.




The X Chart

The X-chart is the most basic of control charts. It provides a plot of all of the

individual points measured. The X-chart provides a direct respresentation of

the process.

X Chart Example

Consider a company which manufacturers and delivers product to meet

specific customer orders. The days taken to fill the past 25 orders have been

recorded and are given in the following table.

Table 5.1 Number of days to fill customer orders

Order

Number

Days to

Deliver

Order

Number

Days to

Deliver

1

2

3

4

5

6

7

8

9

1011

12

13

15

18

23

22

18

15

31

27

13

3335

31

24

14

15

16

17

18

19

20

21

22

2324

25

29

26

17

14

12

14

30

25

24

2015

18

Total 549

1. Calculate the mean value

_

Calculate the mean value, where the mean ( X ) is calculated as:

_ X = Xn

n

Where:

Xn = represents the sum of all the data points or values

n = the number of values recorded




In our example:

X = 15 + 18 + 23 + ...... + 18

25

= 54925

= 21.96 = 22.

2. Calculate the standard deviation

The standard deviation, usually referred to by the symbol or the letters SD or

S, is calculated using the equation:

These symbols have been previously defined. In our example, this is calculated

as follows:

= (15-22)2 + (18-22)2 + (23-22)2 + ...... + (18-22)2

24

= 1156.96 = 48.21

24

= 6.94 = 6.9

3. Calculate the Upper and Lower Control Limits.

The general formulas for the calculation of Upper and Lower Control Limits

are:

_ Upper Control Limit (UCL) = X + 3

Lower Control Limit (LCL) = X - 3 For example, substituting our value of standard deviation, we get:

UCL = 22 + 3 X 6.9

= 22 + 20.7 = 42.7

LCL = 22 - 20.7 = 1.3

σ = Σ (Xn- X)2

n - 1

_




4. Draw the chart

This is shown in Figure 5.7.

1234567891011121314151617181920212223240

10

20

30

40

50

LCL=1.3

MeanX=22

UCL=42.7

Figure 5.7 X-Chart of Delivery Performance

5. Interpret the chart.

The control chart suggests that the process is in statistical control, centred on a

mean performance level of 22 days. The natural limits of variation for this

process are between 1.3 and 42.7 days.




The X-bar and R Chart

_ An X-bar and R chart is one that shows both the mean value X (called X bar)

and the range, R. It is the most common type of control chart for continuous

data. The X-bar portion of the chart mainly shows changes in the mean valueof the process (the location), while the R portion shown any changes in the

dispersion or spread of the process.

X-bar and R Chart Example

An industrial equipment manufacturer and retailer is contemplating launching

a new marketing initiative using their superior delivery performance as a

source of differentiation from their competitors.

Among several options, they are considering giving customers a “rock solid”

guarantee that their order will be delivered within a predetermined number of days and offering a substantial cash rebate if an order is delivered late.

In order to determine what they can and cannot guarantee, they have decided to

monitor the performance of their existing order fulfilment process.

When collecting data for X-bar and R charts, the data needs to be collected in

the form of subgroups or samples. Ideally, each sample should include at least

2 data items but no more than 10. The optimum is approximately 4 or 5.

In this example, we shall be tracking the delivery performance of 5 randomlyselected orders each day, for a period of 10 days. The results are shown in

Table 5.9.

Table 5.9 Delivery performance in days from receipt of order

Day

(Sample )Order A Order B Order C Order D Order E Average

1 11 9 6 4 2 6.4

2 4 2 7 2 4 3.8

3 4 1 4 3 3 34 5 2 3 6 2 3.6

5 4 7 3 4 5 4.6

6 4 4 5 4 9 5.2

7 6 7 3 4 3 4.6

8 2 4 3 2 5 3.2

9 9 2 1 2 7 4.2

10 2 4 3 10 6 5




With reference to Table 5.9, we have sampled 5 orders each time we have

taken a sample ie. 5/day. The subgroup size, usually referred to as n, is

therefore 5. (ie. 5 orders).

Calculate the statistics of interest.

_ 1. Determine the location of the centre-line for the X Chart. Calculate the

average waiting time for the period being monitored.

For the above example this is the sum of all the daily averages divided by 10

(10 days).

=Average Mean X = 6.4 + 3.8 + 3 + 3.6 + 4.6 + 5.2 + 4.6 + 3.2 + 4.2 + 5

= 10

Average Mean X = 4.4 Days _

The daily averages are referred to as X. The average of the averages which

defines the centre-line is called X double bar.

2. Determine the centre-line for the Ranges chart. To determine the centre-

line of the ranges chart, we must first determine the range of each group of

data collected.

The range is the difference between the largest and smallest value in each

sample. eg. for the orders sampled during day one, the fastest was filled in 2

days, the slowest in 11 days.

The range is therefore 11 days - 2 days = 9 days. The ranges for each of the

samples are given in Table 5.10.

Table 5.10 Ranges of order fulfillment samples.

Day 1 2 3 4 5 6 7 8 9 10

Range 9 5 3 4 4 5 4 3 8 8






For the example used here, we sampled 5 orders each day, therefore the

subgroup size n = 5.

From Table 5.11. A2 = 0.577.

Substituting into the above equations:

UCL = 4.4 + 0.577 x 5.3 = 7.5

LCL = 4.4 - 0.577 x 5.3 = 1.3

4. Calculate the Upper and Lower Control Limits for the R Chart. The

equations for the upper and lower control limits for the range chart are:

_ _

UCL = D4R and LCL = D3R

From Table 5.11, D4 = 2.114 and D3 = 0.

The Upper and Lower Control Limits can therefore be calculated as:

UCL = 2.114 x 5.3 = 11.2

LCL = 0

5. Lay out the X-bar and R chart format. Draw the centre-lines, upper and

lower control limits for the X chart on one graph and the centre-line, upper and

lower control limits for the R chart on another.

6. Plot the values. Plot the daily averages (means) on the X chart and the

values of the daily ranges on the R chart. See Figure 5.8.a. (X-bar chart) and

5.8.b. (R-chart).

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

MeanX=4.4

UCL=7.5

LCL=1.3

XChart

SampleDays Figure 5.8.a The X-bar Chart




1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

14

SampleDays

RChart

Figure 5.8.b. The R Chart

7. Analyse the charts. In general, a normal control chart should have points

evenly distributed between the control limits. This indicates that variation is

occurring, but that it is within the normal limits for the process.

Changes in the mean of the process will bring about changes in the X Chart.

The R Chart will remain unchanged. Changes in the spread of a process will

effect both the R Chart and the X Chart. Increases in spread will cause points

on the R Chart to increase and points on the X Chart to show a greater spread

and possibly go beyond the control limits.

When interpreting X and R charts, the R chart should always be read first. The

R chart shows process capability, it shows the degree of variation in the

process and the degree of variation due to common causes. If the R chart is out

of control, it is pointless to attempt to make any process adjustments on the

basis of the X chart.

If the R chart looks stable and the X chart is not, this suggests that the process is

probably inherently stable, and that incorrect or unnecessary adjustment or some

other factor is causing the X chart instability.




The i and m r Chart

When there are few data points and/or data is only available at irregular

intervals, we may not be able to collect enough points to construct X-bar and

R-charts.

For example:

a process that runs in single batches with a long cycle time;

situations where it is uneconomical to take multiple samples;

where destructive testing is used to take measurements;

etc., etc.;

In such situations the i - individuals, and mr - moving range charts are used.

These charts are similar to the X-bar and R-charts except that they useindividual points.

An i and mr Chart Example

A mining company operates a process for extracting small amounts of

previously unrecoverable precious metals for waste slurry. The slurry is stored

in tanks as it is generated, every few days when enough slurry has been

accumulated, the batch is processed.

The number of grams recovered from each batch is recorded every time therecovery process is run. The results of the past 25 runs is shown in Table 5.12.






1. Calculate the moving ranges.

This has already been done, and is given in Table 5.12.

To calculate the moving range values, subtract the previous value of grams

recovered from the current value. If the result is a negative number, record it asa positive number ie. the magnitude of the difference, ignoring the sign.

The moving range value for the first number is recorded as a zero, because

there is no previous number to subtract from it.

2. Calculate the mean of the moving ranges.

The mean of the moving ranges is calculated using the formula:

_

R = R 1 + R 2 + ..... + R n-1 n-1

Where, n is the number of values recorded.

Note: the sum of the range values is divided by n-1 because the first one will

always be zero and therefore be ignored.

In our example, the average moving range is:

_

R = 3 + 5 + 1 + ..... + 3

24

= 136

24

= 5.7

3. Calculate the control limits for the mr-chart.

As for the R-chart in the X-bar and R-chart pairing, the Upper and Lower

Control Limits for the mr-chart are calculated using the same equations. Namely:

_

LCL = D3R

_

UCL = D4R

Because our subgroup size will always be 2 for an mr chart, D3 and our LCL

will always be equal to zero.






Which in our example is:

_

X = 15 + 18 + 23 + 22 + .... + 18

25

= 54925

= 21.96 = 22

6. Calculate the Upper and Lower Control Limits

These are calculated using the equations used for the X-bar chart. That is:

_ _

UCL = X + A2R

_ _ LCL = X - A2R

The value of A2 is 2.66. Therefore:

_ _

UCL = X + 2.66 R, and

_ _

LCL = X - 2.66 R

In our example, X = 22 and R = 5.7. Substituting gives:

UCL = 22 + 2.66 x 5.7

= 22 + 15.16

= 37.16 = 37.2

LCL = 22 - 15.15

= 6.84 = 6.9




7. Draw the i - chart

123456789101112131415161718192021222325

10

15

20

25

30

35

40

MeanX=22

UCL=37.2

LCL=6.9

Figure 5.9b. The completed individuals chart (i-chart)

8. Interpret the chart

One point appears to be due to a special cause. However, given that this is above

the control limit, indicating a higher than expected recovery rate, it warrants

investigation to see if the process can be improved so that the mean is shifted to

this higher level.




The np Chart .

The np chart or Number Defective chart, also referred to as the pn chart is a

chart that shows the number of defective items produced by a process.

np charts are used with Categorical data, ie. attribute data where values are

measured in terms of OK or Not OK.

The np Chart is based on the assumption that count data, where we are

counting OK/Not OK tend to follow the Binomial distribution, which

approximates the Normal distribution. As subgroup size increases, the

accuracy of this approximation increases.

One restriction applying to the use of the np chart is that it requires sample or

subgroup size to be constant. ie. each sample has the same number of items in

it.

np Chart Example

An automatic packaging line which fills and seals bulk wine containers for

export, traditionally has damaged a certain percentage of containers during the

process. These are scrapped and the wine is recycled. The extent of the

problem is going to be investigated using an np Chart.

The first 200 containers filled each hour were examined and the results

recorded for 25 consecutive production hours. The collected data is given inTable 5.12.




Table 5.12 Defective wine container data

Sample (Subgroup)

Number

Sample (Subgroup)

size

Number defective

12

3

4

5

6

7

8

9

10

11

1213

14

15

16

17

18

19

20

21

2223

24

25

200200

200

200

200

200

200

200

200

200

200

200200

200

200

200

200

200

200

200

200

200200

200

200

1518

23

22

18

15

44

47

13

33

42

4638

29

26

17

5

7

14

36

25

2420

15

18

Total 5,000 610

The Subgroup size indicates how many containers were sampled each time a

sample was taken. In our case, this was 200 and remained constant through out

the data collection period.

The number of defectives indicates how many of these were defective.

Note: Subgroup size n should be greater than 50, and the expected mean value

of defectives for each subgroup should ideally range from 3 to 4.

To calculate the required statistics for an np chart we proceed as follows.




1. First, calculate the average number defective. This calculation is to work

out the average number defectives found per sample, overall.

In our case, we took 25 samples and found 610 defective items. The average

number of defectives is calculated as:

_ np = total number of defectives = 610

number of samples 25

_

np = 24.4

2. Calculate the average fraction or proportion defective for all the data

collected.

Average fraction or proportion defective is calculated as follows:

_ p = Total defective = np

Total inspected n

for the data in this example,

_

p = 610 = 0.122 = 12.2%

5,000

This defines the centre-line of the control chart.

Given that the sample size is constant, this could also have been calculated as: _ _

p = average number defective = np

sample size n

= 24.4

200

= 0.122 = 12.2%

3. Calculate the Upper and Lower Control Limits. The equations for calculating the Upper and Lower Control Limits for an np chart are:

_ _ _

UCL = np + 3 x np(1-p)

_ _ _

LCL = np - 3 x np(1-p)

UCL = 24.4 + 13.9 = 38.3

LCL = 24.4 - 13.9 = 10.5




4. Layout the control chart. Draw in the centre line (np) and the upper and

lower control limits on your control chart proforma.

Plot your data points on the control chart. The completed control chart is

shown in Figure 5.7.

13579111315171921230

10

20

30

40

50

Meann p=24.4

UCL=38.3

LCL=10.5

npchart

SampleHours

Figure 5.10.a. The completed np chart

Note, the np chart shows some points lying outside the control limits. These

have been highlighted in Figure 5.10.b.








Table 5.12 Defective wine container data

Sample

(Subgroup)

Number

Sample

(Subgroup)

size

Number

defective %

Defect.

p (%)

UCL

(%)

LCL

(%)

1

2

3

4

5

6

7

8

9

1011

12

13

14

15

16

17

18

19

20

2122

23

24

25

115

220

210

220

220

255

440

365

255

300280

330

320

225

290

170

65

100

135

280

250220

220

220

220

15

18

23

22

18

15

44

47

13

3342

46

38

29

26

17

5

7

14

36

2524

20

15

18

13.0

8.2

10.9

10.0

8.2

5.8

10.0

12.9

5.1

11.014.6

13.9

11.9

12.9

8.9

10

7.7

7.0

10.4

12.8

10.010.9

9.1

6.8

8.2

18.8

16.5

16.6

16.5

16.5

16.0

14.6

15.1

16.0

15.615.8

15.3

16.5

16.4

15.7

17.3

21.6

19.4

18.2

15.8

16.116.5

16.5

16.5

16.5

1.8

4.1

4.0

4.1

4.1

4.6

6.0

5.5

4.6

5.04.8

5.3

4.1

4.2

4.9

3.3

0

1.2

2.4

4.8

4.54.1

4.1

4.1

4.1

Total 5,925 610




To calculate the required statistics for a p chart we proceed as follows.

1. Calculate the average fraction or proportion defective for all the data

collected.

Average fraction or proportion defective is calculated as follows: _

p = Total defective = np

Total inspected n

for the data in this example,

_

p = 610 = 0.103 = 10.3%

5,925

This defines the centre-line of the control chart.

2. Calculate the Upper and Lower Control Limits. The equations used to

calculate the upper and lower control limits for a p chart are as follows.

_ _ _

UCL = p + 3 x p(1-p)

n _ _ _

LCL = p - 3 x p(1-p)

n

Using our previously calculated value for p = 0.013 gives:

UCL = 0.103 + 3 x 0.304

n

LCL = 0.103 - 3 x 0.304

n

A note on calculating the control limits for p charts.

The control limit formulas use the sample size n, as part of the calculation.Because our sample size is different for each sample, we will need to calculate

the UCL and LCL separately, for each individual point that is plotted.

This has been done and is displayed in the right-most two columns on Table

5.12. If the subgroup size is constant, then the UCL and LCL will also be

constant.

Figure 5.11 shows the p chart for the data in Table 5.12.






The c Chart

The c - chart or non-conformities chart, is a chart that shows the number of

occurrences of some event ie. a non-conformity per sampling period or

interval. The c-chart is used to monitor Occurrence Data.

For the p and np charts (Categorical data) we know both the number of

defectives as well as the number of remaining (nondefectives) units in the

sample.

This is not always possible. In many situations we may be able to measure the

number of non-conformities or occurrences of some event only. For example,

if a retailer were monitoring customer complaints (the non-conformities) it

may be impractical to try to measure the total number of customers which

come into the store, so as to determine the total sample size. ie. they can easily

measure the number of complaints per day, but the total number of customers per day is not known.

In such cases, a c-chart is used. A c-chart is used when the sampling period,

interval or unit is constant. The sampling unit may be a fixed length, area,

quantity, time etc.

Examples of fixed sampling units are:

Complaints per day;

Scratches per car;

Errors per form;

etc.

A key difference between Occurrence data and Categorical data, is that for

categorical data, we cannot obtain a count of the parameter we are monitoring

which is greater than the number of items in the sample. ie. if we sample 100

forms to monitor the number or percent defective (ie. incorrectly filled out)

the most we could conceivably measure is 100 assuming they were all

defective.

For Occurrence data, we may obtain a measure which is greater than the

number sampled. For example, if we a measuring the number of errors per

form (Occurrence data), and there is an average of 3 errors per form, we will

obtain a measurement of 300 which is significantly greater than the sample

size.




c - Chart Example

The method for constructing a c-chart will now be illustrated by way of an

example.

Consider a textile firm manufacturing plain white fabric which is later dyed tomeet specific customer orders. Weaving errors and stains (usually oil) which

often find there way into the fabric during the process cannot be allowed in the

finished product which goes to dying. The dye highlights flaws and stains,

causing such fabric to be rejected.

To minimise the amount of finished product which is scrapped, the plain white

fabric is inspected. Any oil or other stains are manually cleaned during

inspection, any sections with weaving faults are highlighted to be cut out the

main roll before dying.

The rolls of plan white fabric are all prepared in 3,000 metre rolls.

Information is collected by the fabric inspectors on the number of weaving

faults found. This information is used by the weaving operators and mechanics

to try to improve the weaving process. Data collected from 25 rolls is shown in

Table 5.14.

Table 5.14 Number of weaving faults found per roll

Roll

Number

Number of

Weaving

Faults

Roll

Number

Number of

Weaving

Faults

1

2

3

4

5

6

7

8

910

11

12

13

15

18

23

22

18

15

44

47

1333

42

46

38

14

15

16

17

18

19

20

21

2223

24

25

29

26

17

5

7

14

36

25

2420

15

18

Total 610






3. Plot the chart

1234567891011121314151617181920212223240

10

20

30

0

50

Centreline

c=24.4

LCL=9.6

UCL=39.2

Figure 5.12. The completed c-chart

4. Interpret the chart

The above chart suggests that the upstream process which contributes to

weaving faults in the fabric is not stable or in statistical control. There is

evidence of several special causes - points outside the control limits.

Improvement efforts should focus on identifying and eliminating the causes of instability in the weaving process.




The u Chart

If we are monitoring occurrence data but the sampling interval/unit varies we

can no longer use the c - chart, as this requires a constant sampling period/unit.

For example, if a department store is monitoring the number of customer

complaints per day and they have late night shopping on Friday and morning

shopping on Saturday, the length of the “day” will not be the same for every

day. A c-chart would not be used in such a situation.

Where the data is occurrence data and the sampling unit/period is not constant

a u-chart is used. The u-chart is to the c-chart what the p-chart is to the np-

chart.

u - Chart Example

The method for constructing a u-chart will now be illustrated with reference tothe textiles example used for the c-chart.

As part of the dying preparation process, the sections of fabric where

significant weaving faults were found are cut out, and the remaining

acceptable fabric sewn back into the roll. Rolls are also batched together or

split into smaller rolls depending on the size of the customer order for a

particular colour or pattern.

This means that the rolls processed in the dying section will be of varying

lengths depending on the customer order and the amount of flawed fabric thathad to be cut out.

Post-dying, the rolls are again inspected to identify any dying errors or faults.

Sections with flaws or shade inconsistencies are cut out of the main roll and

only fabric that meets the customer’s quality specifications are batched into the

finished order, ready to be fabricated into finished items. eg. garments, bed-

linen, curtains etc.

Because our sampling interval or unit (the roll) is no longer constant, we can

no longer use a c-chart to monitor the dying process. A u-chart is now the

appropriate chart to use.

Data collected for 25 consecutive customer orders is given in the following

table.




Table 5.15 Dying faults per customer order

Order

Number

Roll length in

Kilometres

(n)

Number of

dying faults

(c)

Dying Faults

per km

(u=c/n)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

2122

23

24

25

1.15

2.20

2.10

2.20

2.20

2.55

4.40

3.65

2.55

3.00

2.80

3.30

3.20

2.25

2.90

1.70

6.50

1.00

1.35

2.80

2.502.20

2.25

2.20

3.25

15

18

23

22

18

15

25

19

13

33

29

27

32

21

26

17

36

11

14

26

2524

20

15

18

13.0

8.2

11.0

10.0

8.2

5.9

5.7

5.2

5.1

11.0

10.4

8.2

10.0

9.3

9.0

10.0

5.5

11.0

10.4

9.3

10.010.9

8.9

6.8

5.5

Total 66.2 542




1. Calculate u for each subgroup of data collected.

Calculate u for each unit or subgroup of data using the relationship:

u = c/n

where n = size of the sampling unit or subgroup. For example, the first roll is

1.15 kilometres long and the number of faults is 15. Therefore n = 1.15 and c =

15. u is calculated as:

u = c/n = 15/1.15 = 13 per kilometre.

2. Calculate the average nonconformities/unit (u).

This can be calculated as follows:

_ u = c = 542

n 66.2

= 8.2

3. Calculate the Upper and Lower Control Limits

Calculate the UCL and the LCL using the formula:

_ _

UCL = u + 3 uni

_ _

LCL = u - 3 u

ni

Note, the UCL and LCL will need to be calculated for each roll, to reflect the

changing sample size.

For example, for the first roll, the roll length is 1.15 kilometres. Therefore, UCL

and LCL will be:

UCL = 8.2 + 3 8.2

1.15

= 8.2 + 3 7.13

= 8.2 + 3 x 2.67

= 8.2 + 8.01 = 16.2




LCL = 8.2 - 3 8.2

1.15

= 8.2 - 8.01

= 0.19 = 0.2

The completed UCL and LCL calculations for all the rolls (data points) are

given in Table 5.16.

Table 5.16 Dying faults per customer order, completed table

Order

Number

Roll length

in

Kilometres

(n)

Number

of dying

faults

(c)

Dying

Faults

per km

(u=c/n)

UCL LCL

1

2

3

4

5

6

7

8

9

1011

12

13

14

15

16

17

18

19

20

21

22

23

24

25

1.15

2.20

2.10

2.20

2.20

2.55

4.40

3.65

2.55

3.002.80

3.30

3.20

2.25

2.90

1.70

6.50

1.00

1.35

2.80

2.50

2.20

2.25

2.20

3.25

15

18

23

22

18

15

25

19

13

3329

27

32

21

26

17

36

11

14

26

25

24

20

15

18

13.0

8.2

11.0

10.0

8.2

5.9

5.7

5.2

5.1

11.010.4

8.2

10.0

9.3

9.0

10.0

5.5

11.0

10.4

9.310.0

10.9

8.9

6.8

5.5

16.2

14.0

14.1

14.0

14.0

13.6

12.3

12.7

13.6

13.213.3

12.9

13.0

13.9

13.3

14.8

11.6

16.8

15.6

13.313.6

14

13.9

14.0

13.0

0.2

2.4

2.3

2.4

2.4

2.8

4.1

3.7

2.8

3.23.1

3.5

3.4

2.5

3.2

1.6

4.8

- 0.4

0.8

3.12.8

2.4

2.5

2.4

3.4

Total 66.2 542




In the case of roll 18, the calculation for the LCL has given us a negative

number.

In practice we know that it is not possible to record a negative number of

occurrences, therefore this would be recorded as a LCL of zero.

4. Draw the chart

The completed chart is shown in Figure 5.13.

12345678910111213141516171819202122232

0

5

10

15

20

u=8.2

Figure 5.13. The completed u chart

5. Interpret the chart.

The chart suggests that the dying process is in control and centred around a mean

of 8.2 occurrences of dying faults per kilometre of fabric dyed.






Trends. Any tendency of points to drift so as to give rise to a trend, is an

indication that the process may be unstable.

Periodicity. When points in a chart show a regular size and fall, the resulting

pattern is referred to as periodicity. Periodicity is an indication that something

in the process is changing in a regular pattern and therefore the process may beunstable.

Hugging the centreline. If the data tends to hug the centreline, defined as 15

or more consecutive points less than 1 standard deviation from the centreline,

an abnormality is indicated. This condition is usually as a result of data

corruption, poor or inadequate sampling.

Hugging the control limits. An abnormality is said to exist if 2 out of 3, 3 out

of 7 or 4 out of 10 consecutive points fall between 2 and 3 standard deviations.

Even if the points do not all fall on the same side of the centreline, thiscondition could be an indication that the process is unstable. The usual cause

of this type of condition is unnecessary or overadjustment of the process.

Shewharts original tests for control charts have been reproduced in Figure

5.14. In these diagrams, three zones have been defined above and below the

mean, these are:

Zone C - one standard deviation either side of the mean;

Zone B - between one and two standard deviations away from the mean,

one each side of the mean;

Zone A - between two and three standard deviations out from the mean.




Figure 5.14 The Shewhart tests

A

B

CC

B

A

A

B

CC

B

A

A

B

CC

B

A

A

B

CC

B

A

A

B

C

C

B

A

A

B

C

C

B

A

A

B

CC

B

A

A

B

CC

B

A

Test 1. One point beyond zone A Test 2. Nine points in a row in

Zone C or beyond

Test 3. Six points in a row steadily

increasing or decreasing

Test 4. Fourteen points in a row

alternating up and down

Test 5. Two out of three point

in a row in zone A or beyond.

Test 6. Four out of five points

in a row in zone B or beyond.

Test 7. Fifteen point in a row in zone

C (above & below the centreline)

Test 8. Eight points in a row on

both sides of centreline with

none in zone C.




Process Capabil i ty

Process capability is a measure of the ability of a process to meet or exceed the

customer specifications for that process. Process capability is measured

differently, depending on whether or not the process is centred on the mean of

the customer specification.

The term C p is used where the process is centred, C pk if it is not centred. For

these measures to make any sense, the process must first be in statistical

control and approximately normal.

Calculating Cp

When the process is centred on the mean of the customer requirement, process

capability is measured by C p . Where C p is defined as follows:

C p = Specification width

Process width

In practice, the customer requirements are defined in terms of a range from the

lower specification limit to the upper specification limit. LSL and USL

respectively.

The process width is the 6 range defined between the mean plus three

standard deviations to the mean minus three standard deviations.

Process capability is therefore calculated by the formula:

C p = USL - LSL

6

C p is interpreted as follows:

A process with C p = 1 exactly matches the customer’s specification limits;

A process with C p > 1 exceeds the customer’s specification;

A process with C p < 1 fails to meet the customer’s specification.




Calculating Cpk

If a process is not centred on the mean of the customer requirement, process

capability is measured by C pk . Where C pk is defined as follows:

_ _

C pk = Minimum of (USL - X , X - LSL )

3 3

_

Where X is the mean of the process.

The C pk calculation overcomes the problem of the process not being centred by

calculating the capability for each half of the process and then taking the

minimum.

Note: the upper one sided capability index is often referred to as C pu and the

lower one sided capability index as C pl . ie. _

C pu = USL - X

3

_

C pl = X - LSL

3




6. Extensions to the Seven Tools of Quality

This section presents a collection of tools and techniques that have all proved

useful in support of quality based problem solving and continuous

improvement activity, which are in addition to the seven basic tools of Quality.

The list of tools that have been added as extensions to the basic quality

management “toolkit” is ever growing as more of the many tools and

techniques that were previously known about or have recently been developed

are applied within a quality management framework, and in support of

continuous improvement and problem solving activities.

While by no means exhaustive, this section presents a collection of often used

tools and techniques, which we have found be useful and practical extensions

to the problem solving toolkit.

These are:

Interviews;

Questionnaires;

Dot Plots;

Box Plots;

Force Field Analysis.




Interviews

What are interviews?

Interviews are structured conversations focused on a specific topic.

While usually more expensive than questionnaires, interviews allow longer

responses and provide the interviewer with opportunities to pursue or ignore

topics based on how the person being interviewed responds.

Interviews also provide the interviewer with the opportunity to discover about

issues that had not been previously thought of which are raised by the subject,

and which may be of importance.

Because interviews are conducted in person or over the telephone, they give

the interviewer a much better "feel" for the subject's position on the topic.

When to use Interviews

Interviews can help teams get started on the problem solving process.

Interviewing people in a department, work area or the whole organisation, will

often reveal consistent themes about what people see as being major issues or

problems. These can provide insights into areas that can be explored further

using the problem solving process and that may offer greatest opportunities for

improvement.

Interviews can also be used to probe people's attitudes and opinions in depth,

especially when there are relatively few people to survey, and/or when each

person's opinions are very important.

How to use Interviews

1. Decide on the kind of information needed . Opinions, personal

experiences, eye-witness accounts are good topics for interviews, as it may be

difficult to obtain this information by other means. Avoid using interviews to

obtain information available through other means.

2. Determine who you need to interview. Interviews are time consuming,

therefore limit the number of people interviewed to the minimum required to

find out what you want.




3. Prepare questions in advance.

Keep questions to the minimum required to obtain the desired information

and try to keep interviews to under an hour;

Balance your interview by mixing shorter, factual, easier, closed questions

with open-ended, more thought provoking questions requiring longer answers;

Test your questions on some people before conducting the actual

interviews.

4. Prepare your interview subject ahead of time . Tell people in advance that

you will be interviewing them and give them some idea about the sorts of

things you will be asking, what the information will be used for, and how long

the session is likely to take. Most people will want you to make a formal

appointment with them.

5. Conduct the interview. When conducting the interview:

Put your subject at ease by trying to keep the session as informal and

conversational as possible;

Review the purpose of the interview and the points raised in the

preparation step above;

Ask one question at a time and don't interrupt. Don't be afraid of silences;

they can encourage people to volunteer more information. Remember, the

purpose of interviewing is to listen to what your subject has to say - it

should not be used as an excuse for you to tell people what you think;

Take notes. If you use a tape recorder, be sure to ask for permission.

A note on using tape recorders

It is usually more efficient to take notes, than to use a tape recorder. Especially

when interviews are being conducted on a one-on-one basis as opposed to

group interviews. Playing back to tapes to extract the key points which you

would normally note during an interview can often take longer than doing the

initial interviews. This significantly extends the time and effort required to

extract the same information from your subjects. This can become particularlytime consuming when there is a need to interview many people.

Even with groups, many people will often feel threatened that if they

something controversial, that the tape can be used to trace the comments back

to them as individuals. Participants will often offer less input to an interview if

it is being taped.

Finally, not using a tape recorder will assist team members develop their skills

as interviews and analysts. With time, team members will become very




efficient at extracting information using the interview technique. Reliance on

tape recorders can often work against team members fully developing these

skills.

Ask easier questions, closed questions and factual questions earlier in the

interview; Ask more difficult open-ended questions later in the interview;

Take opportunities during the interview to summarise and recap what your

subject is saying;

Allow for opportunities for the subject to raise and explore issues you may

not have anticipated, this may give you additional insights;

At the end of the interview, thank your subject for participating;

After formally closing the interview, stay alert for any final remarks your

subject may make. After the pressure is off, people often volunteer some of

their most interesting observations and remarks.

6. As soon as possible after the interview, review your notes. Review your

interview note, summarise the key points and any impressions you may have

formed during the interview.

7. Assemble and analyse your responses. Depending on the purpose of the

interview, you could tabulate responses for each question, sum up general

reactions or identify recurring themes and issues.




Quest ionnaires

What is a Questionnaire ?A questionnaire is a predetermined and structured proforma used to collect

information about people's attitudes and opinions on specific issues or onspecific dimensions of a problem or issue.

Questionnaires may be completed in writing, verbally in person, or over the

telephone.

When to use QuestionnairesQuestionnaires can be used in any situations where you wish to collect

attitudes and opinions about specific issues or problems, or where you wish to

gauge people’s opinions and attitudes about some specific characteristics or

dimensions of a problem or issues.

Such cases lend themselves to pre-analysis and structuring. The team members

can determine what issues? dimensions? characteristics? etc about which they

seek opinions and attitudes. These can then be worked into a structured

proforma questionnaire, on which subjects provided specific responses to

specific questions.

How to use a Questionnaire

1. Determine what it is you need peoples’ opinions on. Determine the

specific issues, problems, problem characteristics or dimensions you wish to

gauge peoples’ opinions on.

2. Determine the who you need to survey. Determine which group or groups

of people you need to survey. Do you need to survey customers, employees or

only specific groups of employees eg. certain departments, certain shifts,

certain sites. Do you need to compare the responses from different groups? or

will different groups receive different questionnaires.

3. Prepare your questions. Use the following as guidelines to developing

your questionnaire structure:

Use open-ended questions when you're not certain of the nature of the

response, when you need people's actual words or when you are looking

for anecdotes or examples.

Use close-ended questions when you want to focus responses on specific

areas or issues. True-False and multiple choice answers are examples of

this.




Use a rating scale when you want to understand level of feeling. A

commonly used format is to presented each question as a statement and the

subject is asked to rate their level of agreement or disagreement with the

statement.

For example:

I think the existing computer system response is too slow

1:strongly agree 2:agree 3: neutral 4: disagree 5: strongly agree

Use neutral language. Do not pre-empt a “desired” response or any “bias”

through your wording.

4. Prepare your questionnaire. Some hints to assist your team in designing

their questionnaires.

Keep the number of questions to a minimum. When faced with lengthy

questionnaires, many people ignore it completely, answer without much

thought, or give more negative responses than they otherwise would because

they are annoyed at having to answer such a long questionnaire - which is not

indicative of how they really feel about the issues being probed by the

questionnaire.

If your questionnaire has a large number of questions, test it on a small group

first. Responses many indicate many of your questions to be non-issues. These

may be removed from your final questionnaire. Alternately, break up your questionnaire into several smaller questionnaires.

Test your questionnaire first and revise any questions that are confusing or

don't provide the required information.

5. Conduct the Survey When conducting the survey, using the questionnaire:

If surveying a sample, ensure that it is a random sample. When surveying

people from different groups, ensure the sample is representative of the

numbers of people in the different groups.

If possible, allow the responses to be anonymous for the individuals who

complete the questionnaire - people will tend to be more honest with their

answers;

If you are surveying different groups of people, ensure you have allowed

for some system of identifying which group a questionnaire came from

with out breaching confidentiality.




6. Analyse the results.

Consolidate the responses to the categories established during the

questionnaire designed stage.

File the completed questionnaires is case this information is required for futurereference.




Dot Plots

What are Dot Plots?

A dot plot is a pictorial way of displaying data. It is a plot of data points abovea measurement scale with each point representing a single data point.

When to use Dot Plots

Use dot plots to get a quick idea as to the shape of the data you have collected.

A glance at a dot plot will give you a good idea as to the shape, the range and

spread, highlight any skewness, unusual or extreme points. This will often

assist in deciding whether further analysis is worthwhile and what type of

further analysis represents the logical next step.

It allows easier interpretation than looking at a list of numbers.

How to Construct a Dot Plot

1. Determine what it is you need to investigate and collect your data.

Example: Bank staff have complained to management that existing account

withdrawal slips are too complicated. This results in frequent customer errors

when filling out the form, errors which must be corrected by teller staff before

the transaction can be processed. The time taken to make the correction is perceived as contributing to a decreasing level of customer service, forcing

customers to wait while the corrections are made.

Bank staff at one branch have decided to investigate this problem, by

recording how many incorrectly filled withdrawal slips requiring teller staff

correction are presented over a period of 30 working days. The results are as

follows.

9 9 10 14 14 13 7 12 9 10

8 13 8 9 8 11 11 8 8 13

15 16 10 7 6 10 10 15 5 12




2. Lay out a horizontal scale. Make sure the scale spans a large enough range

to cover the range of the data.

From examination of the above data, we can see that the largest number in the

data is 16 and the smallest is 5. Therefore, a scale from 1 to 20 will more than

cover the required range. This is illustrated in Figure 6.1.a.

1234

Figure 6.1.a Layout of a Dot Plot Scale

3. Draw a dot over the number on your line corresponding to each value in

your data for occurrence of that value. A partially completed dot plot for the

above data is given in Figure 6.1.b.

123456

Figure 6.1.b. A partially completed Dot plot

Where a number is repeated several times in the data, the convention is to pile

dots vertically on top of one another.

For example, the number 10 occurs 5 times, the dot plot shows 5 dots over the

value 10. Figure 6.1.c. shows the completed dot plot.

123456789101112131

Figure 6.1.c. A completed Dot plot




Box Plots

What are Box Plots ?

A boxplot is a graphical way of displaying information about the spread andlocation of data.

A boxplot focuses attention on certain features of the data without having to

plot all the values. In particular, box plots are good at highlighting extreme

points which are not typical of the rest of the sample and skewness in the data.

Box plots provide a quick way of assessing data for which the team may be

considering developing a control chart.

When to use Box Plots

Box plots can be used in the same types of situations where you would use a

histogram or dot plot, to establish the location and spread of data.

At the other end of the analytical scale, box plots may be used as an alternative

to a control chart for one-off analytical exercises.

One of the main advantages of box plots, are that we do not have to plot each

individual data point. If we can come to some conclusion will a box plot,

further and lengthier analysis will not be necessary.

The other main advantage of a box plot, is that is can be used to determine

whether or not there is a difference between two sets of data. This makes them

extremely useful in situations where we seek to compare two or more sets of

data. More so than histograms, dot plots and control charts - where apparent

trends may be due to sampling errors or not statistically significant to indicate

a real difference.

Examples of this would include situations where we wish to establish whether

data from to different sources are the same for the purpose of further analysis,

or situations where we have implemented some improvements and we wish to

establish whether the changes have made a difference or not by comparing before and after performance.




How to construct a Box Plot

Unlike histograms and dot plots, box plots required us to have an

understanding of some common terms and concepts associated with analysing

and characterising data.

In particular, we will need to know how to calculate:

The median

The mean

The lower quartile

The upper quartile

These terms and others associated with analysing and characterising data are

presented and discussed in Appendix 1: "Understanding Variation and Data".Refer to this Appendix if you need a refresher on these concepts.

1. Define the problem to be investigated

Example: A bank decides to investigate customer queue waiting times.

2. Collect data. The average waiting times for a random sample of customers

joining a queue in front of a teller position are collected at five randomly

selected times during the day, for a week. The average waiting time is calculated

at each point.

The data is given in Table 6.1.

Table 6.1 Customer Queuing Times in Minutes (Averages of samples taken

5 times per day)

Mon Tues Wed Thur s Fri

Sample 1 6 1 2 12 4

Sample 2 4 10 6 8 9

Sample 3 5 2 9 7 4

Sample 4 12 7 5 4 8Sample 5 5 3 8 3 5




3. Rearrange the data in ascending order

To calculate the median, upper and lower quartiles, requires the data to be in

order from the smallest value to the largest (ascending order) irrespective of

what order the values occurred in when the measurements were taken.

When you have only a few data points, it is relatively easy to re-order the data

by examining it and rewriting it in the appropriate order. When there are many

values, it is some what more difficult to do this by inspection.

A tally chart is a useful tool to use to assist with the reordering of the data. To

develop your tally chart, use the following procedure.

i ) Determine the spread of the data . From Table 6.1, the shortest waiting time

is 1 minute (minimum data value), the longest is 12 minutes (maximum datavalue).

i i) Set the spread of your tall y char t . Set the minimum and maximum values

for your tally chart as equal to the minimum and maximum values of your

data. From Table 6.1, we will need a tally chart spanning the range from 1 (the

minimum data value) to 12 (the maximum data value).

iii) Set the “class boundaries”. The class boundaries need to be set to each of

the discrete data intervals that are naturally occurring in the data.

iv) Fil l in the Tally Chart fr om your data.Analyse the data given in Table 6.1with the tally chart. The completed Tally chart for the data given in Table 6.1 is

shown as Table 6.2.

Table 6.2 Tally chart for data in Table 6.1

Waiting Time

(Minutes)

Number of Occurr ences

(Tally)

Number of Occur rences

1 I 1

2 II 2

3 II 24 III 3

5 5

6 II 2

7 II 2

8 III 3

9 II 2

10 I 1

12 II 2




Total 25

The table tells us how many times each measured value occurred in the

collected data. Using this information we can rewrite the data collected in

ascending order, as is shown in Table 6.3.

This table shows that we have 25 data points, the lowest being 1 and thehighest being 12.

With reference to the tally chart (Table 6.2), we note that the value 5 minutes

was recorded on 5 occasions during the week. This is shown in Table 6.3 as a

block of 5 consecutive 5’s. Similarly, the tally chart shows that the value 8

minutes was observed on three occasions. This appears on Table 6.3 as a block

of three 8’s.

Table 6.3. Table 6.1 data, reordered in ascending order

Position Measured Value

1 1

2 2

3 2

4 3

5 3

6 4

7 4 Lower quartile (middle of the lower half)

8 4

9 5

10 5

11 5

12 5

13 5 Median (the middle value)

14 6

15 6

16 7

17 7

18 8

19 8 Upper quartile (middle of upper half)

20 821 9

22 9

23 10

24

25

12

12




4. Calculate the value required to draw the Box Plot.

The key values we need to calculate in order to draw a box plot are the:

Median;

Upper Quartile;

Lower Quartile;

Interquartile Range;

Mean.

The mean, upper and lower quartiles can be determined from Table 6.3 by

observations.

i) Determine the Median

The median is the middle value in the data. We have 25 data values, the middle

value occupies the 13th position. ie. it has 12 values either side of it. The 13th

data point, the median value is 5 minutes.

ii ) Determine the Lower Quartile

The lower quarti le is the middle value of the lower half of the data .

The usual convention is to include the overall median as the upper limit of the

bottom half of the data.

The middle value of the lower half of the data is the 7th value. ie. It has 6 data

points below it, 1 to 6 and 6 data points above it, 8 to 13. The data value

corresponding to the 7th point is 4 minutes.

Therefore, the lower quarti le is 4 minutes.

ii i) Determine the Upper Quar tile

The upper quarti le is the middle value of the upper half of the data .

The usual convention is to include the overall median as the lower limit of the

upper half of the data. From Table 6.3. we can see that the middle value of the

top half of the data is the 19th data point which corresponds to the value of 8

minutes.

Therefore, the upper quarti le is 8 minutes.




iv) Calculate the I nterquarti le Range

The I nterquartil e range (IQR) is the difference between the Upper Quartile

and the Lower Quartile. That is:

IQR = Upper Quartile - Lower Quartile

IQR = 8 Minutes - 4 Minutes = 4 Minutes.

I nterquarti le Range = 4 minutes.

v) Calcul ate the mean.

Add all the data points ie. 1+2+2+3+3+4+ ..... +12 = 150

Then divide by the total number of points (25) ie. 150/25 = 6

The mean = 6

5. Draw the Box Plot

Draw the Box Plot using the following steps and with reference to the

information previously calculated.

i) L ay out a hor izontal axis and mark off a measurement scale in the units you

used to measure your data. Ensure the line is drawn wider than the range of

your data. This is shown in Figure 6.2.a.

01235

Figure 6.2.a. Layout a horizontal scale

ii ) Mark off the Lower and Upper Quartiles with vertical lines of the same

length and connect them up to form a box shape. See Figure 6.2.b.

LowerQuartileUpperQuartile01234567891011

Figure 6.2.b. Drawing the Upper and Lower Quartiles




ii i) Calculate and draw the Lower I nner F ence

Measure to a length of one-and-a-half interquartile ranges below the lower

quartile. Mark this with a dashed vertical line. This is called the lower i nner

fence.

In our example, 1.5 X IQR = 6. Therefore the lower inner fence is calculated

as the lower quartile minus six ie 4 - 6 = -2. Note, this is a calculated value, in

practice that we cannot have a waiting time of less than zero minutes.

iv) Calculate and draw the Upper I nner F ence

Measure to a length of one-and-a-half interquartile ranges above the upper

quartile. Mark this with a dashed vertical line. This is called the upper inner

fence.

In our example, the upper inner fence is calculated as the upper quartile plus

six. ie. 8 + 6 = 14.

v) Mark i n the lowest & highest data points inside the fences

Mark in the lowest data point that lies inside the lower inner fence with a dot.

Draw the dot in-line with the centre-line of the box and connect it to the box

by a straight line.

Mark in the highest data point that lies inside the upper inner fence with a dot

and connect it to the box by a straight line. See Figure 6.2.c.

The lines connecting the box to the dots are called whiskers.

LowerQuartile UpperQuartile

012345678910111213-2

-11

LowerInnerFence UpperInnerFence

Whiskers Whiskers

Figure 6.2.c. Box plot with Inner Fences and Whiskers

vi) Mark in the median and the mean

Mark the median in the box with cross (+) and the mean with a short straight.

This is illustrated by Figure 6.2.d which shows the completed box plot.





012345678910111213-2-1 14

LowerInnerFence UpperInner Fence

Whiskers Whiskers

Median

Mean

Figure 6.2.d. The completed Box Plot

vii) Mark in any outliers.

If data point occur which lie outside the inner fences, mark these with an asterisk

*. Suppose one of our measurements was 16 minutes. This would be plotted as

shown in Figure 6.2.e.

Data points lying outside the inner fences are called outliers.


012345678910111213-2-1 14

LowerInnerFence UpperInner Fence

Whiskers Whiskers

Median

Mean

15

tl

Figure 6.2.e. Box Plot showing an Outlier




Interpreting a Box Plot

The following points provide some guidance to interpreting a box plot.

The inner fences provide a measure of the likely spread of other samples taken

from the same population.

If the data is normally distributed, 99.3 % of the data will lie within the inner

fences. 99.9% of the data will lie within three interquartile ranges of the

quartiles. This measure is referred to as the outer fences .

If the data is normally distributed,

the median will be in the centre of the box;

the mean will be the same as the median;

the whiskers will be of even length;

The degree to which the median is off-centre gives a good indication as to the

degree to which the data is skewed on non-normal. Similarly, whiskers of

uneven length are also an indication that data is skewed.

Points outside the inner fences or "outliers" are unusual and should be

investigated to determine their cause. They indicate that some change,

aberration or unusual event has caused this particular point to be very different

from the usual performance of the process we are measuring. To fairly assess

the performance of the process, outliers should be excluded as they wouldotherwise excessively skew the data.

In summary, a box plot will show at a glance:

The range of the data

The medians and quartiles

The interquartile range

Whether or not data is skewed (a median that is off-centre or whiskers of

uneven length)

Outliers

Whether there is a difference between groups of data.

Using Box Plots to compare groups of data

Box plots can be used to test whether there is a real difference between two

groups of data, or whether apparent differences are due to random variations in

the process.




For example, a company monitoring customer satisfaction can use a box plot

to determine whether a recent improvements in satisfaction levels is due to a

genuine improvement in customer satisfaction or simply due to the fact that

the group sampled was biased towards "happy" customers and as such did not

represent a "fair" sample. ie. this is usually referred to a sampling error .

In the bank queuing time example previously considered, suppose the bank

staff implemented some changes aimed at reducing waiting time. A second

group of data could be collected after the changes. By drawing a box plot for

the second group (after) data on the same graph as the first box plot we, can

assess whether or not the changes did actually reduce waiting time.

Figure 6.2.f. shows the second group of data collected after the changes,

plotted with the original box plot and illustrates graphically the value of box

plots for comparing groups of data.

012345678910111213-2-1 1415

Nooverlapindicatesa"real"differencebetween

twosetsofdata

Original Data

Afterthechanges

Figure 6.2.f. Using Box Plots to compare two groups of data

If the boxes do not overlap, as is the case in Figure 6.2.f, then we can say that

there is a real difference between the two groups.

If the boxes overlap to any degree, then any apparent change in the data is due to

sampling errors and not due to any fundamental changes or differences in the

processes which the data is measuring.




Force Field Analysis

What is Force Field Analysis?

Force field analysis is a graphic technique that allows a team to display theforces acting for and against the successful implementation of any proposed

change or countermeasure. Also known as a “barriers and aids” analysis.

When to use a Force Field Analysis?

Force field analysis is most useful when formulating an implementation

strategy to ensure the team have comprehensively addressed all of the key

issues.

Force field analysis is particularly good at identifying and highlighting both

problem areas and likely areas of resistance as well as key points of leveragewhich can be exploited by the team to overcome resistance and other

implementation problems.

How to do a Force Field Analysis

1. Decide on and describe the goal or change to be analysed.

Decide on and describe the goal or change to be analysed. Write this on a sheet

of paper or white board and draw a box around it.

Draw a line across the page starting at the box to act as the dividing line

between positive and negative forces. This is illustrated in Figure 6.3.a.

Improve

delivery

performance

Figure 6.3.a. Starting layout for force field analysis.

2. Brainstorm and list all of the positive factors.

Brainstorm and list all of the factors which will support the achievement of the

goal or implementation of the change. Record these on the force field analysis

diagram with arrow pointing toward the horizontal line.

This is illustrated in Figure 6.3.b.




Improve

delivery

performance

Customer demands

Reduction inWIP

inventories

Less hassleswith customer

complaints

Reduceconflict

betweendepartments

Reducetransport

costs

Figure 6.3.b. Record the positive forces supporting the change

3. Brainstorm and list all of the negative factors

Brainstorm and list all of the factors which will oppose the achievement of the

goal or implementation of the change. Record these on the force field analysis

diagram with arrow pointing toward the horizontal line on the opposite side

from the positive forces.

This is illustrated in Figure 6.3.c.

Improve

delivery

performance

Customer demands

Reduction inWIP

inventories


complaints

Reduceconflict

betweendepartments

Reducetransport

costs

Resistance touse of new

procedures

Cost of newcomputer hardware

Gettingagreement tochanges from

the bank

Resistancechanges to

credit policy by accounts

6.3.c. Force field diagram with negative factors added.

4. Highlight the most significant forces

Highlight the forces the team believe will be the most significant by drawing a

larger arrow and stonger line from these. See Figure 6.3.d.




Improvedelivery

performance

Customer demands

Reduction inWIP

inventories


complaints

Reduceconflict

betweendepartments

Reducetransport

costs

Resistance touse of new

procedures

Cost of newcomputer hardware

Gettingagreement tochanges from

the bank

Resistancechanges to

credit policy by accounts

6.3.d. The completed force field analysis.

5. Assess the results

Assess the results of the force field analysis and modify your implementation

strategy to take into account the new information.




7. The Seven Quality Management and Planning

Tools

The seven quality management and planning tools were identified during the

early 1970’s by the Japanese Society of Quality Control and TechniqueDevelopment, as part of a deliberate initiative aimed at identifying and

evaluating management control techniques which had been proven to be the

most effective.

They identified seven new management techniques. These are:

The affinity diagram;

Interrelationship diagram;

Systematic diagram;

Matrix Diagram/Decision Matrix;

Prioritisation Matrix;

Process decision program chart;

Activity network diagram;

In contrast to the seven basic quality tools, which are predominantly

quantitative in nature, based on the use of “hard” data and applied at the

shopfloor level, the seven quality management and planning tools are aimed at

problems that are predominantly qualitative.

They are mainly used by the middle and upper management levels to help

identify problems, recommend and establish plans for corrective action.

The relationship between the different tools when they are used as part of an

integrated approach to address some management issue or problem is illustrated

in Figure 7.1.




Relations

Diagram

Affinity

Diagram

Systematic

DiagramMatrix

Diagram

Decision

Matrix

Prioritisation

Matrix

Aretasksknown?

Network Diagram

Process

Decision

ProgramChart

Reliesoncreativity Reliesonlogic

Stage 1

Stage 2

Stage 3

Figure 7.3. The Seven Quality Management & Planning Tools

Figure 7.1 illustrates the various tools used during three major stages, as follows:

Stage 1: to identify and clarify the nature of the problem, the key issues and

dimensions;

Stages 2: to identify and clarify the relationships and interactions between issues

and relationship to the objective;

Stage 3: to develop time phased plans for implementation, addressing risk and

developing contingencies.

This section provides a description of the usage of each of these tools and

techniques.




The Aff ini ty Diagram

What is an Affinity Diagram?

The affinity diagram is a means of collecting a large amount of verbal data andorganising it into natural clusters.

The clusters will ideally represent the intrinsic structure of the problem being

investigated. The process of creating an affinity diagram promotes the

generation, organisation and consolidation of information about a problem or

other complex issue. The process of developing affinity diagrams is also

known as the KJ method (its Japanese name), after its developer Mr Jiro

Kawakita, a Japanese anthropologist.

When do you use an Affinity Diagram?

The strength of the affinity diagram is in the way it can help with unravelling

and understanding complex problems and issues. It is useful for collecting and

consolidating team member’s thoughts on unknown or unexplored areas.

In particular, the affinity diagram is best used when dealing with problems and

issues that:

are complex in nature and difficult to “get your mind around”;

are disorganised or chaotic;

have resisted attempts to resolve them using other approaches eg. the seven basic tools and problem solving process;

require a large number of ideas and inputs, all of which must be organised;

require a degree of creativity if they are going to be solved;

required team efforts.

How do you use an Affinity Diagram?

Identify the problem or issue to be addressed.

Consider an organisation which has had ongoing problems meeting delivery

targets on customer orders .

Significant internal conflict has arisen as managers and staff in the various

departments involved in the order fulfilment process try to assign blame for

the delays to each other’s department.




The organisation has decided to examine the order fulfilment process to

identify and resolve the problems that affect the organisation’s delivery

performance.

Nominate a team leader or facilitator to lead the session. Developing an

affinity diagram requires strong facilitation. The team should nominate a teammember or if necessary, invite some one external to the team who has a good

command of the affinity diagram development process to lead the session(s).

Develop a problem or issues statement. Prepare a formal problem or issue

statement, to focus the attention of the team - this is often best done by stating

the problem or issue in the form of a question eg. “how do we accelerate our

product development cycle?” or “what are the issues associated with

implementing this new technology?”

In our case, “What are the problems that impact on customer delivery performance.”

Individual and Team Brainstorming.

The brainstorming phase can be progressed as a group brainstorming session,

as individual brainstorming or as a combination of both. The key part is that as

each idea is thought of or verbalised, it is written on a small piece of paper or

card. (Post-it notes are particularly good for this).

One approach is to have each person brainstorm individually and list their

ideas on a sheet of paper.

When this is done, the session leader has every one offer one idea . This idea is

written on a piece of paper or card (one idea per card) and the card is placed on

the table. This process continues until everyone has exhausted their ideas.

The same rules that apply to brainstorming are applied. Any ideas that are

thought of as this process progresses are written down on cards and added to

the pile.




NoInstallationManual inBox


Credit checktakestoolong

Notransportorganised

Bickeringbetweendepartments

Order heldupininternal mail

Not clear whatcustomer wants

Deliveryaddresswrong

NoInstallationManual inBoxNoInstallation

Manual inBoxCredit checktakestoolong



Order heldupiinternal mail



Credit checktakes

toolong

Notransport

organisedBickeringbetweendepartments

Order heldupiinternal mail

Not clear whatcustomer wants

Deliveryaddresswrong



Credit checktakestoolong


Order helduiinternalil

Not clear what

customer wants

Techniciansbusyonother work

Official order incorrect

Consolidate cards into like piles. Spread all the cards out on a table. Everyindividual in the group then participates in arranging the cards into similar or

related groups ie. cards that have an “affinity” to each other.

Some guidelines to conducting this exercise include:

While grouping the cards into like piles, there should be no talking

between members;

Cards can be moved between piles by different team members as many

times as required until every one is happy with the arrangement;

Cards that do not seem to fit in any one pile can be grouped into a“miscellaneous” pile.

The exercise is finished when team members are no longer moving cards

between piles.




Order ininternal mailsystem

Not typedinto

computer

Official order notmadeup

Etc., Etc.,

Official order incorrect

Stockcodeincirrect,cannot input

Newcustomer, nodetailsoncomputer

Etc., Etc.,

Techniciansbusyonother work

Notechnicianallocated

Techniciannotavailable

Etc., Etc.,

Itemdamaged

Itemdoesn't work

Incorrect itemdelivered

Etc., Etc.,

Itemnot instock,needtopurchase

Itemwaitingtobepicked

Backloginwarehousetoohigh

Etc., Etc.,

Equipment sittingondespatchdock

loadingdocks jammedwithother

product

Turnaroundindespatchtoolong

Etc., Etc.,

Waitingonbankapproval

Cannot findcreditdetails

Banker notavailable

Etc., Etc.,


Nosuitabletruckavailable

Wait for availablespaceonnext truck

Etc., Etc.,

Wrongmanual ibox

Noinstallation

manual inbox

Partsmissingfroinstallationkit

Etc., Etc.,

Bickeringbeteedepartments

Nobodyhelpsouththereisaproble

Nocommunicatioonpriorities

Etc., Etc.,

Figure 7.4. Cards segregated into piles with similar or related cards

Allocate a title to each pile. Examine the cards in each pile. Based on the theme

of the cards in each pile, allocate titles to the piles which are descriptive of the

theme of ideas in the pile.

This can be progressed through group discussion. The titles for each pile are then

written on a card which is placed at the top of the pile as a header. Note: the

most useful titles are usually those expressed in the form of a short phrasedescribing the theme of the pile rather than a single word title.




Order in internal mailsystem

Not typed into

computer

Off icial order not

madeup

Etc., Etc.,

Official order

incorrect

Stock code incirrect,

cannot input

New customer, no

detai ls on computer

Etc., Etc.,

Technicians busy on

other work

No technician

allocated

Technician not

available

Etc., Etc.,

I tem damaged

I tem doesn' t work

I ncorrect item

delivered

Etc., Etc.,

I tem not in stock,

need to purchase

I tem wait ing to be

picked

Backlog in

warehousetoo high

Etc., Etc.,

Equipment sitting

on despatch dock

loading docksammed wi th other

product

Turnaround in

despatch too long

Etc., Etc.,

Waiti ng on bank

approval

Cannot find credit

detail s

Banker not

available

Etc., Etc.,

No transport

organised

No suitable truck

available

Wait for available

spaceon next truck

Etc., Etc.,

Wrong manual in

box

No installation

manual in box

Parts missing from

installation kit

Etc., Etc.,

Bickering between

departments

Nobod hel s out whenhere is a

No communicationon priorities

Etc., Etc.,

Figure 7.5. Piles with title cards

Review the miscellaneous pile. Review the miscellaneous pile to see if any of

the cards can be reallocated to the named piles.

Draw the affinity diagram. Use adhesive tape to position the cards, in the

groupings that emerged on a large flip chart or pieces of butcher’s paper which

can be stuck together, to shown the whole diagram. The header card should be at

the top of each section.




PickingDelays

Itemnot instock, needto

purchase

Itemwaitingtobe

picked

Backloginwarehouse

toohigh

Etc., Etc.,

OrderheldupinDespatch

Equipment sittingon

despatchdock

loadingdocksjammed

withotherproduct

Turnaroundindespatchtoolong

Etc., Etc.,

DelayswithCreditCheck

Waitingonbank

approval

Cannot findcredit

details

Bankernot available

Etc., Etc.,

Transportscheduling

&coordination

Notransport organised

Nosuitabletruckavailable

Wait foravailable

spaceonnext truck

Etc., Etc.,

Orderheldupinthe"system"

Orderininternal mail

system

Not typedintocomputer

Etc., Etc.,

Notenough

informationcapturedonorder

Official orderincorrect

Stockcodeincirrect,

cannot input

Etc., Etc.,

Schedulingof technicians

Techniciansbusyonother

work

Notechnicianallocated

Etc., Etc.,

Itemnotfunctional

Itemdamaged

Itemdoesn't work

Etc., Etc.,

Cannotinstall, ite

missing

Wrongmanual in

Noinstallationmanul

inbox

Etc., Etc.,

LackofCooperationbetweenDepts.


Nobodyhelpsout whenthereisaproblem

Nocommunicationonpriorities

Etc., Etc.,

Official ordernot made

up

Newcustomer, nodetailsoncomputer

Techniciannotavailable

Incorrect itemdelivered

Partsmissingfroinstallationkit

What aretheproblemsthat impact on

customerdeliveryperformance

Figure 7.6. The completed diagram

Evaluate, assess and discuss the affinity diagram. The team members now

assess and discuss the diagram, the categories or titles in which the cards

grouped, the individual cards in each pile, in order to gain more insight into the

problem or issue.

The grouping categories should flag the major dimensions or components of the

problem or issues - understanding these will add greater structure and focus to

activities aimed at addressing these issues.

What next?

The affinity diagram can greatly enhance a team’s understanding of a problem or

issue, by flagging the major elements. However, it may still not be obvious what

to do next.

This is where the interrelationship diagram can be used to build on the outputs of

the affinity diagram, by identify which element may be more important or exerts

undue influence on the problem. These areas, once identified should provide the

initial point of focus for improvement efforts.




Relat ions Diagram

What is a Relations Diagram?

The relations diagram is a graphical method for clarifying and representingcomplex cause and effect relationships. It illustrates the logic that exists

between the many factors or elements of a problem or issue.

This technique may also be used for displaying complex objectives means-to-

ends relationships.

When do you use a Relations Diagram?

The relations diagram is used to determine the root causes and root effects of a

problem.

Root causes are those factors or elements of a problem that generate the

majority of the symptoms. Root effects are the major symptoms.

The relations diagram is particularly useful for determining the root causes of a

problem or issues in cases where quantified data is not available, or where

there is a large number of interrelated issues to be defined and understood.

Where there are a large number of factors to be understood, it is often useful

to use the affinity diagram as a method for identifying the key factors or issues,

which are then used as an input to the relations diagram.

How do you use a Relations Diagram?

Define the problem or issue to be addressed.

Agree a problem or issue statement. Prepare a short problem or issue statement

to focus the attention of the team - this is often best done by stating the

problem or issue in the form of a question eg. “how do we accelerate our

product development cycle?” or “what are the issues associated with

implementing this new technology?”

In our case, “What are the problems that impact on customer delivery

performance.”

Layout the major factors/elements.

Write the problem statement in the centre of a large sheet of paper or chart.

Draw a circle around the problem statement.




Lay out the key factors or elements of the problem, previously identified using

the affinity diagram evenly around the problem statement. This is illustrated in

Figure 7.5.

Cannot install, items

missing

Itemnot functional

Order heldupin

Despatch

Not enough

informationcaptured

onorder


PickingDelays

Transport scheduling

&coordination

Schedulingof

technicians

DelayswithCredit

Check

Lackof Cooperation

betweenDepts.

What aretheproblemsthat

impact oncustomerdelivery

performance

Figure 7.7. Starting layout for a relations diagram

Analyse the relationships

Consider each factor or element in the context of the other factors/elements.

Assess whether or not a cause or effect relationship exists between the factors.

ie. does this factor/element influence any other? Is this factor/element the result

of or affected by any other?

If a relationship exists between two factors, draw a line between them. Draw an

arrowhead on the end of the line in the direction of the effect relationship. For

example, in Figure 7.6, the factor “Credit Check Delays” was assessed as being

caused by the factors “Not enough information captured on order”. The line is

draw with the arrow pointing to “Credit Check Delays”.





missing

Itemnot functional

Order heldupin

Despatch

Not enough

informationcapturedonorder


PickingDelays


&coordination

Schedulingof

technicians

DelayswithCredit

Check

Lackof Cooperation

betweenDepts.



performance

Figure 7.8. Arrow illustrating cause-and-effect relationship

The team continues to analyse the relationships until all factors have been

compare to all others. The result of this analysis is shown in Figure 7.7.


missing

Itemnot functional

Order heldupin

Despatch

Not enough

informationcaptured

onorder


PickingDelays


&coordination

Schedulingof

technicians

DelayswithCredit

Check

Lackof Cooperation

betweenDepts.



performance

Figure 7.9. A completed analysis of relations








The favoured strategy is to focus on resolving the root causes, commencing

with the primary root cause first, as this will eliminate most of the effects.

However, depending on the nature of the required solution, we may need to

take shorter term measures aimed a coping with the root effects ie. dealing

with the symptoms.

The relations diagram highlights both.

When it comes to formulating strategies for dealing with root causes (or

effects) the systematic diagram is a useful tool for generating the actions

required to resolve them. This is discussed in the next section.




The Systematic Diagram (Tree Diagram)

What is a Systematic Diagram?

The systematic diagram is used to illustrate the means or activities needed toachieve specific goals and objectives. It provides an overview of the cascade

of objectives and subobjectives through to the specific tasks and activities

required to achieve them.

It is a graphical representation of the different levels of objectives and tasks

required to accomplish a broader goal which illustrates the logical

relationships between each level and the tasks which must be achieved.

When do you use a Systematic Diagram?

The systematic diagram is most useful when broad goals or objectives need to

be broken down into executable tasks, or complex tasks need to be broken

down into their component parts.

Difficulties with implementing goals and objectives often arise in situations

where it may not be clear what exactly needs to be done in order to achieve the

objectives. The systematic diagram allows the team to resolve such issues by

providing a structured approach for working through objectives and translating

them into actionable tasks.

How do you use a Systematic Diagram?

State and record the problem, goal or objective.

The goal or objective may come from a strategic plan which is to be

implemented or as a result of a factor identified using the relations and affinity

diagram techniques.

Write down the problem, goal or objective on the far left of a large sheet of

paper and draw a box around it, as shown in Figure 7.10. This defines the

primary objective.

I

Figure 7.12. The Goal Statement - "Improve Delivery Performance"




Generate the next level of the diagram.

To generate the next level of the diagram, ask the question “How will this

objective be achieved”.

The answers to the question “how” will either define tasks to be actioned or other objectives, the achievement of which will fulfil the primary objective.

In our example, using the results of the relations diagram as an input to the

process, the answer to the question “How” do we improve delivery performance

generates the secondary objectives shown in Figure 7.11.

Improvedeliveryperformance

Makecredit check

processfaster

Ensureall necessar

informationcaptured

order

Eliminatepicking

delays

Improvetechnician

scheduling

Primary

Objective

Secondar

Objective

How?

Figure 7.13. Ask the question "How?" to generate the next level

Complete the diagram

Continue building the systemic diagram until all branches have been completed.

To do this, continue asking the question “How?” for each objective. When all

the answers for a particular objective represent actionable tasks, then the branch

can be considered completed.

Continue until all the branches lead to actionable tasks. A completed systematic

diagram is shown in Figure 7.12.

Note: not all the branches will extend neatly together or generate tasks at the

same level. Some objectives will generate both tasks and sub-objectives. These




sub-objectives must then be followed through until all branches end in

actionable tasks.

Improve deliveryperformance

Make credit check

process faster

Ensure all necessary

information captured on

order

Eliminate pickingdelays

Improve technician

scheduling

Change procedure tobypass credit check for prequalified customers

Modify computer inputscreen to check for allrequired information

Provide warehouse withadvance notice of orders

in the system

Provide copy of dailywork list to Sales Dept.

Redesign orders

proforma to ensure allinformation captured

Change procedure toensure incomplete orders

cannot to approved

Introduce online creditcheck facility with bank

Give techniciansadvance notice of work

that is coming up

Install online link tobank for online credit

check

Provide terminal for technicians to reviewnew orders received

Primary

Objective

Secondary

Objectives

Sub-objectives

and tasks

Tasks

Install terminal inwarehouse to allow daily

check on due dates

Change procedure tosend out of stock

notification to Sales rep.Objectives

Actionable tasks

Figure 7.14. The completed systematic diagram

Figure 7.12 shows a systematic diagram which has been completed within four

levels. Every primary objective or problem will have its own unique hierarchy of objectives which may extend for considerably more than four levels.

Do not be misled by the simplicity of the above example. It is important to

follow through each branch however many levels it takes until all the actionable

tasks which represent the final level are identified for each branch.

These actionable tasks are also referred to as the “fundamental means” of a

systematic diagram.

The relationship between the various levels in the systematic diagram is defined by the questions “How?” and “Why?” illustrating the Ends and Means

relationship between each two levels. This is illustrated in Figure 7.13.




Improvedeliveryperformance

Makecredit check

processfaster

Ensureall necessary

informationcapturedon

order

Eliminatepicking

delays

Improvetechnician

scheduling

Changeproceduretobypasscredit checkfor prequalifiedcustomers

Modifycomputer inputscreentocheckfor allrequiredinformation

Providewarehousewithadvancenoticeof orders

inthesystem

Providecopyof dailyworklist toSalesDept.

Redesignordersproformatoensureallinformationcaptured

Changeproceduretoensureincompleteorderscannot toapproved

Introduceonlinecreditcheckfacilitywithbank

Givetechniciansadvancenoticeof workthat iscomingup

Install onlinelinktobankfor onlinecredit

check

Provideterminal for technicianstoreviewnewordersreceived

Install terminal inwarehousetoallowdailcheckonduedates

Changeproceduretosendout of stock

notificationtoSalesrep.

How? How?

How?

Why? Why?

Why?

Ends Means

Figure 7.15. The Ends-Means relationship between the levels

Assess the systematic diagram

To understand the Ends-Means relationships illustrated by the systematic

diagram: Start with any objective box in the diagram and ask the question “How?”

to move “down” the hierarchy, ie. move to the right or ask the question

“Why?” to move “up” the hierarchy, ie. move to the left.

Start with any task box in the diagram and ask the question “Why?” to

move “up” the hierarchy, ie. move to the left.

Asking “How?” identifies the “Means” asking “Why” identifies the “Ends”.

A completed systematic diagram will identify all the tasks which must be

actioned in order to achieve all of the objectives identified in the diagramand in turn achieve the primary objective.

Assess the results of the diagram to ensure that completion of the tasks

identified do indeed achieve the higher level objective from which they were

generated. If they do not, reassess the objective to see if you have missed

some tasks or sub-objectives.

Responsibility for completion of the action items is then assigned to team

members.




The Matrix Diagram

What is a Matrix Diagram?

The matrix diagram is used to illustrate the relationship or interaction between two or more sets of factors. There are many variations on the

basic matrix diagram including the:

decision matrix;

allocation matrix;

prioritisation matrix.

This section shall consider the basic matrix diagram.

When do you use a Matrix Diagram?

The basic matrix diagram is most useful when you wish to assess the

interaction or impact changes to a series of factors may have on a groups of

other factors or areas. This is best illustrated by way of an example. which

follows.

How do you use a Matrix Diagram?

Example: An organisation wishes to implement changes to their order

fulfilment process. There are a number of planned changes including changesto written and computerised procedures, changes to responsibilities and job

descriptions across several departments.

In order to facilitate effective training and implementation in each group, the

implementation team has decided to assess the degree to which each major

group involved in the order fulfilment process is affected by each change, to

ensure they are made aware of what they specifically will need to know and do

differently.

List the first group of factors along one of the matrix axes.

In our case, the team have decided to list the changes to be made along the

vertical axis of the matrix.

This is illustrated in Figure 7.14..




Changes

New order input screen

Authority tables change

Online credit check facility New credit update screen

Warehouse pick list update

screen

New orders list

Technician backlog report

Technician work allocations

screen

Figure 7.14 Matrix Diagram showing changes to be implemented

List the second group of factors along the other matrix axis.

In our example, the departments involved in the order fulfilment process have

been listed along the horizontal axis. ie. along the top of the axis. This shown

in Figure 7.15.

Groups affected >>

Changes Sales Credit W/Hs Desp. Techs

New order input screen

Authority tables changeOnline credit check facility

New credit update screen


screen

New orders list

Technician backlog report


screen

Figure 7.15 Matrix Diagram showing departments affected.

Rate the level of interaction between the two groups of factors.

Usually some form of rating system is used to indicate the level or type of

interaction between the two groups of factors where some interaction exists.




In our case, the team decided to use a system based on the letters:

H = High, indicating the change has a high level of impact on this

department;

M = Moderate, indicating the change will have a moderate level of impact

on this department;

L = Low, indicating the change will have a low level of impact on this

department;

Blank, indicating the change will have no impact on this department,

The completed matrix diagram is shown in Figure 7.16.

Use the results of the Matrix Diagram to guide future actions.

In our example, the team would use the knowledge of which departments are

most affected by which changes to develop specific implementation strategies,training and awareness sessions, focussed on the specific changes the different

departments will need to master.

For example, the implementation and training for the Technicians Department

would focus on ensuring they were aware of the changes to authority tables

and had access to the warehouse pick list. It would then focus on ensuring they

had specific knowledge and skill in the use of procedures relating to, new

order lists, backlog reporting and the work allocation screen.

Alternately, the Despatch Department would only need to be aware of the

authority table changes and have a moderate working knowledge of the

warehouse picklist screen.

Figure 7.16 The completed Matrix Diagram

Groups affected >>

Changes Sales Credit W/Hs Desp. Techs

New order input screen H

Authority tables change M H L L L

Online credit check facility M H New credit update screen H


screen

L H M L

New orders list H H M

Technician backlog report H H


screen

H M




The Decisio n Matr ix

What is a Decision Matrix?

The Decision Matrix is a worksheet made up of columns and rows which isused to rank the options or alternatives which must be decided between,

against a set of agreed criteria which the decision must meet, so as to facilitate

decision making.

It is best used by a team to arrive at a group decision in a manner that

overcomes potential influences from personal biases of group members.

When do you use a Decision Matrix?

The decision matrix is most useful when a choice must be made between more

than one clear alternative, and there are set of definable criteria which thedecision must satisfy.

How do you use a Decision Matrix?

Determine the alternatives

The first step before using a decision matrix is to determine the alternatives to

be decided between.

Consider an example of an organisation that wishes to progress a performanceimprovement initiative in their operations division. The alternatives have been

defined as:

Use an external consultant to progress the initiative;

Use and internal team, trained and facilitated by an external consultant;

Use an internal team only.

Determine the criteria to be satisfied by the ideal outcome.

The criteria the successful course of action must meet, against which thealternatives will be evaluated against have been defined as:

Implementation must be able to be fast tracked. A quick result is required;

There must be a high degree of ownership of any changes by the employees;

The results need to be sustainable in the long term;

Implementation of recommendations should be easy;




The methodology/approach should reflect leading edge management

thinking;

The project should be able to be done for the lowest cost possible;

The conducting the project should not disrupt existing operations.

Lay out the decision matrix.

Lay out the decision matrix with the alternatives along the horizontal axis and

the criteria along the vertical axis.

This is illustrated in Figure 7.17.

Evaluation Criteria

Weighting ScoreWeighted Score

ScoreWeighted Score

Scoreei t Scor

Fast trackimplementation

Ownershipof anyrecommendedchanges

Sustainableresults

Easeof implementation

Leadingedgeapproach

Lowcost

Minimisedisruptionstoexistingoperations

Total

Useexternal consultants

Consultantsled internal team

Internal t only

Alternatives

Figure 7.17. Lay out the Decision Matrix

Apply a weighting to each of the criteria.

Assign a score to each of the criteria, which reflects the relative importance of

that element. This is usually done by assigning a score out of 10 to each criteria.

A Decision Matrix with the weightings applied to the criteria is shown in Figure

7.18.




Evaluation Criteria


ScoreWeighted Score

Scoreei t Scor

Fast trackimplementation8

Ownershipof any

recommendedchanges

4

Sustainableresults 9

Easeof implementation4

Leadingedgeapproach2

Lowcost 3


7

Total



Internal teonly

Alternatives

Figure 7.18. Decision Matrix with each criteria weighted

Score each alternative along each criteria.

That is, assign a score out of ten for how each alternative performs along each

element of the criteria.

A scored decision matrix is shown in Figure 7.19.

Evaluation Criteria


ScoreWeighted Score

Scoreei t Scor

Fast trackimplementation8 7 6 3

Ownershipof any

recommendedchanges

4 2 5 8

Sustainableresults 9 5 6 8

Easeof implementation4 8 7 5

Leadingedgeapproach2 8 8 4

Lowcost 3 4 6 7


7 8 7 6

Total



Internal t only

Alternatives

Figure 7.19. A scored Decision Matrix

Determine a weighted score for each alternative

Multiply the score by the weighting for each criteria for each alternative to

obtain a weighted score. Add up the weighted scores to obtain a total for each

alternative.

This completes the decision matrix, shown in Figure 7.20.






The Prior i t isat ion Matr ix

What is a Prioritisation Matrix?

The Prioritisation Matrix is an application of the basic matrix diagram whichis used to assign priorities to a group of activities needing to be implemented.

Alternatively, this type of matrix may be used for evaluating and comparing a

list of possible solutions against a set of guidelines, in the same way as a

decision matrix is used.

As with the other types of matrix based techniques, the prioritisation matrix is

best used in the team environment, to arrive at a group decision in a manner

that overcomes potential influences from personal biases of group members.

When do you use a Prioritisation Matrix?

A prioritisation matrix is most useful when a there are several

countermeasures that may be implemented to solve a problem or several

actions which may potentially be taken to implement a strategy, and where

trade-offs need to be assessed between costs, benefits, ease of implementation,

timing or similar characteristics.

A typical example would be a situation where there may be a need to

implement a quick fix to address the symptoms of a problem while progressing

longer term actions aimed at resolving the root causes. A prioritisation matrixcould be used to establish implementation priorities between the range of

available actions.

How do you use a Prioritisation Matrix?

Determine the guidelines the countermeasures or actions should meet

Determine the guidelines or criteria the countermeasures or actions to be

implemented must meet. These will be the criteria against which the

countermeasures or actions shall be evaluated.

Consider the example of an organisation wishing to implement a range of

measures aimed at improving the responsiveness of their order fulfilment

process. To develop a detailed implementation strategy, the team need to

prioritise the actions to establish the best order to implement so as to maximise

the benefits and the speed with which they are achieved.






Add up the score in each criteria to give a total for each action or option. The

scored and completed matrix is shown in Figure 7.22.

Actions Cost Time Ease Authorisation Tot l


1 3 2 2

Modifycomputerinput screentocheckfor all requiredinformation

3 5 2 5 1


2 2 3 7 1

Changeproceduretobypasscredit checkforprequalifiedcustomers

2 3 5 9 1

Install onlinelinktobankforonlinecreditcheck

8 7 3 9

Changeproceduretosendout of stocknotificationtoSalesrep.

2 2 1 2


2 1 1 2

Install terminal inwarehousetoallowdaily

checkonduedates

5 5 1 7 1

Provideterminal fortechnicianstoreviewnewordersreceived

5 5 1 7 1

Guidelines Actions or Options

Figure 7.22. Each action scored for each criteria/guideline

Use the resulting total scores to determine priorities.

The general rule is to prioritise the actions in order of ascending score. That is,

implement the lowest scoring option/action first. The completed and prioritised

matrix is shown in Figure 7.23.

Actions Cost Time Ease Authorisation Total


1 3 2 2 8

Modifycomputerinput screentocheckfor all requiredinformation

3 5 2 5 15


2 2 3 7 14

Changeproceduretobypasscredit checkforprequalifiedcustomers

2 3 5 9 19

Install onlinelinktobankforonlinecreditcheck

8 7 3 9 27

Changeproceduretosendout of stocknotificationtoSalesrep.

2 2 1 2 7


2 1 1 2 6

Install terminal inwarehousetoallowdailycheckonduedates

5 5 1 7 18

Provideterminal fortechnicianstoreviewnewordersreceived

5 5 1 7 18

Guidelines

3

5

4

8

9

2

1

6

7

Implementati

prioritie Actions or Options

Figure 7.23. The completed and prioritised matrix




The Allocat ion Matr ix

What is a Allocation Matrix?

The Allocation Matrix is usually used as an extension to the systematicdiagram to allocate responsibilities for actioning the various tasks that are

identified as a result of applying the systematic diagram tool to an objective.

When do you use an Allocation Matrix?

An allocation matrix is most useful when there are many tasks to be completed

in order to achieve some higher order goal/objective, and tasks must be

allocated to individual team members for completion in a coordinated fashion.

How do you use an Allocation Matrix?

Layout the matrix

Commence with the systematic diagram. At the far right of the systematic

diagram, once all the required tasks or actions have been identified, draw a

matrix consisting of three columns and a row for each task identified by the

systematic diagram.



Make credit checkprocess faster

Ensure all necessaryinformation captured

on order


Improve technicianscheduling


in the system


Redesign ordersproforma to ensure allinformation captured


cannot to approved


Give techniciansadvance notice of

work that is coming up


check



check on due dates

W ho W he n S ta t u s


notification to Salesrep.

Provide copy of dailywork list to Sales

Dept.

Change procedure tobypass credit check

for prequalifiedcustomers

Figure 7.24. Lay out the allocation matrix




Label the three columns “Who”, “When” and “Status” as shown in Figure

7.24.

Assign tasks to team members.

Assign tasks to team members by writing in the team member name in the“Who” column and specify completion date requirements in the “When”

column.




Ensure all necessaryinformation captured

on order


Improve technicianscheduling


in the system


Redesign ordersproforma to ensure allinformation captured


cannot to approved


Give techniciansadvance notice of



check



check on due dates

W ho W he n S ta t u s

John End

June

Sue End

Sept

Peter End

June

Peter End

July

Rob Jan

next

year

Sue End

Oct

John End

July

Deb End

June

Sue End

Sept


notification to Salesrep.

Provide copy of dailywork list to Sales

Dept.

Change procedure tobypass credit check

for prequalifiedcustomers

Figure 7.25. The completed allocation matrix

Use the allocation matrix to monitor progress.

Use the allocation matrix to monitor progress towards the achievement of the

overall goal/objective. Use the status column to check off completed tasks.





Improve delivery

performance


Ensure all necessary

information captured

on order


Improve technician

scheduling

Provide warehouse with

advance notice of ordersin the system

Modify computer input

screen to check for allrequired information

Redesign ordersproforma to ensure all

information captured


cannot to approved


Give technicians

advance notice of


Install online link to

bank for online creditcheck

Provide terminal for technicians to review

new orders received

Install terminal in

warehouse to allow daily

check on due dates

W h o W h e n S ta t u s

John End

June

Sue End

Sept

Peter EndJune

Peter End

July

Rob Jan

next

year

Sue End

Oct

John End

July

Deb End

June

Sue EndSept

Change procedure to

send out of stocknotification to Sales

rep.

Provide copy of daily

work list to SalesDept.

Change procedure to

bypass credit check

for prequalified

customers

Figure 7.26. Using the allocation matrix to track progress




The Process Decision Pro gram Chart

What is a Process Decision Program Chart?

The Process Decision Program Chart (PDPC) is a tool which helps a teamanticipate and plan for dealing with problems which may arise during

implementation. It identifies likely weaknesses and potential for failure.

The team can then use the PDPC to formulate and assess contingency plans

and countermeasures to minimise the risk of failure. The Failure Modes and

Effects Analysis Technique (FMEA) often used in conjunction with new

product development is based on the use of the PDPC tool.

When do you use a Process Decision Program Chart?

The PDPC is best used to help a team with the development of contingency plans. It is also useful as a tool for evaluating alternative courses of action.

How do you use a Process Decision Program Chart?

Identify the goal or objective to be achieved.

Consider an organisation whose objective is to ensure all customer orders are

delivered on time. The objective can be defined as “on-time order delivery”.

Brainstorm all the possible unexpected problems

Identify all the possible unexpected problems which could occur in each part

of the process associated with filling customer orders. Ask the question “What

if ... ?”.

Figure 7.27 illustrates a Process Decision Program Chart showing the things

which might go wrong and act against the achievement of the objective “on-

time order delivery”.




On-timeorder delivery

Credit check

Salesand

order receipt

Warehousepicking

Customer

deliveries

Itemnot instock

Suitabletransport notavailablewhenrequired

Noresponsefrombank

Notificationof requirementsnotreceivedintime

Promiseddeliverytimetooshort

Not enoughinformatiprovidedtofill order

Customerfailscreditcheck

Figure 7.27. PDPC with "what if's" identified

Formulate contingencies and countermeasures.

Develop contingency plans and countermeasures which can be used to overcome

the effect of the “what if’s” so as to still achieve the objective of on-time order

delivery. This is illustrated in Figure 7.28.


Credit check

Salesand

order receipt

Warehousepicking

Customer

deliveries

Itemnot instock


Noresponsefrombank



Not enoughinformationprovidedtofill order

Customerfailscreditcheck

Checkwithlogisti beforepromisideliverytimes

Redesign proformatoensr all infocapture

Supplyanywa

Recheckall accoifnoresponsefor

hours

Raisepurchase

order

Provideonlineaccesstoneorders

Usethirdpartycourier

Figure 7.28. Countermeasures/contigencies identified for "what if’s"




The countermeasures or contigencies are indicated in the ovals to distinguish

them from the “what if’s” represented in boxes.

Assess the PDPC

Assess the viability of implementing the identified countermeasures andcontingencies. This is illustrated in Figure 7.29.


Credit check

Salesand

order receipt

Warehousepicking

Customer

deliveries

Itemnot instock


Noresponsefrombank



Not enoughinformationprovidedtofill order

Customer failscreditcheck

Checkwithlogistics beforepromisingdeliverytimes

Redesign proformatoensureall infocaptured

Supplyanyway

Recheckall accountsifnoresponsefor2

hours

Raisepurchaseorder

Provideonlineaccesstoneworders

Usethirdpartycourier

Difficult orImpossible

Recommendedaction

Figure 7.29. The completed PDPC




The Netwo rk Diagram (Crit ical Path)

What is a Network Diagram?

A Network Diagram is a technique used for the planning and tracking of pro jects. It is a technique which identifies the “critical path” of a project,

which represents the shortest possible time in which the project may be

completed.

It also forms the basis for the development of bar charts or gantt charts for

monitoring and controlling projects.

When do you use a Network Diagram?

The network diagram is best used whenever there is a requirement to

implement a project that uses significant resources and requires the time phased coordination of several types of skills to complete.

It is also particularly useful in situations where specific completion dates must

be met and to identify the available options and flexibility for reducing time to

completion and optimising the use of resources.

How do you use a Network Diagram?

The use of the network diagram technique, known as critical path planning is

outside the scope of this handbook.






1. Introd uct io n to Variat ion

One of the laws of nature is that no two things are exactly identical. No two

manufactured items are exactly the same, no two services are delivered in

exactly the same manner.

Variation, however small, is a fact of life and of business. It is therefore

important to understand variation so that we may manage it proactively to our

benefit, and not be continually reacting in order to compensate for the impact

it may be having on our processes and on our business.

2. Observin g Variat ion

If we collect data on any process and plot the data values on a histogram, we

can observe the variation in the process. The distribution of points plotted will

give rise to a pattern that characterises the observed variation. Some typical patterns that are often formed by different processes are illustrated in Figure

2.1.

3. Characteris ing Data

For a given group of data, we can determine several characteristics that allow

us to describe and characterise the data and its variation. The key measures

that allow us to do this are measures of:

Shape

Spread

Location

These are illustrated in Figure 2.2.




Normal Distribution

Skewed or "cliff like" distribution

"Comb like" distribution

Bi-modal distributionie. two peaks

Normal with outlying data

Figure 2.1 Examples of Variation Patterns




Location Location

Spread Spread

Shape- Normal Shape- Skewed

Figure 2.2 Characterising Data




3.1 Measures of Location

There are three measures of location used in statistics.

Mean

_ X or the mean is the ordinary arithmetic average of a group of numbers. It is

referred to as X-bar when spoken.

_

The mean X = Xn

n

Where Xn = represents the values in the sample of data

Xn = the sum of all the values in the sample

n = the number of values in the sample (sample size)

Example: Suppose an organisation collects some data on the performance of

its order fulfilment process. The number of days it had taken to fill eleven

consecutive orders was recorded as:

9, 6, 4, 2, 4, 2, 4, 7, 2, 4, 3.

The mean or average time to fill an order, based on this sample is calculated

as:

_

X = Xn = 9 + 6 + 4 + 3 + 4 + 2 +5 + 7 + 2 + 6 + 3n 11

= 51 = 4.6 days

11

The mean time to fill an order is 4.6 days.




The Median

The median is the middle value of a group of data points. It is the value such

that half the data points are less than the median and half are greater.

If data is skewed or there are a few extreme values, these will distort thecalculation of the mean. The result being, the value obtained for the mean will

not be typical of most of the values in the data. ie. the value of the mean will

not be where most of the data points are located.

For example: the median is often used when reporting housing prices, because

the occasional sale of a very expensive house distorts the average calculation.

Prospective home buyers, are more likely to be interested in what the typical

house in a particular area is likely to sell for. In such cases, the mean will not

be a good indicator of this.

Consider the following data, showing the values of houses sold in a particular

suburb during a month.

Five houses were sold, for the following amounts:

$ 130,000, $ 132,000, $ 420,000, $ 137,000, $ 135,000

The mean housing price from this data is:

$130,000 + $132,000 + $420,000 + $137,000+$135,000

5

= $ 190,800

We can see from observation, that with the exception of the $420,000 house,

the others are all in the range between $130,000 and $140,000. The

prospective home buyer wanting to buy a typical home in this suburb would

therefore need to budget for somewhere in this range.

The mean value of $190,800 has been distorted by the single $420,000 home

which was not typical of the others. To prospective home buyers, this would be a misleading representation of housing values in this suburb.

To calculate the median of the above data, we re-list the values from the

lowest to the highest value ie. ascending order. eg.:

$130,000, $ 132,000, $135,000, $137,000, $420,000

The middle value is the third, or $ 135,000. Therefore, we can say that the

median house price in this suburb during the month the data was collected was




$135,000. We can see that this is indeed typical of what most of the houses

sold for, and has overcome the distorting effect of the single $420,000 house.

Therefore, in situations where the data is skewed or there are extreme values

present, the median is a much better indicator of location than the mean.

Let use reconsider the performance of the order fulfilment process, for which we

have previously calculated the mean.

9, 6, 4, 2, 4, 2, 4, 7, 2, 4, 3.

To find the median of this data, we reorder it from the lowest to the highest

value. ie.

2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 9

There are 11 values in our group of data points, the middle value will be the

6th. ie. their are 5 values below it, 5 values above it. The 6th value is 4 days.

Therefore we can say the median = 4 days.

In cases where there are an even number of data points, the median is

calculated as the sum of the middle two divided by 2. Suppose we had ten

data points as follows:

2, 2, 2, 3, 4, 5, 5, 6, 6, 7

There is no middle value. The two middle values, the 5th and 6th are 4 and 5respectively. The median is then calculated as follows:

Median = 4 + 5 = 9 = 4.5

2 2






3.2 Measures of Spread

Range

The range indicates the spread of extreme values.

It is calculated by subtracting the smallest value in the sample from the largest

and is represented by the symbol R. With reference to the data referred to in

our previous examples.

9, 6, 4, 2, 4, 2, 4, 7, 2, 4, 3.

The smallest value = 2, the largest value = 9. The Range can be calculated as:

R = 9 - 2 = 7 days.

The Standard Deviation

The range is an easy way to get an indication of the amount of variation, but it

does not take into account the overall spread of values. Figures 3.1a to 3.1c

show three different distributions of data.

Mean

Range

Figure 3.1.a Data points "tightly" clustered around the mean




Mean

Range

Figure 3.1.b. Data points evenly spread across the range

Mean

Range

Figure 3.1.c. Data points clustered around the range extremes

Depending on the values of specific data points, all three distributions could

conceivably have the same values for the mean, median and range. Yet, they

are very different from each other and would indicate significantly different

process performance situations.

The standard deviation, often referred to as SD, S, or the Greek symbol sigma

is a measure which overcomes this problem, and allows us to develop a

more complete picture of what our data it telling us.

The standard deviation is a measure of how tightly clustered around the mean,

our data is. It is a measure which reflects the variability and dispersion of data.

It is effectively a measure of the average distance from the mean of all of the

data points. Therefore, data which is tightly clustered around the mean will




have a relatively low value for standard deviation compared to data which is

dispersed away from the mean. With reference to Figure 3.1a to 3.1c. Figure

3.1.a would have the smallest standard deviation - most points clustered close

to the mean, Figure 3.3.c. would give the highest value - most number of

points relatively far from the mean.

The standard deviation is calculated as follows.

_

s = ( Xn - X )2

n-1

_

The term ( Xn - X )2 is referred to as the Variance (Var or S2 ).

n-1

The standard variation is the square root of the variance.

The term Xn refers to our data points;

n is the number of data points we have;

X is the mean of the data.

With reference to our sample data about a company’s order fulfilment process,

we can calculate the standard deviation as follows.

9, 6, 4, 2, 4, 2, 4, 7, 2, 4, 3

We know from our previous calculation, that the mean is 4.6 days.

Variance = (9-4.6)2 + (6-4.6)2 + (4-4.6)2 + ...... + (3-4.6)2

(11 - 1)

= 19.36 + 1.96 + 0.36 + ......... + 2.56

10

= 51.36

10

Variance = 5.14

Standard Deviation = Var

Standard Deviation = 5.14

Standard Deviation = 2.27




4. Understandin g Variat ion

4.1 Common and Special Causes

Irrespective of what individual data points are produced by a process, if theshape, location and spread of the data remains consistent, then we are able to

predict how the process will perform.

This allows us to make decisions that take into account the variation which we

now is there, in this way minimising the negative impact it may potentially

have on the operation of our processes.

If the shape, location and spread is forever changing, then we are unable to

predict how a process with perform, giving rise to uncertainty in the decision

making process and in the way we manage our business.

An American statistician, Dr. W.A. Shewhart, studied variation and patterns of

variation during the 1920's. The results of his studies yielded a major

breakthrough in the understanding of variation and how it should be managed.

The results of his studies can be summarised by three simple statements:

All processes display variation;

Some display controlled variation;

Some display uncontrolled variation.

Another American statistician Dr. W. Edwards Deming, renamed these two

different types of variation by calling them variation due to special causes and

variation due to common causes.

Variation due to common causes was due to the many potential variables

interacting in different combinations as part of the normal operation of a

system or process. This type of variation was purely random and people

working in a system have no control over it. Measuring and plotting data from

a process which exhibited common causes only would produce distributions

with consistent shape, location and spread.

Such processes are said to be in a controlled state, stable or in statistical

control.

Variation due to special causes was due to causes which were not a natural

part of the process or system. This type of variation could always be traced to

an specific or "assignable" cause, such as an unusual event, a specific person,

machine or localised condition.




Data collected at different times from processes or systems in which special

causes are present, will produce distributions which are not consistent as far as

shape, location and spread are concerned.

Such processes are said to be uncontrolled, unstable or not in statistical

control.

Shewhart's breakthrough pointed the way to quality and productivity

improvement through the reduction of variation by removing special causes

first, to make the process stable, and then working on the common causes to

reduce the variation inherent in the process.

Deming went further with his definition of quality as:

Good quality does not necessarily mean high quality. It mean a predictable

degree of uniformity and dependability at low cost, with a quality suited to themarket.

To Deming, quality meant reducing variation, so that customer requirements

could be consistently met. In addition, Deming highlighted the fact that

because common causes "belong" to a system or process, and are a

fundamental property of a process, people working in the process had no

control over them.

It was pointless blaming employees for poor performance. If the substandard

performance was within the limits of the common cause variation of the

process they were working in, employees were effectively "prisoners of the process". Equally pointless was rewarding managers for above standard

performance if this too was within the limits of natural variation of the

process. Both these results are due to the process and not as a result of the

actions of any individual on the process.

To remove common causes requires the implementation of fundamental

changes to the process or system which only management have the power to

change.

Special causes on the other hand, can be traced to an individual, machine,event or local condition. Employees and supervisors working in a process or

system can usually act to identify and remove special causes.

Therefore, for an organisation to work towards continuous improvement, it

needs to train and empower employees to identify and remove special causes

from their work processes until a state of statistical control was achieved.

When processes have been stabilised and only common cause variation exists,

management can either themselves, or through the use of empowered






95.44 % of all data values will fall within the band of plus or minus two

standard deviations around the mean;

99.73 % of all data values will fall within the band of plus or minus three

standard deviations around the mean.

If we have a process or system, whose performance generates data that is

“normally” distributed, we can use our data to calculate and draw an upper

control limit three standard deviations above the mean and a lower control

limit three standard deviations below the mean, as illustrated in Figure 4.2.

The range spanned by these limits will enclose 99.73% of all the data points

that are likely to be produced by the process or system.

Mean=X

UpperControl Limit =X+3xSD

LowerControl Limit =X-3xSD

99.73%ofall datapoints

Figure 4.2 A Control Chart Layout

These limits would effectively define the limits of common cause variation

attributable to a system (ie. covering 99.73% of all possible outcomes). Data

points which lying outside these limits, will usually be as a result of special

causes. Such a chart, showing the upper and lower control limits, the mean and

plotting the data points is known as a control chart.

Fortunately, most naturally occurring data in business and in the natural worldtends to follow the normal distribution, or follows distributions which for

practical purposes may be approximated to normal. Where this is not the case,

the Normal distribution can be approximated with appropriate sampling

procedures.

In addition, when data collection and analysis is based on samples of data and

sample averages are taken as data points rather than the individual points,

Shewhart proved that regardless what the original distribution was, the

averages will approximate the Normal distribution.




This tendency of averages of data to be more normally distributed than the

original data is often referred to as the Central Limit Theorem.

This means that the control chart and Shewhart’s principles in general have

widespread application for understanding and managing variation.

4.2. Collecting Data

When you collect data you will usually be collecting a sample which you hope

is representative of all the outcomes for a particular process. eg. a process may

produce 1,000 manufactured items per day, or process 200 transactions per

day. In most cases it will be impractical to examine each item or transaction,

and so a sample is be taken.

In general, the total number of outcomes eg. transactions, items etc is referred

to as the population. The subgroup which is selected for examination is calleda sample.

The two basic approaches to sampling are:

Random sampling , where sampling is carried out in such a way to ensure

that every unit in a population has an equal chance of being included in a

sample, regardless of the unit's appearance or position.

Systematic sampling , where samples are taken at fixed intervals.

Because we are only looking at a small part of the total population with our

sample, there will inevitably be some difference between the results obtainedfrom our sample and the result we would have obtained had we looked at the

whole population.

The variation between the population and the sample results in sampling error

or sampling variation.

The topic of sampling is a complex subject in its own right and outside the

scope of this booklet. Suffice to say, one needs to be aware of the impact of

sampling error on calculations, so as not to jump to incorrect conclusions on

the basis of small or limited samples. eg. small apparent improvements in a process may be due to sampling error effects and not due to any genuine

improvement.

In all critical situations, one should seek skilled advice on sampling and

sample size selection.



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