7 SSGB Amity BSI Stability Control Charts

8/9/2019 7 SSGB Amity BSI Stability Control Charts

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Module-7Control Charts


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Control Charts Learning Objectives

At the end of this section, delegates will: Understand how control charts can show if a

process is stable

Generate and interpret control charts for variableand attribute data

Understand the role of control charts within the

DMAIC improvement process


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Control Charts Agenda1. Introduction to Statistical Process Control, SPC

2. Control Limits

3. Individual and Moving Range Chart

4. Workshop on Control Charts

5. Defective (Binomial) p-Chart

6. Defects (Poisson) u-Chart

7. Workshop on Attribute Control Charts

8. Uses of Control Charts

9. Summary


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4

What is Statistical Process Control?

Statistical Process Control is a method ofmonitoring and detecting changes inprocesses.

SPC uses an advanced form of Time Seriesplots.

SPC provides an easy method of deciding ifa process has changed (in other words, is

the process in-control?).


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We Need Ways of Interpreting Data

Everyday we are flooded by data and we are

forced to make decisions:

Calls handled decreases by 4%

UK trade deficit rises by 5 billion

Company Xs earnings are $240Million less

than the previous quarter

Should we take action ?


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Leave it alone -it aint broke

Pain &suffering

Pain &suffering

Lower CustomerRequirement

Upper CustomerRequirement

How do we manage data historically?

This Method

Tells you where you are in relation to customers needs It will NOT tell you how you got there or what to do next

Means that pressure to achieve customer requirements will cause you to:

Actually Fix The Process

Sabotage The Process

Sabotage The Data (Integrity)


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What do Control Charts detect?

Control Charts detect changes in a process.

All processes change slightly, but process control

aims to detect statistically significant changes that

are not just random variation.

Processes can change in several different ways

the process average can change

the process variation can change

the process may contain one-off events


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Process Control

Process control refersto the evaluation ofprocess stability overtime

Process Capabilityrefers to the

evaluation of how wella process meetsspecifications

LSL USL

0 5 10 15 20 25

Time

UCL

LCL


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Why would a Process be Incapable?There are a number of reasons why aprocess may not be capable of meeting

specification:1. The specification is incorrect!

2. Excessive variation

3. The process is not on target

4. A combination of the above

5. Errors are being made

6. The process is not stable


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The specification is incorrect This issue was discussed during the

Customer Focus section of this course

If specifications are not clearly related tocustomer requirements, then it is always agood idea to challenge the specificationbefore attempting to improve the process


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Excessive variationUpper

Specification

Limit

Lower

Specification

LimitTarget

Excessive variation means that we have avariation reduction issue

We will need to understand which process inputsare causing the variation in the process output


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The process is not on targetUpper

Specification

Limit

Lower

Specification

LimitTarget

In this situation we have a process targeting issue

We will need to understand which process inputs

are causing the process to be off-target

This situation is sometimes simple to solve!


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Excessive variation and not on targetUpper

Specification

Limit

LowerSpecification

LimitTarget

In this situation we have both excessive variationand a process targeting issue

We will need to understand which process inputsare causing the excessive variation and whichare causing the process to be off-target


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Errors are being madeUpper

Specification

Limit

Lower

Specification

LimitTarget

A situation such as this might indicate that errors arebeing made which result in occasional excursions

outside of the specification

This is often an indication of a mistake proofing issue


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The process is not stable

A situation such as this is an indication that the processis unstable

Whenever this situation is encountered in a DMAICactivity, then the reason(s) for the instability mustbefound and removed before assessing process capability

Upper

Specification

Limit

Lower

Specification

Limit Target

Last week

This week

Next week?


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The process is not stableUpper

Specification

Limit

LowerSpecification

LimitTarget

Last week

This week

Next

week?

Causes of process instability are sometimes referred

to as special causes

Removing these special causes may result in theprocess becoming capable of consistently meeting the

target


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Unstable Process

Special

causes ofvariation arepresent

Time

TotalVariation

Target


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Stable Process

Time

Target

TotalVariation

Only Common

causes ofvariation arepresent


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Capable Process

Time

Spec Limits

CAPABLE

NOT

CAPABLE Process is Stable but

Process is not Capable

Process is Stable andProcess is Capable

Management Action(DMAIC) to reducecommon cause variation


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Control Charts test for Stability(Control Chart of Average)

0 5 10 15 20 25

Time

1.26

1.27

1.28

1.29

1.3

Proce

ssAverage

Upper Control Limit

Lower Control Limit


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Transactional Improvement Process

Select Project

Define Project

Objective

Form the Team

Map the Process

Identify Customer

Requirements

Identify Priorities

Update Project File

Select Project

Define Project

Objective

Form the Team

Map the Process

Identify Customer

Requirements

Identify Priorities

Update Project File

Control Critical xs

Monitor ys

Validate ControlPlan

Identify furtheropportunities

Close Project

15 20 25 30 35

LSL USL

Phase Review

1 5 10 15 20

10.2

10.0

9.8

9.6

Upper Control Limit

Lower Control Limit

y

Phase Review

Develop DetailedProcess Maps

Identify CriticalProcess Steps (x s)by looking for:

Process Bottlenecks

Rework / Repetition Non-value Added

Steps

Sources of Error /Mistake

Map the IdealProcess

Identify gapsbetween current andideal

START

PROCESSSTEPS

DECISION

STOP

Phase Review

Brainstorm PotentialImprovement Strategies

Select ImprovementStrategy

Plan and ImplementPilot

Verify Improvement

Implement

Countermeasures

Criteria A B C D

Time + s - +

Cost + - + s

Service - + - +

Etc s s - +

15 20 25 30 35

LSL USL

Phase Review

Analyse Improve ControlMeasureDefine

Phase Review

Define

Define Measures (y s)

Check Data Integrity

Determine ProcessStability

Determine ProcessCapability

Set Targets forMeasures

15 20 25 30 35

LSL USL

15 20 25 30 35

LSL USL

Phase Review

1 5 10 15 20

10.2

10.0

9.8

9.6

Upper Control Limit

Lower Control Limit

y

Phase Review



Process Bottlenecks

Rework / Repetition Non-value Added

Steps



Identify gapsbetween current andideal

START

PROCESSSTEPS

DECISION

STOP

Phase Review




Verify Improvement

Implement

Countermeasures

Criteria A B C D

Time + s - +

Cost + - + s

Service - + - +

Etc s s - +

15 20 25 30 35

LSL USL

Phase Review


Phase Review

Define







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Role of Control ChartsMeasure Phase:

used during capability studies to assess process stability

Improve Phase:

used to establish if the modified, improved process is stable

Control Phase

used to control critical process input variables (xs) in order to

reduce variability in process outputs (ys)

used to monitor process outputs (ys) on an ongoing basis to

ensure that the process remains in control


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Control ChartsVariable

Data

NoSubgroups

Subgroupsn = 2-9

Subgroupsn > 9

Individuals &Moving Range

Chart

X Bar & RChart

X Bar & sChart

AttributeData

Defect Data(Poisson)

Defective Data(Binomial)

VaryingSubgroup

Size

ConstantSubgroup

Size

VaryingSubgroup

Size

ConstantSubgroup

Size

u Chart c Chart p Chart np Chart


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What do Control Charts tell us?

Is the process stable? Should we be taking action?

Are there any special causes? What is the average process output? What is the variability?

0 5 10 15 20 25

Subgroup

1.26

1.27

1.28

1.29

1.3

X-bar


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Control Limits


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Total Variation

TotalVariation

Within SubgroupVariation

Between SubgroupVariation


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Control Limits Use Within SubgroupVariation

The total variation and Within Subgroup variation arethe same only if the process is stable

The Within Subgroup variation is an estimate of what

the total variation would be if the process werestable

The Within Subgroup variation is used to calculatethe control limits since these limits represent the

range of values expected for a stable process


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Controls Limits

Controls limits are always:

Average 3 Standard DeviationsWhere the average and standard deviation are the

average and standard deviation of whatever data

is plotted:

99.7%99.7%99.7%99.7%

4444 3333 2222 1111 +1+1+1+1 +2+2+2+2 +3+3+3+3 +4+4+4+40


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Control LimitsUpper Control Limit

Lower Control Limit

Control Limits are statistical boundaries which tell us whether ornot the process is stable

Based on the normal distribution, 99.7% of the points plot withinthe control limits if the process is stable

The chance of a point outside the control limits, falsely indicatingthe process is unstable, is only 0.3% or 1 in 370


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Individuals Control Chart


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Individuals Control Chart Used when only a single observation per time period

(subgroup): Monthly reporting data:

On-time shipments, In-process Inventory, Complaints, etc.

Rare events

Sales

Stock Price

Inventory Levels

Customer Response Time

Lost Time Accidents

Complaints Anything that can be measured and varies


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Within Subgroup Variation The best estimate is obtained by taking the differences between

consecutive samples i.e. the Moving Range (MR).

We can use the the average MR, R, or the median MR, R

When using R the Short Term standard deviation is estimated by:

1.128

R

d

R

2

Within ==

When using R the standard deviation is estimated by:

0.954

R~

d

R~

4

Within ==


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Table of Constants for ImR chartsSample size d 2 d 3 d 4 D 3 D 4 D 5 D 6 E 2 E 5

2

3

456

7

8

9

10

0.853

0.888

0.8800.8640.848

0.833

0.820

0.808

0.797

0.954

1.588

1.9782.2572.472

2.645

2.791

2.915

3.024

3.267

2.574

2.2822.1142.004

1.924

1.864

1.816

1.777

2.970

3.078

3.865

2.744

2.376

0

0

00 2.179

0.209

1.075

1.029

0.9921.809 0.975

0

0.055

0.119

0.168

2.054

1.967

1.901

1.850

1.128

1.693

2.0592.3262.534

2.704

2.847

0

0

000

0.076

0.136

0.184

0.223

2.660

1.772

1.4571.2901.184

1.109

1.054

1.010

3.145

1.889

1.5171.3291.214

1.134

We would generally calculate the differences betweenconsecutive samples, which corresponds to a samplesize of 2 in this table.Minitab will calculate the control chart limits for us!


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Control LimitsThe controls limits for the average, based on R are:

R2.66XREX1.128

R3XdR3X3X 2

2

Within ====

The controls limits for the range, based on R are:

R3.267RDUCL

0R0RDLCL

4Range

3Range

==

===


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Control Limits

R~3.145XR~EX0.953

R

~

3XdR

~

3X3X 54

Within ====

~The controls limits for the average, based on R are:

The controls limits for the range, based on R are:~

R~

3.865R~

DUCL

0R~

0R~

DLCL

6Range

5Range

==

===


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R Versus R Some of the differences may be contaminated by

shifts in the mean (special Causes).

R, the median MR, is more robust to thiscontamination so is generally preferred.

When many of the differences are zero, it mightbe necessary to use R instead.

A conversion factor can be developed:

182.1R~

954.0

128.1R~

R

954.0

R~

128.1

Rwithin

========

========

~


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Call Out TimeSample Number Call Out Time

1

2

3

4

5

6

7

8

9

10

1112

13

14

15

16

1718

19

20

5.35

3.28

1.07

1.06

4.29

3.23

5.40

6.42

3.25

8.55

4.267.48

5.35

2.14

4.24

6.44

3.219.66

4.28

5.33


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Call Out TimeSample Number Call out Time

1

2

3

4

56

7

8

9

10

11

12

1314

15

16

17

18

19

20

Difference

5.35

3.28

1.07

1.06

4.293.23

5.40

6.42

3.25

8.55

4.26

7.48

5.352.14

4.24

6.44

3.21

9.66

4.28

5.33

2.07

2.21

0.01

3.231.06

2.07

1.02

5.30

4.29

3.22

2.13

3.21

2.10

2.20

3.23

6.45

5.38

1.05

2.21

4.71 2.82

Average Average Difference

Ordered

0.01

1.02

1.05

1.062.07

2.07

2.10

2.13

2.20

2.21

2.21

3.21

3.22

3.23

3.23

4.29

5.30

5.38

6.45

Median


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Individuals chart - MinitabOpen Worksheet: Call Out Time

Stat>Control Charts>Variables Charts for Individuals>I-MR

Select Variable: Call Out Time

Click I-MR Options

Click Estimate select Median moving range

Click Tests - select 1 point > 3 standard deviations from center line


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IMR Chart Minitab (using R)

Observation

Individual

Value

2018161412108642

12

8

4

0

_X=4.71

UC L=11.66

LCL=-2.24

Observation

MovingRange

2018161412108642

8

6

4

2

0

__MR=2.613

UC L=8.538

LC L=0

I-MR Chart of Call out Time

613.2182.1R~

R

21.2R~

Median

========

====


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Lognormal and other non normal data

When dealing with lognormal and other non-normal data

we need to be cautious.

X-bar and Range charts will be acceptable for most non-normal data with a sub-group size of 5 or larger.

I-MR charts may give false indications of instability.


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Workshop Individuals Control ChartOpen Minitab worksheet: PAYMENT TIMES.MTW

Use Minitab to create:

Individuals and Moving Range chart

Use the Median with a moving range of 2

Assess the stability of the process

What would you want to do next?

Prepare a short report of your findings


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Attribute Control Charts

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Control Charts for Defective Items (Binomial)

A p-Chart is used to track the

proportion defective The p-Chart is constructed using data

on the number of defectives fromvarying (or fixed) subgroup sizes

The data opposite shows the numberof defective orders from randomsamples taken over 10 working days

The subgroups should be large

enough to contain 5 or more defectiveitems

Sample

Number

Defectives

(np)

Subgroup

Size

1 8 96

2 12 104

3 13 99

4 8 100

5 7 103

6 13 110

7 6 97

8 7 88

9 10 11110 8 105

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Control Charts for Defective Items (Binomial)

The p-chart must satisfy the requirements for the Binomial

Distribution. The particular requirements affecting the p-chart are:

1. Each unit (e.g., transaction, invoice, ) can only be classifiedas pass or fail

2. If one unit (e.g., transaction, invoice, ) fails, then the chance

of the next unit failing is not affected

If the Binomial distribution is not appropriate then it may bepossible to use the Individuals control chart already discussed

Since we are charting defective items this chart should not be

used when the number of defectives is zero or there are a large

number of zeros (80-90%)

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P Chart Construction

Sample

Number

Defectives

(np)

Subgroup

Size (n)

Proportion

Defective

(p)

Average

Proportion

Defective

(pbar) 3 Sigma UCL(p) LCL(p)

1 8 96 0.083 0.091 0.088062 0.179062 0.002938

2 12 104 0.115 0.091 0.084608 0.175608 0.006392

3 13 99 0.131 0.091 0.086718 0.177718 0.0042824 8 100 0.08 0.091 0.086283 0.177283 0.004717

5 7 103 0.068 0.091 0.085017 0.176017 0.005983

6 13 110 0.118 0.091 0.082268 0.173268 0.008732

7 6 97 0.062 0.091 0.087607 0.178607 0.003393

8 7 88 0.08 0.091 0.091978 0.182978 -0.00098

9 10 111 0.091 0.091 0.081896 0.172896 0.009104

10 8 105 0.076 0.091 0.084204 0.175204 0.006796

Total 92 1013

n

)p-(1p3-p3pLCL,

n

)p-(1p3p3pUCL

n

)p-(1p0.091,

1013

92

n

npp

pp ==+=+=

====

47

P Ch Mi i b


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P Chart - Minitab

Open Worksheet P Chart

Stat>Control Charts>Attributes Charts>P

Variable: DefectivesSubgroups in: Subgroup Size Click P Chart Options

Click Tests select 1 point > 3 standard deviations from center line

Sample

Proportion

10987654321

0.20

0.15

0.10

0.05

0.00

_P=0.0908

UCL=0.1749

LCL=0.0067

P Chart of Defectives

Tests performed with unequal sample sizes

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Control Charts for Defects (Poisson)

A u Chart is used to track the number of

defects per unit (e.g., transaction,invoice, ).

The u chart is constructed using data onthe number of defects from varying

subgroup sizes (number of units).

The data opposite shows the number ofdefects in the given number of invoicessampled randomly from 10 weeks of

invoicing.

Sample

Number

Defects

c

Invoices

n

1 7 40

2 4 45

3 8 33

4 5 40

5 3 396 8 46

7 5 27

8 7 45

9 9 38

10 4 39

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Control Charts for Defects (Poisson)

Since the u-chart is based on the PoissonDistribution, the data should be tested to see if it fitsthe Poisson distribution (e.g., some count datasuch as complaints and late shipments may not fitthe Poisson distribution)

If the Poisson distribution does not fit then it may be

possible to use the Individuals control chart alreadydiscussed

Since we are charting defects, this chart should notbe used when the number of defects is zero or thereare a large number of zeros (80-90%)

50

C C


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U Chart - ConstructionSampleNumber

Defectsc

Invoicesn

DPUu u bar LCL(u) UCL(u)

1 7 40 0.175 0.153 0 0.34

2 4 45 0.089 0.153 0 0.328

3 8 33 0.242 0.153 0 0.307

4 5 40 0.125 0.153 0 0.339

5 3 39 0.077 0.153 0 0.341

6 8 46 0.174 0.153 0 0.326

7 5 27 0.185 0.153 0 0.378

8 7 45 0.156 0.153 0 0.327

9 9 38 0.237 0.153 0 0.343

10 4 39 0.103 0.153 0 0.341Total 60 392 0.153

n

u3u3uLCL,

n

u3u3uUCL

u0.153,392

60

n

cu

uu ========++++====++++====

================

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U Chart Minitab


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U Chart - Minitab

Open Worksheet: U Chart

Stat>Control Charts>Attributes Charts>U

Variable: Defects Subgroups in: UnitsClick U Chart Options

Click Tests select 1 point > 3 standard deviations from center line

Sample

SampleCountPerUnit

10987654321

0.4

0.3

0.2

0.1

0.0

_U=0.1531

UCL=0.3410

LCL=0

U Chart of Defects

Tests performed with unequal sample sizes

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Workshop - Attributes Control Chart Using the packets of sweets provided (assume

that each packet has been taken from a different

batch of production over the last few days): Randomly select 20 sweets from each packet

Inspect the sweets for two types of defect-

Badly mis-shaped/damaged sweet

Missing or poorly printed logo

Using Minitab, assess the stability of the process Prepare a short report of your findings


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Uses of Control Charts

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Control Charts

Variable

Data

No

Subgroups

Subgroups

n = 2-9

Subgroups

n > 9

Individuals &Moving Range

Chart

X Bar & R

Chart

X Bar & s

Chart

Attribute

Data

Defect Data

(Poisson)

Defective Data

(Binomial)

Varying

Subgroup

Size

Constant

Subgroup

Size

Varying

Subgroup

Size

Constant

Subgroup

Size

u Chart c Chart p Chart np Chart

55


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Improvement Control charts are one of many variation reduction

tools

Controls charts detect change of the output variable

(y)

The output changes because a critical input variable(x) has changed

Control charts provide clues that can help to identify

these critical inputs (xs)

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Clues to Discovering Critical xs When did the change occur?

What patterns are emerging? Shifts

Gradual or Sudden?

Trends Increasing or Decreasing?

Unusual patterns or cycles?

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Identification of Critical xs To determine the critical x, i.e., the input causing

the shift, we need to consider:

Delayed detection

Multiple inputs causing shifts

Lack of information on inputs

We can also use screening experiments, scatter

diagrams, to determine critical xs

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Transmission of Variation, y = f(x) Control charts can help to discover critical xs that

are causing the process to shift

Tighter control of these critical xs will make the

process more stable

OUTPUT

INPUT

Relationship BetweenInput and Output

Variation of Input

TransmittedVariation

59



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Select Project

Define Project

Objective

Form the Team

Map the Process

Identify CustomerRequirements

Identify Priorities

Update Project File

Select Project

Define Project

Objective

Form the Team

Map the Process

Identify CustomerRequirements

Identify Priorities

Update Project File

Control Critical xs

Monitor ys

Validate ControlPlan

Identify furtheropportunities

Close Project

15 20 25 30 35

LSL USL

Phase Review

1 5 10 15 20

10.2

10.0

9.8

9.6

Upper Control Limit

Lower Control Limit

y

Phase Review



Process Bottlenecks

Rework / Repetition

Non-value AddedSteps



Identify gaps

between current andideal

START

PROCESSSTEPS

DECISION

STOP

Phase Review




Verify Improvement

ImplementCountermeasures

Criteria A B C DTime + s - +

Cost + - + s

Service - + - +

Etc s s - +

15 20 25 30 35

LSL USL

Phase Review


Phase Review

Define






15 20 25 30 35

LSL USL

15 20 25 30 35

LSL USL

Phase Review

1 5 10 15 20

10.2

10.0

9.8

9.6

Upper Control Limit

Lower Control Limit

y

Phase Review



Process Bottlenecks

Rework / Repetition

Non-value AddedSteps



Identify gaps

between current andideal

START

PROCESSSTEPS

DECISION

STOP

Phase Review




Verify Improvement

ImplementCountermeasures

Criteria A B C DTime + s - +

Cost + - + s

Service - + - +

Etc s s - +

15 20 25 30 35

LSL USL

Phase Review


Phase Review

Define






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Control Charts - Summary Charts can be constructed for variable or attribute data

I-MR Charts should always be considered for attribute data

Control Charts are used during capability studies to

determine process stability

Real-Time control charts are used to detect shifts so that

causes of shifts can be identified and eliminated

Should be used to control critical xs (process input

variables) in order to reduce variability in process outputs

(ys).

Used to monitor ys on an ongoing basis to ensure that theprocess remains in control.

Documents

7 SSGB Amity BSI Stability Control Charts