Lean Six Sigma Mentor Guide

1

Lean Six Sigma Mentor Guide

Basic Variance Reduction Tools Basic Statistical Tools Lean Tools

2

Focus

This guide will use the DMAIC roadmap in discussing Lean Six Sigma tools. 14 questions “Managers need to ask their people” will step you through the DMAIC process

The emphasis will be on proper use and common mistakes with Lean Six Sigma tools and completing projects

SPC XL from Air Academy Associates will be used in the computer generated graphs

3

14 Questions Managers Need to Ask Their People by Air Academy Associates

1. Which value stream are you supporting and who is the recipient of the value, i.e., who is the customer? Who is the value stream owner and who are the players or team members? How well does the team work together?

2. Within the value stream, which process or processes have the highest priority for improvement? Show me the data that led to this conclusion.

3. How is the process performed? How does the value flow? What activity is value added and what is non-value added?

4. What are the process performance measures, i.e., how ill we gauge if a process is improving? Why did we choose those? How accurate and precise is the measurement system? Show me the data.

5. What are the customer-driven requirements or specifications for all of the performance measures? Are the process performance measures in control and how capable is the process? Show me the data. What are the improvement goals for the value stream or process performance measures?

6. What kinds of waste and cost of poor quality exist in the value stream or process and what is the financial and/or customer impact? Show me the data.

7. What are all the sources of variability in the value stream or process and which of those do we control? How do we control them and what is our method of documenting and maintaining this control? Show me the data.

8. Are any sources of waste or variability supplier-dependant? If so, what are they, who are the suppliers, and how are we working together to eliminate waste and variability? Show me the data.

9. What are the key input variables that affect the average and standard deviation of the measures of performance? How do you know this? Show me the data.

10. What are the relationships between the measures of performance and the key input variables? Do any of the key input variables interact? How do you know for sure? Show me the data.

11. What settings or values for the key input variables will optimize the measures of performance? How do you know for sure? Show me the data.

12. For the optimal settings of the key input variables, what kind of variability still exists in the performance measures? How do you know? Show me the data.

13. Have we implemented a process flow and control system to sustain the gains and continuously improve the process? Show me the data?

14. How much improvement has the value stream or process shown in the past sic months? How much time and/or money have our efforts saved the company? Show me the data.

Def

ine

Mea

sure

An

alyz

e Im

prov

e C

ontr

ol

4

Tools Listed by DMAIC Roadmap Define:

Input Process Output Diagram (IPO), Failure Mode and Effects Analysis (FMEA), Pareto

Measure: Process Flow (PF) Diagram, Histogram,

Cause and Effect (CE) Diagram, Run Chart, Measurement System Analysis (MSA), Process Capability (Cpk)

Analyze: Scatter Plot, Control Chart, Hypothesis Test

Improve: Design of Experiments (DOE)

Control: Standard Operating Procedures (SOPs)

5

Common Concerns to Project Completion Focus is not achieved early.

IPO Diagram not completed or sufficient

COPQ not completely realized Champion support lacking Team not well organized, represented

or trained Prioritization is lacking

Following the DMAIC roadmap is the key. If this is done, there is a much higher likelihood of success

Understanding of the proper use and interpolation of the Lean Six Sigma tools is a must

A project timeline helps to move the project along to completion

6

IPO Diagram

This tool is used to diagram a the key components of a process – Inputs – sources of variation Process – a description of the

process Outputs – measures of

performance Using this tools will allow all

involved to have a common picture of the process

7

Input Process Output Diagram

Process

A blending of Inputs to

achieve the desired Output

Performance

Cost

Time

Manpower

Machines

Materials

Methods

Measurement

Mother-nature

Inputs Outputs Sources of Variability Measures of Performance

Inputs and Outputs should be in units of measure. Outputs should be measuring the process performance

to be:

Better, Faster, Lower Cost !!!!!

8

How to Construct an IPO? First Step: “P” “P” Label the process box

Often this is done in a subjective statement, i.e., “reducing downtime of pumps”

Instead, “Pump operation” might be a better name for the process

Often the process listed is too large in scope. If this is the case, one can consider to narrow the process or consider the overall scope to be a “macro” view. Later the process can be narrowed by making smaller “input” IPOs cascading into the larger, macro version. See example on next page.

9

Input – Process – Output Diagram

Process

Oil and Gas Production

CPI

Corporate Level

SH&E

Oil (MBOPD)

Gas (MBOEGPD)

Capital Expenditure ($MM/mo)

Oil Price ($/Bbl)

Economic

Gross Production (MBOEPD)

Reserves Replacement (%)

Cash Flow and Net Earnings ($MM/mo)

ROCE (%)

OEB ($MM/mo)

Depreciation ($MM/mo)

Inventory ($MM)

Recordable Incidents (# / MM)

PMVA (# / MM km)

Spills (# / MM bbl)

Lifting Cost ($/bbl)

Avails (MBOPD)

Fuel/Own Use (MBO)

Note: This is an overall, macro view, many of the input factors could be incorporated in their own IPO diagram feeding into the

overall IPO shown here

10

“O”, list the outputs to the process. These are the measures of performance often referred to as: KPI: Key Performance Indicators CTC: Critical to Customer CTQ: Critical to Quality

These measures should be used to track the process as Better, Faster, Lower Cost as well as Safely and Environmentally Sound

All outputs should list the units of measurement

How to Construct an IPO? Second Step: “O”

11

Common Concerns in Listing “Outputs” Units of measure not listed. Example: “Quality”

does not explain HOW this will be measured. A better performance indicator might be % rejects.

Measures of quality should be “normalized” if possible. Instead of # of rejects, % of rejects normalizes the data. This is important in the area of opportunity changes – if production increases, a determination of improvements can be seen % reject depicted data.

Use goals for the performance measures as arrows on the far right side. An up arrow would indicate you want that metric to increase. Stay away from writing these goals on the output line. Example: Production rate (units/day) 1200

Write simply: Production rate (units/day) and off to the right put an up arrow indicating you want that metric to increase.

All outputs should be agreed upon by the process improvement team and management support. They should be aligned with key business strategies, drive behavior, help to assess accountability and responsibility. They should be captured on a process scorecard as well

12

“I”, list the inputs variables of the process. These are referred to as sources of variation.

As a memory jogging tool, the 6 M’s can be used to form categories: Manpower, Measurement, Methods,

Materials, Mother Nature, Machines Known input categories can used

instead of, or in conjunction with the 6 M’s.

Components of the main Inputs can be added. i.e., Manpower could have branches such as skill, training, morale

How to Construct an IPO? Third Step: “I”

13

All major inputs to the process should be listed. Lesser inputs can be listed on the Cause and Effect Diagram

Try not to be subjective in listing the inputs, i.e., inadequate skill level, merely state “skill level”.

Common Concerns in Listing “Inputs”

14

Cascading IPO

Some process are inputs to a downstream process. Some refer to this as SIPOC as shown below

Supplier

Input

Process

Output

Customer

15

ProduceOil

Sludge Oil

Fluid Properties

Water OilInterface

ChemicalTreatment

RecycleProcess

CollectFluid

ProduceWater

ProduceOil

Sludge Oil

Fluid Properties

Water OilInterface

ChemicalTreatment

RecycleProcess

CollectFluid

Fluid Properties

Water OilInterface

ChemicalTreatment

RecycleProcess

CollectFluid

ProduceWater

SkimmedOil/Water

RemoveOil

ChemicalTreatment

SkimmerSetting

GasBlanket

Oil “Free”Water

SkimmedOil/Water

RemoveOil

ChemicalTreatment

SkimmerSetting

GasBlanket

Oil “Free”Water

SkimmedSolid/Water

RemoveSolid

ChemicalTreating

Back Washing

GasBlanket

Solid & Oil “Free” Water

SkimmedSolid/Water

RemoveSolid

ChemicalTreating

Back Washing

GasBlanket

Solid & Oil “Free” Water

InjectCleanWater

ChemicalTreating

StoreWater

GasBlanket

Clean Waterto Wells

MaintainPressure

InjectCleanWater

ChemicalTreating

StoreWater

GasBlanket

Clean Waterto Wells

MaintainPressure

Often one process is theInlet to another!

IPO Diagram Water Flooding Process

If the project desire is producing clean water for injection, upstream processes will need to be addressed to

Improve the final listed process as injecting clean water

16

Complex IPO Example

AdministrationProcessProcedures

Qualified Vendor

END User

Quality

Cycletime

(Dpm)

(Day/Req)

System

Poor IT System

Duplication or repetition

Personnel

Lack of personnel to control doc.

No good communication

Late request for quotation

Lake of manpower

Higher approver reluctant toimplement

Procedures

No status report

Unattractive procedures

No standard bid packagefor services

No standard lead time

Incomplete flowchart

System

Personnel

Inspection Procedures

Tender CommeetteeApprover

Unclear Role & Respons.

No standard lead timeField Proc. Procedures not

clearly defineTerm of Payment

Warning letter to supplier

Detail sanction forsupplier

End user

Unclear spec.

Poor tech. eval.

Late bid evalaluation

Improper POclassification

Uncommon goods req.

Not understand procedure

Bypass Authority approver

Bad attitude

Specific goods preference

Urgent need / Emergency

Lower price

DeliveryProcess

Vendor qualification

Quality

Late time

(Dpm)

(Day/Req)

VendorQualification

Vendor not profesional

Vendor Eval. process

Multi place procurement

AI Darajat & Cogen ProcurementProcess IPO

No back up from principal

Unrealistic offer

MaterialAvailabilityPartial Delivery

No stock

Poor handling

Custom problems

User change spec.

Improper deliveryschedule

17

Pareto Charts

Used to separate the vital few from the trivial many, answering what key inputs effect the performance measures. Using this tool will help to prioritize what we are to improve in the process.

The charts can be constructed by data in tabulated or raw form

This tool can be used to determine root cause by forming multiple Pareto charts on various failure mechanisms – see examples.

Pareto charts should be constructed on both financial and frequency basis.

18

Data Examples

Tabulated form: Raw Form:

Frequency CostSeals 45 $34,567Gaskets 33 $24,975Electrical 23 $37,432Lube Oil 12 $12,643

Reasons for Pump Failures

Reasons for Pump Failures

Seals Gaskets Gaskets

Lube Oil Seals Seals

Lube Oil Electrical Electrical

Electrical Seals Lube Oil

Seals Lube Oil Seals

Seals Seals Electrical

Seals Electrical Seals

Lube Oil Seals Seals

Seals Lube Oil Electrical

Electrical Gaskets Electrical

Electrical Seals Seals

19

Pareto by Cost and Frequency

Cost: Frequency:

Pareto Chart Reason for Pump Failure

0

5000

10000

15000

20000

25000

30000

35000

40000

Electrical Seals Gaskets Lube Oil

Failure Type

Cos

t of F

ailu

re

Pareto Chart Reasons for Pump Failures

0

5

10

15

20

25

30

35

40

45

50

Seals Gaskets Electrical Lube Oil

Failure Type

# O

bser

vatio

ns

20

Pareto Charts Used to Determine Root Cause

Failure Reasons: What Causes

Main Failure?:

Pareto Chart Reasons for Pump Failures

0

5

10

15

20

25

30

35

40

45

50

Seals Gaskets Electrical Lube Oil

Failure Type

# O

bser

vatio

ns

Pareto Chart Reasons for Seal Failures

0

5

10

15

20

25

30

35

Bad Installation Material Operation

Failure Reason

# O

bser

vatio

ns

21

Root Cause

One more Pareto shows root cause:

Pareto Chart Reasons for Installation Failure

0

5

10

15

20

25

Not aligned correctly Not tight enough No oil

Failure Reason

# O

bser

vatio

ns

Work should be done here to effect process improvement

22

Common Pareto Concerns By constructing Pareto charts by both frequency

and cost, one can make the best decision on what to work on first – not necessarily the highest frequency failure, might be the most costly one

Not always should a team work on the highest failure reason, sometimes the easiest to affect might be the one to improve.

Team might not have enough data to make Pareto charts. At that point, measures should be put in place to capture data in the future.

In capturing the data, reliability of the data should be of focus. Some have used Access and other data bases to capture this data. Have pull down menus for people to choose from a list of failure types and then train them on how to distinguish failure types as well.

If many categories of failure types exist, the user should reduce the number of categories on the Pareto chart capturing the very small categories in an “other” category as the last column of data.

23

Failure Mode and Effects Analysis (FMEA)

Used to help prioritize where to make process improvements

Detailed FMEA generates numerical data to point to problematic areas, however this tool is difficult to construct

Basic FMEA is easy to construct but does not give a numeric value. This basic tool can point to root cause if performed correctly – see next slide

24

Basic FMEA – Texas Style

Texas Style FMEA (Failure Mode and Effects Analysis):This is a short cut version to help determine a prioritized list of problem

areas within a process.Steps Involved:• Form a team of people closely associated with the process.• Ask all involved the question “What can cause this process to go wrong/

fail/or other?”.• Brainstorm a list of answers to the above question. Refrain from commenting

on the answers from the group! Just document comments on a flip chart.• Clarify the list, ask if anyone needs more information to understand the answers

listed. If so, ask the author of the answer to clarify further.• Ask the group to combine answers if possible.• Every team member should vote for the most important based on a preset criteria such as

frequency of occurrence, cost, etc. A good method to determine the number ofvotes everyone receives is to add the total number of items on the list, thendivide that number by 3 (N/3 technique). They can place one of their votes for eachitem they select (weighing votes should not be used).

• As a general rule of thumb, circle the top 3-5 items.• Perform the 5 Whys to help determine root cause for these problems. Continue to ask

ask “why” does this happen until you can go no further, that answer is typically the root cause.• This information is used to prioritize where to work first to improve a process, data

collection items needed, and to help identify the most important noise variables on a cause and effect diagram, etc.

25

5 Whys Example CPI EXAMPLE: Finding Root Cause Using the 5 Whys

Duri Well Location Clean-Up Project 1. Why are the locations getting dirty in the first place?

Because the operators cannot keep the stuffing boxes from leaking.

2. Why can’t the operators keep the stuffing boxes from leaking?

Because the packing seals are failing too frequently.

3. Why are the packing seals failing?

Because the polish rod is wearing out the seals prematurely.

4. Why is the polish rod wearing out the seals?

Because the polish rod is bend.

5. Why is the polish rod bend?

Because the transportation trailer is too short and the polish rods are not properly supported. <= Root Cause

26

Standard FMEA

Product or

ProcessFailure Mode Failure Effects

SEV

CausesOCC

ControlsDET

RPN

Actions PlansPS

PO

PD

prpn

Stuffing BoxLeaking Oil Spill 3 mis-aligned 4 align 4 48 meas. 2 1 1 2

3 packing bad 5 go see 3 45 2 1 1 2Belts

Failure Well Down 3 thrown 2 go see 1 6 go see 3 1 1 33 broken 3 go see 1 9 go see 3 1 1 3

MotorFailure Well Down 5 broken 2 go see 3 30 go see PM 2 1 1 2

2 power outage 4 go see 1 8 go see 2 1 1 2

Pump StuckPump Failure No Production 5 scale 2 pres. test 4 40 test PM 5 1 4 20

3 corrosion 2 pres. test 4 24 test PM 3 1 4 123 sanded 4 pres. test 4 48 test PM 3 1 4 12

Failure Mode and Effects Analysis (FMEA):A procedure used to identify and assess risks associated with

Product or process failure modes.

This risk analysis tool can be used to allocate resources to address problem areas.FMEA looks at the Severity, Occurrence, and likelihood and problem will go

undetected. Risk can be reduced by lowering one or all of these factors.These charts can be generated in SPC XL: Quality Tools, FMEA.

27

How to Use the FMEA Data Standard form:

Look at the Risk Priority Number (RPN) column for high numbers. Work on improving those failure reasons

Of the highest priority failure reasons, you need not improve every category: Severity, Occurrence and Avoiding Detection, typically only one area will require improvement to reduce the RPN

Make a plan to reduce RPN, control with Standard Operating Procedures (SOP)

Basic Form – Texas Style Brainstorm list of failure reasons with people

how have process knowledge. Determine priority based on frequency of

failure and cost impact Perform 5 Whys to point to root cause of

failure. Work to improve high priority areas

28

Process Flow Diagram

Use to see HOW your process is performed

Traditional symbols as well as Lean symbols can be used. Lean symbols help to distinguish between value added and non-value added steps.

29

How to construct a Process Flow Form a cross-functional team of

people with process knowledge Decide the start and stop of the

process Agree upon the detail of process

steps – micro vs. macro Use Post its and have team

members list steps Place steps in proper order Go look at the process to confirm

accuracy. Make changes to the process flow if needed

To make the process flow “Lean”, mark the steps as to the type of step – see next page

30

Lean Process Flow

Storage Transport / Operation Inspection Delay(wait) Delivery (wait)

Transport Storage Transport Operation Operation Delay Transport Operation Transport Operation Operation Operation Operation Operation Transport Operation Transport Operation

Pallet to Storage at Transport to Remove Push to Delay on Transport to Cleaner Transport to Fill #1 Fill # 2 Fill # 3 Fill Co2 Valve Transport Crimping Transport Gasing thestagng area stagng area turntable area strappng turntable turn table cleaner fill #1 placement to crimper to gas room cans

Transport Inspection Transport Operation Transport Operation Operation Operation Operation Transport Operation Inspection Transport Operation Transport Operation Transport Operation

Transport to Check Transport to Turntable Transport to Twister to Waterbath Twister to Turntable Transport to Actuator Inspect Transport to Put cap on Transport to Cleans cans Transport to Packingweighing weigher turntable twister lay cans down upright cans actuator actuator capping cleaner packing into box

Operation Operation Transport Operation

Seal box Code box Transport to Put box onpallet pallet

LOGICAL PROCESS MAPLine #5

2 4

30

7

35 37

1 6 11 3 5 8 9 10 12 13 14 15 16 17 18

22 21 23 27 25 2624 28 29 31 32 34 33 36 38

41 42 43 44

31

Traditional Process Flow with Responsibility Columns

FIELD AREA OWNER HES DURI CORP. HES CPI / EPT JKT

Spill Discovered

Investigate

Estimate Volume> 15BBLS

To MajorRiver Malaca

Straits

FollowCriticalIncident Report

Report toCorp. HES &

HES Duriby phone

Submit written report to CSHE, cc SHE DRI

Prepare KKP 2

Report to CPI EPTby phone

Report toMIGAS/BPPKA

by phoneEnd

Review FinalizeFax. KKP2to CPI/EPTcc PA SMTR

Fax. KKP2 toBPPKA/MIGAS

cc PA JKTEnd

OIL SPILL REPORT PROCESS

Update Report toCSHE, cc SHE DRI

every 3 days File & update Database

Update report toEPT JKT

Update report toBPPKA/MIGAS End

Submit F 059(Approved by TM Prod,TM HES DRI) to C HES

Keep copy file & update

Database

Keep Original File

Submit F 059 toTM Prod. & HES DRI

MNGR > 5 BBLVP > 100 BBL

Review Finalize & send

KKP - 3 (Incl. Monthly Oil Spill & Prel.

Report to EPT JKT

Route Report toBPPKA/MIGAS End

2 hrs

24 hrs

48 hrs

3 days

5 days

No

No

Yes

Yes

Prepare KKP 3

32

What to do with the Process Flow Diagram

Note non-value added steps and remove as many as possible

Look for bottlenecks and problem areas – mark them appropriately

Are process steps out of sync, change where needed

Is there enough detail? If not, add steps or detail to the steps listed

Do all on the team agree with the process flow? Does it match the actual process? Make changes where needed.

33

Removal of Non-Value Added Steps Value added steps are those that

the customer sees as adding value to the product. A good way to determine value added: “Would the customer pay for this step?”

Non-value added steps usually fall into these categories: Motion, Transportation, Over-

production, Over-processing, Rejects/Defects, Inventory, Waiting

Remove as many non-value added steps as possible in the process

Process flow charting points to non-value added steps

34

Common Lean Tools to Reduce Non-Value Added Steps 5S

Sort, Set in Order, Shine, Standardize and Sustain

Basic Housekeeping Tool Can reduce clutter and time looking

for things After 5S in completed, regular audits

are needed to assure compliance A reward system is beneficial to

sustain gains Often, extra tool sets and other

expenses might be needed to achieve success – these items should have a cost benefit analysis done to justify purchase

Best practices should be shared

35

Visual Controls Working along with 5S will help to

improve communication in the workplace and reduce time spent looking for things

Safety issues can also be addressed with Visual Controls. Marking of danger, fire equipment, caution, etc., could be used.

Coloring tools to indicate size and shape might help to reduce mistakes in using the wrong items.

Inventory areas can be improved with Visual Controls

Common Lean Tools to Reduce Non-Value Added Steps, Continued

36

Cause and Effect Diagram Commonly called a Fishbone diagram Used to capture the sources of variation in the

process Should be constructed in a cross-functional team

setting Should have at least 20-25 bones on the “fish”.

This would assure capturing most of the sources of variability in the process

Variables should be listed as C for constants, N for noise and X for experimental.

These graphs can easily be constructed in the SPC XL software by first filling in the PF/CE/CNX/SOP template (listed under Problem ID Tools). Then, use the SPC XL software to construct the diagram (listed under Problem ID Tools).

Branches of the variables can also be added The head of the fish should be the performance

variable(s).

37

SPC XL Cause and Effect

Located under Problem ID Tools, PF/CE/CNX/SOP Template

Here is the blank template

CNX TemplateCNX Measurement

CNX Method

CNX Machine

CNX Manpower

CNX Materials

CNX Environment

Variable 1Variable 2Variable 3Variable 4Variable 5Variable 6Variable 7Variable 8Variable 9Variable 10Variable 11Variable 12

You can change the category names if you want. Fill in the template, then choose Problem ID Tools, create PF/CE/CNX/SOP diagram – see next page

38

SPC XL Cause and Effect Continued The example shows no labels on the bones since

the template was empty. After your graph is constructed you need to fill in

the output performance metric Measurement Method Machine

Manpower Materials Environment

Output

39

Cause and Effect Example

Bones on the fish could use the 6 M’s or other

categories such as step 1, step 2 and so on

Performance Measure

(Goal: Better, Faster,Lower Cost)

Materials

Machines

Mother N

ature

Mea

sure

men

t

Meth

ods

Man

power

Cause and Effect Diagram

Note Variables to be:C = ConstantN = NoiseX = Experimental

Goal = Change noise variables to constant, when economicallypossible through the use of SOPs

40

Cause and Effect Example

MOTHER NATUREMACHINEMAN POWER

MEASUREMENTMATERIALMETHOD

# of Technicians & Helpers (C)

Technicians Skills & Experience (N)

Elect. Safety Understanding (N)

Commitment & Ownership (N)

Elect. Safety Training (X)

Equipment Condition (N)

PM/PdM Tools (X)

Equip. that identify

the potential problem (X)

PPE (X)

Lightning, Rain, & Animal (N)

Environment (N)

- Dust,

- Dirt Accumulation,

- Presence of Moisture,

PM/PdM Program (X) :

- Schedule (X) (C)

- Asset data & condition (X),

- Manufacturer recommendation (X)

- Eliminating the defect (X) (C)

- System that alert the potential

problems (X),

Literature that identified parts (X)

Original specifications & Drawing

Ensure Compatibility (X)

Immediate Shipment from

Manufacturing Locations (X)

Stock Available from Local Distributors

& National Warehouse (X)

Potential Failure Parameter (X)

MP2 Optimization & Development (X)

PU3

PM/PdM Training (X)

MP2 Optimization & Development (X)

Equip. that reduce/prevent

the unnecessary downtime (X)

Areas are circled that indicate where the work will focus, arrows are used To indicate what the team wanted that metric to do.

41

Cause and Effect Concerns These should be constructed in a team setting. Not

one person can know all the variables in the process Decide how the team is to label the variables. Some

choose to mark C, constant, for all variables that are, at the time of the graph construction, constant. Some list C for all variables they WANT to hold constant. Some mark N to C for variables they plan to make C through the use of SOPs. The choice is the team’s – but it should be understood and constantly done.

Remove subjectivity of the variables, i.e., do not write poor condition, simply write “condition”

When brainstorming the list of variables, do not critique the list, just get it on the chart. If the variable IS important, it will surface later.

Some IPO diagrams list several performance or outputs. If the variables for each of the outputs are different, then a cause and effect diagram should be constructed for each.

If a variable on the CE diagram has many variables associated with it, then it might have to have it’s own CE diagram

After the CE diagram is completed, root cause analysis to determine what variables affect the performance measures should be performed. Then, the team should mark the CE diagram to indicate the variables they plan to improve. Not all noise variables should be controlled.

42

Histogram

This graph is used to see the distribution of the data and key statistically information such as mean and standard deviation.

From this information, one can gather much insight as to the performance of the process

Before constructing a Histogram, one should question the reliability of the data used. See the section on measurement error and MSA.

Using the next slides, many of the common distributions will be shown and conclusions one can make from them.

43

Histogram – Normal Distribution

Histogram of Average of Four Dice Rolled

0

10

20

30

40

50

1.5 to<=

1.783

1.783to <=2.067

2.067to <=2.35

2.35 to<=

2.633

2.633to <=2.917

2.917to <=3.2

3.2 to<=

3.483

3.483to <=3.767

3.767to <=4.05

4.05 to<=

4.333

4.333to <=4.617

4.617to <=4.9

4.9 to<=

5.183

5.183to <=5.467

5.467to <=5.75

Average of 4 Dice Rolled

# O

bser

vatio

ns

Normal Distribution Mean = 3.5112Std Dev = 0.8381KS Test p-value = .0627

This is an example of a normal distribution plotting the average of four dice rolled. With a normal distribution, using the mean and standard deviation, one can use the 68/95/99 rule to assess response probability.

44

Histogram – Exponential Distribution

Histogram Oil Production on Wells with StuffingBox Failures in Duri

0

10

20

30

40

50

60

2. to<=

45.6

45.6to <=89.3

89.3to <=132.9

132.9to <=176.6

176.6to <=220.2

220.2to <=263.9

263.9to <=307.5

307.5to <=351.1

351.1to <=394.8

394.8to <=438.4

569.4to <=613.

BOPD

# O

bser

vatio

ns


With an exponential distribution, one might want to use the more conservative number of the median instead of the average to access the COPQ. To run a Cpk from this data, you could transform the data by taking the log of the data or simply place the specifications on this chart and physically count the product not in spec.

45

Histogram – Uniform Distribution

Histogram of One Die Rolled

0

10

20

30

40

50

60

70

80

90

0.0 to <=1.0

1.0 to <=2.0

2.0 to <=3.0

3.0 to <=4.0

4.0 to <=5.0

5.0 to <=6.0

Die Number

# O

bser

vatio

ns


This is an example of a uniform distribution. Each of these classes of data has an equal chance of occurring in this process.

46

Histogram – Bimodal Distribution

This data set on water densities indicates a bimodal distribution. Typically, bimodal indicates two somethings are going on. In this

case further investigation points to old and new data. The process Is changing, so old data will have a different distribution than the new data. Knowing this, the team increased sampling to have all new data

to make their process decisions based on.

47

Histogram – Parabolic Example

Histogram of Survey Results on a Scale of 1-5

0

10

20

30

40

50

0.0 to <=1.0

1.0 to <=2.0

2.0 to <=3.0

3.0 to <=4.0

4.0 to <=5.0

Survey Response Number

# O

bser

vatio

ns


This is an example of a Parabolic Distribution. On controversial topics, survey results often have this type of result. This indicates people have an opinion on one side or the other, very few people are in the middle.

48

Histogram Concerns There should be enough data to show

how the process is performing. A minimum of 25 data points is adequate.

A Histogram should be run on all data sets before statements are made about the process.

Reliability of the data should always be in question.

If the distribution is not normal, a Cpk analysis will not be reliable to determine accurate dpm and other quality measures

A histogram looks at all the data without regard to time. A run chart is needed to look at trends over time.

For the most part, accept the software defaults when constructing a chart. Changing the settings, might make the chart misleading.

49

Run Charts

Used to track data over time Good tool to see how

performance variables are responding over time.

Very good tool to motivate teams in making process improvements and sustain results

These graphs can be enhanced to show many aspects of process improvements and goals

50

Basic Run Chart Example #1

Run Chart of Duri Sponsor Statapult Data

50

70

90

110

130

150

170

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Shot Number

Dis

tanc

e in

Inch

es

This example shows Statapult data before and after PF/CE/CNX/SOPs. One can clearly see where the process improved, shot number 21. Many items can be added to this simple chart to help to motivate team members and show people what the process is doing, stretch goals, and much more information. See next slide.

51

Basic Run Chart Example #2

Run Chart Aerosol Services CompanyDaily Scrap %, Jan - Mar 2003

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1/2/20

03

1/9/20

03

1/16/2

003

1/23/2

003

1/30/2

003

2/6/20

03

2/13/2

003

2/20/2

003

2/27/2

003

3/6/20

03

3/13/2

003

3/20/2

003

3/27/2

003

X Axis

Y A

xis

Average Scrap = 0.799%Stretch Goal = 0.5%

This example shows the process over time in tracking scrap %. The red line is the current process mean and the green is the stretch goal. The arrow in the upper right corner shows the direction we want the graph to do. The lines and arrows were drawn in. This is a great graph to post in the operations area of a plant to give all a picture of how the process is performing.

52

Run Chart With Added Information Example

Run Chart Cost/Job Duri Acid Job

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

Jan_

98

Mar_98

Oct_98

Jan_

99

Mar_99

May_9

9

Jul_9

9

Sep_9

9

Nov_9

9

Jan_

00

Mar_00

May_0

0

Jul_0

0

Sep_0

0

Nov_0

0

Jan_

01

Mar_01

May_0

1

Jul_0

1

Sep_0

1

Nov_0

1

Jan_

02

Mar_02

Month

Cos

t/Job

$

Reduce FDA # of Jobs (done prior to Six Sigma effort)

Six Sigma EffortsBegin

Mean = $ 34,316

Mean = $ 28,464Significant Shift in Mean After Six-Sigma

Mean = $ 50,220

Time Period I Time Period II Time Period III

Average Cost/jobTime Period II = $ 34,316

Average Cost/job Time Period III = $ 28,464

Cost Saving /job = $5,852Total jobs in Period III = 167

Total Cost Saving in Period III After Six Sigma Efforts = $ 977,284

Information has been added to this chart. As in the previous slide, Constructing a Run chart will only produce a simple graph of the data. From this, a person can use the software drawing tools to add, 1) means Of the process before and after process changes, 2) what was done to the Process, 3) performance goals, 4) economic results, etc.

53

Run Chart Concerns

Baseline data is not always available. The performance measures should be captured as soon as possible.

Often, before and after Six Sigma is put on the graph by means of a drawn in vertical line. Placing the “after” line should be at the time SOPs and other action items are in place.

What should be done with outliers as they will shift the means before and after improvements. Discussion with the process Champion could be best in handling this data. In short, take a conservative approach to assessing improvements and financial gains.

These graphs should be easy to read. Avoid using bar graphs as they fill in the area where text can be written detailing improvements.

Draw in a trend arrow in the upper right corner so all involved in the process know the direction the graph SHOULD go.

Continue to use the run chart after the project is completed. This will help sustain gains.

54

Process Capability Chart (Cpk) This tool is used to track the

performance metrics of the process vs. customer specifications

Assure the data is reliable – account for measurement error, see MSA

Confirm the specifications with the customer. Ask for foundation for the specifications such as economics, operational needs, etc.

Determine the distribution of the data to be normal by constructing a histogram. If the distribution is not normal, the measures of quality derived from the Cpk graph will not be accurate

55

Cpk Chart Example

Run a Histogram first to confirm a normal distribution

Then, construct a Cpk

chart imputing the customer specifications

Histogram

0

5

10

15

20

25

30

17.82 to<= 19.07

19.07 to<= 20.31

20.31 to<= 21.56

21.56 to<= 22.8

22.8 to <=24.05

24.05 to<= 25.29

25.29 to<= 26.54

26.54 to<= 27.78

27.78 to<= 29.03

29.03 to<= 30.27

Class

# O

bser

vatio

ns


Cpk Analysis

13.6

14.3 15

15.6

16.3 17

17.6

18.3 19

19.6

20.3 21

21.7

22.3 23

23.7

24.3 25

25.7

26.3 27

27.7

28.3 29

29.7

30.3 31

31.7

32.3 33

33.7

34.3 35

35.7

In specOut spec leftOut spec rightLSLUSL

Mean = 24.752StdDev = 2.4711USL = 28.5LSL = 21.5Sigma Level = 1.3159Sigma Capability = 1.4164Cpk = .4386Cp = .4721DPM = 158,759N = 100

56

Measures of Quality

The Cpk chart will generate these measures of quality: Cp, Cpk, Sigma level, Sigma

capability, Dpm Cp and Sigma Capability will not

be generated with a one sided specification

Other information regarding the process will be shown: mean and standard deviation

57

What Happens if the Process Distribution is Not Normal?

If the distribution is exponential, the data could be transformed by taking the log of the data. The transformed data can be used for a Cpk chart with a newly scaled specification

The user can take the histogram, impose the specification on the graph and count the percent data outside the specs.

58

Interpret Cpk Results of Normally Distributed Data If the Cpk is 2 or more, the process

is very good and might not need improvement

If the Cp and the Cpk are not the same, the process is not centered. Centering the process performance between the specs involves adjusting the mean of the process. This is typically easier to do that reducing process variance. This will get the team a quick win.

Ask the customer to reconsider the specifications. They might be in a position to relax the specifications

Reduce the variation in the process. This is done by PF/CE/CNX/SOPs.

59

Cpk Concerns

Do not use x bar data for this tool. Using x bars will reduce the standard deviation of the distribution and might fausely indicate a capable process. Instead, us the raw data used to calculate the x bars.

Work to make the process stable before assessing capability. Stability can be assessed with control charts. Stability can be achieved by PF/CE/CNX/SOPs

An adequate amount of data is needed to assess accurate capability

60

Cpk Example for Process Improvements

Cpk Analysis

4.98

4.99

5.01

5.02

5.04

5.05

5.07

5.08 5.1

5.11

5.13

5.14

5.16

5.17

5.19

5.21

5.22

5.24

5.25

5.27

5.28 5.3

5.31

5.33

5.34

5.36

5.37

5.39 5.4

5.42

5.43

5.45

5.46

5.48


Mean = 5.2305StdDev = 0.056434USL = 5.25LSL = 5Sigma Level = .3449Sigma Capability = 2.2150Cpk = .1150Cp = .7383DPM = 365,114N = 149

Cp and Cpk not equal indicating the process is not centered.

A large DPM should alarm the process team

Steps to improve the process: 1. Center the process 2. Ask the customer if they can relax the specifications 3. Reduce the process variance – PF/CE/CNX/SOPs

61

Cpk Improvements by Centering the Process

Cpk Analysis

4.98

4.99

5.01

5.02

5.04

5.05

5.07

5.08 5.1

5.11

5.13

5.14

5.16

5.17

5.19

5.21

5.22

5.24

5.25

5.27

5.28 5.3

5.31

5.33

5.34

5.36

5.37

5.39 5.4

5.42

5.43

5.45

5.46

5.48


Mean = 5.2305StdDev = 0.056434USL = 5.345LSL = 5.11Sigma Level = 2.0282Sigma Capability = 2.0821Cpk = .6761Cp = .6940DPM = 37,612N = 149

Cp and Cpk is similar indicating a centered process

By centering the process, Dpm were reduced from 365,114 to 37,612. Further improvement could be achieved through variance reduction.

62

Measurement System Analysis

An MSA is used to determine the reliability of the performance data. Measurement error should be 10% or less

Since many process decisions are based on performance data, one must ask if that data is reliable.

63

MSA Planning What are the performance metrics and

how are they measured? In an MSA, both repeatability and

reproducibility are determined. To conduct an MSA looking for

differences in operators, the parts measured, SOPs and measurement materials should be constant, only the operators change.

70% of the process variance should be represented in the part measured

A general rule of thumb, measure at least 10 parts twice to meet resolution requirements

Assure the parts are marked blindly so the operators are not aware of the part they are measuring

64

Set up an MSA

First, look at a histogram of the performance metrics. In the example on the next page, there is a huge spread in the data. Upon further investigation, there are three processes going on with this data. A first stage, second stage and third stage of treatment.

65

MSA Set Up Continued

Histogram

0

5

10

15

20

25

30

34.7

to <= 5

0.2

50.2

to <= 6

5.8

65.8

to <= 8

1.3

81.3

to <= 9

6.8

96.8

to <= 1

12.4

112.4

to <= 1

27.9

143.5

to <= 1

59.

159.

to <= 1

74.5

174.5

to <= 1

90.1

190.1

to <= 2

05.6

205.6

to <= 2

21.1

221.1

to <= 2

36.7

Class

# O

bser

vatio

ns


There are three distributions to this data. To determine the Measurement error, three separate MSAs should be conducted. by doing this, you can see if the measurement is reliable in each range of data. You should have samples representing 70% of the process variance for each of the three data sets to conduce each MSA. If all the data were put into one large MSA, the total variance compared to the measurement error might be skewed on the low side.

66

Conduct an MSA

Develop the MSA template with SPC XL

MSA Data Template

Date:Part Type:

USL:LSL:

Operator 1 Operator 2 Operator 3Part # Reference Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2

12345678910

4/22/2003

For Attribute data enter A for Accept and R for Reject

Description:

67

If a known standard is available, place that in the reference column on the template

If specifications are known, use them when building the template

Develop SOPs to conduct the MSA and make sure all involved know and follow them

Do not throw out data Make sure all data is imputed

correctly BEFORE analyzing

68

Analyze the Data

The preferred method to analyze the data is ANOVA. However, if you have only one measurement per part, you cannot use this method.

ANOVA analysis will generate a part to operator interaction and is less sensitive to outliers.

First, is the measurement error (PTOL) 10% or less, if not, which is highest, repeatability or reproducibility? This will point to process improvements. Repeatability problems point to inadequate SOPs. Reproducibility points to some operators performing fine with others are not. What are the differences? How could the SOPs be changed to have all operators perform best?

If customer specifications were used, was the PTOL less than 10%? If the PTOL < 10% but the PTOT > 10%, the measurement is still OK. This point to a capable process and will not suffer from misclassification.

69

A completed Template

MSA Data Template

Date:Part Type:

USL:LSL:

Operator 1 Operator 2 Operator 3Part # Reference Rep 1 Rep 2 Rep 1 Rep 2 Rep 1 Rep 2

1 5 5.1 5.1 5.3 5 5.32 4.9 5.1 4.9 5.2 4.9 4.73 4.5 4.3 4.6 4.9 4.7 54 3.8 4 4 4.3 4.2 3.95 4.9 5.2 4.9 5.2 4.8 4.96 3.9 3.8 4 3.8 3.9 4.27 5.5 5.7 5.6 5.9 5.4 5.68 5 5.3 4.9 5.3 5 5.19 4.5 4.6 4.3 4.6 4.7 4.410 3.5 3.7 3.8 3.4 3.4 3.6

4/22/2003

5.53.5

For Attribute data enter A for Accept and R for Reject

Description:

Customer Specifications are listed

Look over the data making sure it is imputed correctly. Look for decimal placement and such. After checked, the data can be analyzed. No reference was used in this example.

70

The Results Table

MSA ANOVA Method Results

Source Variance Standard Deviation % ContributionTotal Measurement (Gage) 0.03102257 0.17613225 7.18% Repeatability 0.03057639 0.174861056 7.07% Reproducibility 0.00044618 0.021122986 0.10% Operator 0.00044618 0.021122986 0.10% Oper * Part InteractionProduct (Part-to-Part) 0.40126196 0.633452413 92.82%Total 0.43228453 0.657483482 100.00%

USL 5.5LSL 3.5Precision to Tolerance Ratio 0.52839675Precision to Total Ratio 0.26788848Resolution 5.1

BIAS ANALYSISReference Bias

Not Available

Specs are listed here

Both PTOL and PTOT are too high, well over 10% error

Repeatability is the problem

With repeatability the main issue, the overall SOPs should be reviewed. There is no bias analysis due to lack of a reference or standard in this analysis.

71

Operator by Part Analysis

Operator By Part

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

Part #

Mea

sure

men

t

Operator 1Operator 2Operator 3

This graph shows the average measurement of each part by each 0perator. The best result of this graph would be three completely overlying lines indicating they all made the same readings on average.

Here you see where operator #1 had a much different readying than operators 2 and 3.

72

Sigma Total vs. Sigma Product

Sigma Product vs Sigma Total

2.677549554 3.177549554 3.677549554 4.177549554 4.677549554 5.177549554 5.677549554 6.177549554

Measurement

Sigma TotalSigma ProductLSLUSL

With this graph you can see the difference between the Sigma Total and the Sigma Product. When there is a gap on the top aspect of the curve, that illustrates the degree of measurement error. If the measurement system was good, this graph would have one curve with one line superposed over the other. The red lines are the spec limits

A large gap here indicates a large measurement error.

73

Misclassification

Misclassification Due To Measurement Error

2.677549554 3.177549554 3.677549554 4.177549554 4.677549554 5.177549554 5.677549554 6.177549554

Measurement

Sigma TotalLSL Sigma MeasUSL Sigma MeasLSLUSL

dpm Potentially Misclassified = 461,226.805

This graph takes the distribution of the measurement error and places it over the spec area. This example shows that with the large measurement error, over 46.1 % of the product would be misclassified as being in spec.

74

Pareto of Measurement Areas

Part-to-PartRepeatability

Reproducibility

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Z Axis

XAxis Category

Measurement System Variance Components

This is the variability in the process itself. This is supposed to be The largest bar.

The repeatability is much higher Than reproducibility, indicating Repeatability is the problem

75

X Bar Chart MSA- Xbar Chart

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Part Number

Part

Ave

rage

Operator 1Operator 2Operator 3UCL = 5.101Center = 4.65LCL = 4.199

In this graph the control chart limits are established from +/- 3 standard deviations of the measurement error. The smaller the limits, the better the measurement process is. The rule of thumb is to see at least 50% of the measurements outside the control chart limits.

76

Range Chart MSA- Range Chart

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

Part Number

Part

Ran

ge

Operator 1Operator 2Operator 3UCL = .784Center = .24LCL = .

The Range charts shows the range of measurements for each operator. The control chart limits are based on +/- 3 standard deviations of the overall range. The lower the range the better, so operators with data near 0 would be the best.

77

MSA Conclusions Data should not be used to make

process decisions until the measurement error is known. If the measurement error is < 10%, the measurement system is fine. If the error is > 10%, the system should be improved.

Spend enough planning time as necessary to plan and conduct an MSA. The better the experimental discipline, the more accurate the results will be.

78

Hypothesis Testing

This tool is used to determine if a process has changed, either in mean, standard deviation, both or neither

This is a paired test, so we look pairing of various data sets to see if they are significantly different from one another.

The rule of thumb for significance is a p value ≤ 0.05, this would indicate less than a 5% chance of falsely stated the data sets are different.

79

Conduct the Hypothesis Test

Change the process. Before and after Six Sigma, temperature high and low, angle 45◦ and 90◦ , etc.

Collect the data in rows or columns.

Use SPC XL, Analysis Tools, T test and/or F test. T test will look for differences in the means, F test in the standard deviations

80

Sample Data

Statapult Launching Data:

Highlight each

column or row, and run a T test and/or F test

Group 1Before After

130 121.5133 122136 119138 119.5134 119119 118.5116 120110 116.557 117

104 120113 118112 118.5117 119110 121110 116115 118124 119121 121142144146

81

T-test and F-test Results

t Test Analysis (Mean)P-value = 0.755

The results below represent the p-values from a two sample, 2-tailed t-test. This means that the probability of falsely concluding the alternative hypothesis is the value shown (where the alternate hypothesis is that the means are not equal). Another way of interpreting this result is that you can have (1-pvalue)*100% confidence that the means are not equal.

F Test Analysis (Std Dev)P-value = 0.0

The results below represent the p-values from a 2 sample F-test. This means the probability of falsely concluding the alternative hypothesis is the value shown (where the alternate hypothesis is that the variances are NOT equal). Another way of interpreting this result is that you can have (1-pvalue)*100% confidence that the variances are not equal.

T-test is NOT significant, the P-value > 0.05. Conclusion, the SOPs On launching the Statapult did not affect the mean of the process

F-test IS significant, the P-value > 0.05. Conclusion, the SOPs on launching the Statapult does affect the standard deviation of the process

82

How to Use Hypothesis Test Results in a Project Report

The T-test and F-test results show only significance, not the process means and standard deviations

The means and standard deviations should be calculated then cut and pasted into a document along with the hypothesis test results explaining what the team was trying to prove

The mean and standard deviation can be obtained by running a summary stats of the data – see next page

The results summary might look like the following example

83

Summary Stats

Here is the data summary before and after PF/CE/CNX/SOPs on launching the statapults

Before AfterCount 21 18Mean 120.52 119.08Median 119 119Mode 110 119Max 146 122Min 57 116Range 89 6Std Dev (Pop) 18.87 1.62Std Dev (Sample) 19.34 1.66Variance (Pop) 356.25 2.62Variance (Sample) 374.06 2.77Skewness -1.62 -0.06Kurtosis 4.97 -0.43

95% Conf. Interval for MeanUpper Limit 129.33 119.91Lower Limit 111.72 118.26

99% Conf. Interval for MeanUpper Limit 132.53 120.22Lower Limit 108.52 117.95

84

Alternative Hypothesis Statement

t test = looking for a difference in means

t Test Analysis (Mean)P-value = 0.000088

Conclusion: Changing the machine setting DOES effect the average fill weight means.Increasing machine setting, increases fill weight

f test = looking for a difference in standard deviation

F Test Analysis (Std Dev)P-value = 0.004235

Conclusion: Changing the machine setting DOES effect the average fill weight standard deviationsIncreasing machine setting from 5.2 to 5.25 reducing standard deviation

These lots (data sets) of fill weights, run at different machine settings, are different both in Mean and Standard Deviation

Hypothesis Testing - Summary of Results

If the lots are signifantly different, it could be concluded that machine settings effect fill weight

Lot Number Mean Machine Setting70907100

5.26685.2075

5.255.2

There is a (1-p value) or 99.9% statistical confedence that there is a difference between lots

Note: To determine optimal settings, regression analysis might be needed as well as confirmation of results

Lot Number Standard Deviation Machine Setting

There is a (1-p value) or 99.6% statistical confedence that there is a difference between lots

Note: To determine optimal settings, regression analysis might be needed as well as confirmation of results

7090 0.0364 5.257100 0.0644 5.2

The results below represent the p-values from a 2 sample F-test. This means the probability of falsely concluding the alternative hypothesis is the value shown (where the alternate hypothesis is that the variances are NOT equal). Another way of interpreting this result is that you can have (1-pvalue)*100% confidence that the variances are not equal.

The results below represent the p-values from a 2 sample t-test. This means that the probability of falsely concluding the alternative hypothesis is the value shown (where the alternate hypothesis is that the means are not equal). Another way of interpreting this result is that you can have (1-pvalue)*100% confidence that the means are not equal.

σ7090 ? σ7100 μ7100 ? μ7090

85

Hypothesis Test Concerns Sometimes the process did

change, but not enough “after” data is there to see a P-value ≤ 0.05. Gather more data, test again and see if there is a significant shift.

Do not use Xbar data for this analysis. Use the raw data it took to make the Xbars with. This would apply with any form of average listed data.

T-test and F-test is for continuous data only. The next slide explains how to hypothesis testing with attribute data sets

86

Test of Proportions

Used to perform hypothesis testing on attribute data sets.

More data is typically needed to make good decisions with this tool

Make a process change and look for process results. Change speed, monitor failures.

Use SPC XL, Analysis Tools, Test of Proportions

87

Results

User defined parameters

Number Defective Group #1 (x1) 14Size of Sample #1 (n1) 54Number Defective Group #2 (x2) 14Size of Sample #2 (n2) 77

Proportion Sample #1 (p1) 0.25926Proportion Sample #2 (p2) 0.18182p-value 0.28721

Test of Proportions

Results

SPC XL is Copyright (C) 1999 Digital Computations, Inc. and Air Academy Associates, LLC. All Rights Reserved. Unauthorized duplication prohibited by law.

Measure the defects and the total number in each sample set, type in the sample size first, then the defects

Proportion of defects for each sample is shown.

The P-value is shown here. For a significant shift in the Proportion of defects, the P-value should be ≤ 0.05. The results show the proportion of group 1 is 0.25926, the Proportion of group #2 is 0.18182. Most would say there IS A significant difference. But, the P-value is not close to ≤ 0.05. On the next page, the sample size was doubled With each data set, keeping the proportion the same. See results next page.

88

Results Continued

User defined parameters

Number Defective Group #1 (x1) 42Size of Sample #1 (n1) 162Number Defective Group #2 (x2) 42Size of Sample #2 (n2) 231

Proportion Sample #1 (p1) 0.25926Proportion Sample #2 (p2) 0.18182p-value 0.06528

Test of Proportions

Results

SPC XL is Copyright (C) 1999 Digital Computations, Inc. and Air Academy Associates, LLC. All Rights Reserved. Unauthorized duplication prohibited by law.

These are the same proportions as before. The sample size is triple in size.

With the sample size tripled, the P-value points to a number almost meeting the criteria of being significantly different (P-value ≤ 0.05). The take away is, in using attribute data, more data is often needed to prove significance.

89

Control Chart Basics

Control Charts are used to determine process stability

Control Charts are run charts with added features:

Upper and Lower Control Chart limits: +/- 3 standard deviations of the process

Centerline: the mean of the process

Control Charts could be used to track output as well as input variables

90

Control Chart Types

For continuous data sets Xbar R (plotting averages of data sub

sets and the range within those subsets)

Xbar S (plotting averages of data sub sets and the standard deviation of those subsets)

IMR (individuals moving range: plotting one data set instead of an average of a subgroup, range is established by the difference of one point from the last point plotted

For attribute data sets: P-Chart (plotting proportions of

defectives) C-Chart (plotting counts of defects)

91

Spreadsheets for Data Collection For continuous data sets, it is best

to sample in sub sets, such as 4 random samples daily. The spreadsheet to capture this might look like this

Date Sample 1 Sample 2 Sample 3 Sample 4 Xbar1/1/2003 59.92 48.90 53.88 46.48 52.291/2/2003 56.88 44.19 55.49 57.39 53.491/3/2003 46.70 42.21 48.08 39.31 44.071/4/2003 43.36 45.81 43.11 47.08 44.841/5/2003 48.77 43.77 40.84 42.90 44.071/6/2003 41.88 47.13 43.73 42.50 43.811/7/2003 52.82 47.07 51.72 51.21 50.711/8/2003 46.13 46.87 43.53 48.64 46.291/9/2003 50.34 43.42 48.56 42.03 46.09

1/10/2003 50.40 42.22 52.18 41.93 46.681/11/2003 53.52 41.51 45.62 53.81 48.621/12/2003 50.68 50.27 46.06 54.71 50.431/13/2003 52.16 51.95 57.29 56.63 54.511/14/2003 48.37 61.60 50.95 51.72 53.161/15/2003 56.05 51.03 44.48 48.23 49.951/16/2003 59.15 55.08 56.99 53.54 56.191/17/2003 44.53 59.57 48.52 48.70 50.331/18/2003 53.15 49.86 48.17 49.40 50.141/19/2003 49.89 53.25 52.31 54.64 52.521/20/2003 55.94 44.27 48.51 47.63 49.091/21/2003 51.79 47.87 47.65 51.06 49.601/22/2003 50.66 55.73 55.95 50.13 53.111/23/2003 40.43 48.95 52.56 48.14 47.521/24/2003 48.23 54.15 46.58 54.91 50.97

Data can be collected In column or rows, This example shows Columns.

92

Histograms by Raw Data vs. Xbar Data Here is a histogram using the raw

data from the previous example Histogram - Raw Data

0

5

10

15

20

39.31 to<=

41.54

41.54 to<=

43.76

43.76 to<=

45.99

45.99 to<=

48.22

48.22 to<=

50.45

50.45 to<=

52.68

52.68 to<=

54.91

54.91 to<=

57.14

57.14 to<=

59.37

59.37 to<= 61.6

Class

# O

bser

vatio

ns


The standard deviation of this process is 5. the distribution is normal. Does this mean the process is stable? We can only determine that by constructing a control chart looking at the data over time.

93

Histograms Continued

Here is a histogram of the XBar data – using the averages of the subgroups

Histogram - XBar Data

0

1

2

3

4

5

6

7

8

9

43.81 to <=46.29

46.29 to <=48.76

48.76 to <=51.24

51.24 to <=53.72

53.72 to <=56.19

Class

# O

bser

vatio

ns


Note the standard deviation of this distribution is 3.5 This is much lower than the raw data due to the central limit theorem. The means are the same, but the standard deviation of the Xbar is less. This is the reason NOT to use Xbars with Cpk analysis, it gives a false reading on the process standard deviation.

94

Construction of the Control Chart The SPC XL Control Chart Wizard can

be used to help determine what control chart to use and build a data collection template. You can cut and paste data from an existing spreadsheet into this template. You will not need to paste in Xbar information, just the raw data.

After the data is either in the SPC XL template or on your own spreadsheet, go into control chart menu, choose the chart you want, in the example with the previous spreadsheet, XBar R is the choice, highlight data if using your own spreadsheet, just click if using the SPC XL template and the chart will appear.

95

XBar R Chart

Here is the charts generated on a “stacked” format, one on top of the other

Xbar Chart

UCL=55.764

LCL=43.276

CEN=49.52

0

10

20

30

40

50

60

R Chart

UCL=19.545

LCL=0.0

CEN=8.565

0

5

10

15

20

25

1/1/200

3

1/2/200

3

1/3/200

3

1/4/200

3

1/5/200

3

1/6/200

3

1/7/200

3

1/8/200

3

1/9/200

3

1/10/2

003

1/11/2

003

1/12/2

003

1/13/2

003

1/14/2

003

1/15/2

003

1/16/2

003

1/17/2

003

1/18/2

003

1/19/2

003

1/20/2

003

1/21/2

003

1/22/2

003

1/23/2

003

1/24/2

003

The top chart is the Xbar the bottom one is the range chart

96

XBar Chart

Xbar Chart

UCL=55.764

LCL=43.276

CEN=49.52

0

10

20

30

40

50

60

Dates for the data points are listed

Red points indicate out of control symptoms. To find out what symptom they are, pull down the menu called “Out of Control” located directly above the chart. Choose a symptom and the chart will be reconstructed showing the points in red for only that symptom. Never print out only one symptom and show to others as they will assume only that symptom exists. This feature is for you to look at symptoms one by one.

The goal of the XBar chart would be to have the mean of the process match the target from the customer with no out of control

symptoms. Small control chart limits indicate low process variability and better process performance vs. customer specifications.

These charts look at BETWEEN group variability.

97

Range Chart

R Chart

UCL=19.545

LCL=0.0

CEN=8.565

0

5

10

15

20

25

1/1/200

3

1/2/200

3

1/3/200

3

1/4/200

3

1/5/200

3

1/6/200

3

1/7/200

3

1/8/200

3

1/9/200

3

1/10/2

003

1/11/2

003

1/12/2

003

1/13/2

003

1/14/2

003

1/15/2

003

1/16/2

003

1/17/2

003

1/18/2

003

1/19/2

003

1/20/2

003

1/21/2

003

1/22/2

003

1/23/2

003

1/24/2

003

The range chart is plotting the range of the sample sets. A range chart control limits are +/- 3 standard deviations of the overall range. The closer to zero the points are the less variability in the sample. This chart has no RED points indicating the range is stable in this process This graph looks at WITHIN group variability.

Overall, a good range chart is one indicating points near zero with small control limits.

98

Correlation Study, Scatter Plot Example

Documents

Lean Six Sigma Mentor Guide