8 ssgb amity bsi capability

8/9/2019 8 SSGB Amity BSI Capability

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Module-8

Process Capability



At the end of this section delegates will be able to:

• Recognise the difference between process controland process capability

• Carry out capability studies on variable and

attribute data• Assess and interpret the data from capability

studies

• Convert data from capability studies into DPM orCpk values

Process Capability Learning Objectives



1. Process Control v Process Capability

2. Process Capability – Variable Data3. Capability Study – 6 steps

4. Capability Study – Minitab

5. Workshop6. Process Capability – Non-Normal Data

7. Process Capability – Attribute Data

8. Summary

Process Capability Agenda



Process Control

• Process control refers tothe evaluation of processstability over time

• Process Capability refersto the evaluation of how

well a process meetsspecifications

LSL USL

0 5 10 15 20 25

Time

UCL

LCL



15 20 25 30 35

LSL USL

Define Measures (y’s)

Check Data Integrity

Determine ProcessStability

Determine ProcessCapability

Set Targets forMeasures

Phase Review

Control Critical x’s

Monitor y’s

Validate ControlPlan

Identify furtheropportunities

Close Project

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 AddedSteps

– Sources of Error /Mistake

Map the Ideal

Process

Identify gapsbetween current andideal

START

PROCESS

STEPS

DECISION

STOP

Phase Review

Brainstorm PotentialImprovement Strategies

Select ImprovementStrategy

Plan and ImplementPilot

Verify Improvement

ImplementCountermeasures

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 Select Project

Define Project

Objective

Form the Team

Map the Process

Identify CustomerRequirements

Identify Priorities

Update Project File

Phase Review

Define

Six Sigma Transactional Improvement Process



Process Capability – Variable Data



“Special” causesof variation arepresent

T i m e

TotalVariation

Target

Unstable Process



T i m e

Target

TotalVariation

Only “Common”causes of variationare present

Stable Process



T i m

e

Spec Limits

CAPABLE

NOTCAPABLE

Process is Stable butProcess is not Capable

Process is Stable andProcess is Capable

Capable Process



• Defined as:

• USL-LSL represents the width of the spec

• 6σσσσWithin represents width of process (±3σσσσ)

−−−−≈≈≈≈

−−−−====

2

p

d

R6

LSLUSL

6σσσσWithin

LSLUSLC

Process Capability, Cp Index



LSL

USL

Cp = 0.5 Cp = 1 Cp = 2Cp = 1.5

Process Capability, Cp Index



• Defined as:

• Numerator represents the distance

to the nearest spec

• Denominator represents the amount of this distance

consumed by variation

(((( ))))

3σσσσWithin

LSLX,XUSLminCpk

−−−−−−−−====

d2

RσσσσWithin ≈≈≈≈

Process Capability, Cpk Index



LSLUSL

Numerator

Target

Denominator

Process Capability, Cpk Index



LSL

USL

Cpk

= 2

Cpk = 0.5

Cpk = 0.5Cpk = 1

Cpk = 1

Cpk = 1.5

Cpk = 1.5

Cpk When Cp=2



LSL

USL

Cp= 1Cp= 2

Cp= 2

Cp= 4

Cpk = 1



• Cpk ≤≤≤≤ Cp

• Cpk = Cp only when the process is perfectly centred

• Cp represents the highest possible value for Cpk

Cpk and Cp



• Cp is not defined – requires 2 spec limits

• Cpk can still be calculated – requires only one speclimit

One Spec Limit



• Determines if process is stable and capable, i.e. can

it consistently produce good outputs.

• Measures success and progress achieved using the

other tools.

20

10

0

74.8 74.9 75.0 75.1 75.2 75.3

Response Time

30

NUMBE

R

USLLSL

Capability Study



Capability Study – 6 Steps



1. Collect data

2. Draw Control Charts

3. Interpret charts and draw conclusions

4. Draw histogram5. Test for Normality

6. Calculate Cp and Cpk and draw conclusions

Capability Study



(1) Collect Data

Month No. of Month No. of

number absences number absences

1 48 21 51

2 56 22 59

3 63 23 42

4 51 24 47

5 39 25 60

6 45 26 41

7 56 27 52

8 38 28 45

9 45 29 61

10 41 30 6911 57 31 53

12 53 32 60

13 64 33 57

14 54 34 51

15 58 35 55

16 65 36 42

17 42 37 37

18 48 38 48

19 57 39 46

20 66 40 38

• Collect data over sufficient

period to capture knownsources of variation

• In this example, 40 months

of data on absences has

been captured



• Open Worksheet Absences.MTW

• Stat> Control Charts> Variables Charts for

Individuals>I-MR

(2) Draw Control Charts

Enter absence as

variable

Select I-MR

Options




Select Median

Moving Range

Select Estimate

Select Moving

Range of 2




Observation

I n d i v i d u a

l V a

l u e

403632282420161284

70

60

50

40

30

_ X=51.5

UCL=76.66

LCL=26.34

Observation

M o v

i n g

R a n g e

403632282420161284

30

20

10

0

__ MR=9.46

UCL=30.91

LCL=0

I-MR Chart of absence



(3) Interpret Control Charts and Draw Conclusions

• The control limits representthe range of valuesexpected for the individual

values and the movingrange, if the process isstable

• Points outside the control

limits indicate the processis possibly unstable

Conclusions• The process is stable

Observation

I n d i v i d u a

l V a

l u e

403632282420161284

70

60

50

40

30

_ X=51.5

UCL=76.66

LCL=26.34

Observation

M o v

i n g R a n g e

403632282420161284

30

20

10

0

__ MR=9.46

UCL=30.91

LCL=0

I-MR Chart of absence



(4) Draw Histogram

absence

F r e q u e n c y

72666054484236

10

8

6

4

2

0

Histogram of absence



(5) Normal Probability Plot

absence

P

e r c e n t

7060504030

99

95

90

80

70

60

50

40

30

20

10

5

1

Mean

0.533

51.5

StDev 8.641

N 40

A D 0.314

P-Value

Probability Plot of absenceNormal



1. A shift occurred in the middle of the data

2. Mixed populations3. Truncated data

4. Rounding to a small number of values

5. Outliers6. Too much data

7. The underlying distribution is not normal

Reasons for Failing a Normality Test



Open Worksheet: Absences

(6) Calculate Cp and Cpk



1. Enter absence

4. Select Estimate

3. Enter Specs:

LSL = 0 (Boundary)

USL = 50


2. Enter Subgroup

Size (1)

5. Select Options



Select:

Median moving range


Select:

Moving range of length 2




Select “Include

confidence intervals”




7260483624120

LB USL

LB 0

Target *

USL 50

Sample Mean 51.5

S ample N 40

StDev (Within) 8.38574

StDev (Overall) 8.69655

Process Data

Low er C L *

U pper C L *

PPL *

PPU -0.06

Ppk -0.06

Lower CL -0.16

Upper CL 0.05

Cpm *

Low er C L *

Cp *

Low er C L *

U pper C L *

CPL *

C PU -0.06

C pk -0.06

Lower CL -0.16

Upper CL 0.04

Pp *

Ov erall Capability

Potential (Within) Capability

PP M < LB 0.00

PPM > USL 575000.00

PPM Total 575000.00

Observed Performance

PPM < LB *

PPM > USL 570982.07

PPM Total 570982.07

Exp. Within Performance

PPM < LB *

PPM > USL 568470.77

PPM Total 568470.77

Exp. O verall P erformance

Within

Overall

Process Capability of absence(using 95.0% confidence)



Capability Analysis Individuals – Sixpack



1. Enter absence

4. Select Estimate

2. Enter Subgroup Size

3. Enter Specs





Select:

Median moving range

Select:

Moving range of length 2

C bilit Si k Ab



Capability Sixpack – Absences

I n d i v i d u a

l V a

l u e

37332925211713951

80

60

40

_ X=51.5

UCL=76.66

LCL=26.34

M o

v i n g

R a n g e

37332925211713951

30

15

0

__ MR=9.46

UCL=30.91

LCL=0

Observation

V a

l u e s

4035302520

70

55

40

7260483624120

LSL USL

LS L 0

USL 5 0

Specifications

80604020

Within

Overall

Specs

StDev 8.38574

C p 0.99

Cpk -0 .0 6

Within

StDev 8.69655

P p 0.96

Ppk -0.06

C pm *

Overall

Process Capability Sixpack of absenceI Chart

Moving Range Chart

Last 25 Observations

Capability Histogram

Normal Prob Plot AD : 0.314, P: 0.533

Capability Plot

D C l i



Draw Conclusions

• This process is stable, but more than 50% of

months have absences in excess of the target of no

more than 50• To improve this process will require detailed

investigation of all of the reasons for absences

I di id l D t W k h



Individuals Data Workshop

• Open the Payment Times Worksheet

• Perform a Stability and Capability study on the

process assuming that the specification is for

payments to be made within 72 hours

• Draw conclusions



Process Capability - Non-normal Data

R f F ili N lit T t



1. A shift occurred in the middle of the data

2. Mixed populations3. Truncated data

4. Rounding to a small number of values

5. Outliers6. Too much data

7. The underlying distribution is not normal

Reasons for Failing a Normality Test

Non Normal or Unstable Data Sets



Non - Normal or Unstable Data Sets

• Some data sets are non-normal because the

underlying distribution is non-normal

• If the process is non-normal or unstable, we canestimate the process capability by calculating the

percentage of occurrences which fall outside of the

specification• This can be shown graphically in a histogram with the

specification drawn on



Process Capability – Attribute Data

Target 3 4 dpm



3.4 defects per million(99.9997% Good Quality)

Target – 3.4 dpm

C / DPM Conversion Table



• We need a minimum Cpk value of 1.5 to achieve 3.4 DPM

when we have a stable process• We can test for stability and calculate Cpk for variable

data using the Capability Study described earlier

Cpk / DPM Conversion Table

Capability Study – Binomial Data



• Over 10 working days a random sample of orders

were checked for accuracy

• A pass / fail criteria was used for assessment

Capability Study – Binomial Data

Order Accuracy Data



Day Sample Size Defectives

1 87 0

2 95 13 76 0

4 124 1

5 69 2

6 86 0

7 77 1

8 98 0

9 87 010 96 1

Order Accuracy Data

Minitab – Binomial Capability



Open Worksheet: “TSS Binomial Capability”Select: Stat> Quality Tools>Capability Analysis>Binomial

Minitab Binomial Capability

Minitab Output



Minitab Output

Sample

P r o p o r t i o n

10987654321

0.03

0.02

0.01

0.00

_ P=0.00670

UC L=0.03169

LC L=0

Sample

% D e f e c t i v e

108642

1.6

1.2

0.8

0.4

0.0

Summary Stats

0.00

PPM Def: 6704Low er C I: 2464

Upper C I : 14534

Process Z: 2.4727

Lower CI:

(using 95.0% confidence)

2.1826

Upper CI : 2.8117

%Defective: 0.67

Low er C I: 0.25

Upper C I: 1.45

Target:

Sample Size

% D e f e c t i v e

12010080

6

4

2

0

3.02.52.01.51.00.50.0

4.8

3.6

2.4

1.2

0.0

Tar

Binomial Process Capability Analysis of DefectivesP Chart

Tests performed with unequal sample sizes

Cumulative %Defective

Rate of Defectives

Dist of %Defective

P – Chart



The P-Chart indicates that the process is stable

(no points outside the control limits)

P Chart

Summary Statistics



This gives the actual PPM Defective (DPM) = 6704This value can be converted to an approximate Cpk

Value using the Cpk /DPM conversion table

A 95% confidence interval is returned for DPM(2464 to 14534)

The confidence interval assumes the process is stable

Su a y Stat st cs

Capability Study – Poisson Data



• The data on the next page was collected from 20

consecutive working days

• The data refers to the number of errors found indaily transactions

p y y

Transactional Errors Data



Day Trans Errors

1 326 3

2 543 13 456 2

4 301 1

5 297 1

6 420 07 421 1

8 564 3

9 289 0

10 378 3

Day Trans Errors

11 345 5

12 432 413 573 4

14 387 2

15 361 1

16 489 217 317 0

18 379 1

19 423 2

20 499 4

Minitab – Poisson Capability



Open Worksheet: “TSS Poisson Capability”Select: Stat> Quality Tools>Capability Analysis>Poisson

p y

Minitab Output



p

Sample

S a m p l e

C o u n

t P e r

U n

i t

191715131197531

0.015

0.010

0.005

0.000

_

U=0.00488

UC L=0.01426

LCL=0

Sample

D P U

2015105

0.010

0.008

0.006

0.004

Summary Stats

0.0000

Max DPU: 0.0145Targ DPU: 0.0000

(using 95.0% confidence)

Mean DPU: 0.0049

Lower CI: 0.0035

Upper CI: 0.0066

Min DPU :

Sample Size

D P U

500400300

0.015

0.010

0.005

0.000

0 . 0 1 4

0 . 0 1 2

0 . 0 1 0

0 . 0 0 8

0 . 0 0 6

0 . 0 0 4

0 . 0 0 2

0 . 0 0 0

4.8

3.6

2.4

1.2

0.0

Tar

Poisson Capability Analysis of ErrorsU Chart

Tests performed with unequal sample sizes

Cumulative DPU

Defect Rate

Dist of DPU

U – Chart



The U-Chart indicates that the process is stable

(no points outside the control limits)

Summary Statistics



Yield = e–DPU = e–0.00488 = 0.995131

This is equivalent to a DPM of 4869

Our DPM of 4869 can be converted to anapproximate Cpk Value using the Cpk /DPM

conversion table

A 95% confidence interval is returned for DPU

(0.0035 to 0.0066)

The confidence interval assumes the process is stable



Process Capability – Summary

Variable v Attribute Data



• Variable Data allows us to calculate capability indices(Cp, Cpk) directly

• Achieving a stable process with a Cpk value of 1.5 or

more at the end of our project means that we haveachieved 6 Sigma

• Achieving a Cpk value of 1.5 for a variable measure (y)would mean that we would have 3.4 DPM or less

• The Six Sigma target for each attribute measure is thesame – 3.4 DPM or less

Capability Metrics



Process

Output

yAttribute

Data

Variable

Data

Defective Items

Defects per Unit

DPM

Cp

Cpk

Role of Capability Studies



• Capability studies are the primary tool for managing

variation reduction. They act as the scorecard.

• Capability studies help characterise the type of problem

(unstable, off-target, excessive variation) guiding which

tools and strategies to apply.

Six Sigma Transactional Improvement Process



15 20 25 30 35

LSL USL

Define Measures (y’s)

Check Data Integrity

Determine ProcessStability

Determine Process

Capability

Set Targets forMeasures

Phase Review

Control Critical x’s

Monitor y’s

Validate ControlPlan

Identify furtheropportunities

Close Project

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

ImplementCountermeasures

Criteria A B C DTime + s - +

Cost + - + s

Service - + - +

Etc s s - +

15 20 25 30 35

LSL USL

Phase Review

Analyse Improve ControlMeasureDefine Select Project

Define Project

Objective

Form the Team

Map the Process

Identify Customer

Requirements

Identify Priorities Update Project File

Phase Review

Define

DMAIC – Measure Phase



• Capability studies can be used to determine:

• process stability

• process capability• the nature of the problem, e.g. unstable process,

off-target, excessive variation, outliers

DMAIC – Improve Phase



• Capability Studies can be used to determine the

stability and capability of critical x’s

• Capability Studies can be used to verify processimprovement

• Capability studies measure the current state of the

processes, track progress and are used todemonstrate improvements

• They measure the success of the other variation

reduction tools and processes

DMAIC – Control Phase



• In conjunction with the use of control charts,

process capability can be used during the

control phase to:

• Control critical x’s

• Confirm process capability during Process

Validation

• Ensure effective long-term monitoring of the y’s

(measures)

Process Capability – Summary



• Long-term studies are more reliable than short-term

studies. We must ensure that a sufficient time period is

sampled.

• Always check whether the process is stable before or

during a capability analysis. Special causes should be

removed, or at least understood, before continuing.

• Test for normality. Some types of data will requiredifferent capability analyses.

• If the process is stable and a sufficient time period is taken,

then achieving a Cpk of 1.5 at the end of your projectmeans that you have achieved the Six Sigma Target!

8 ssgb amity bsi capability

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