Quantitative Capability Assessment. Cp, Cpk, Pp Ppk These are non dimensional constants used to...

Quantitative Capability Assessment

Cp, Cpk, Pp Ppk

• These are non dimensional constants used to describe capability

• In 6 Sigma organizations they are more useful than percentage yields

• Flowserve is Six Sigma capable in only a few processes so we tend not to use these indices. However it is not uncommon for Six Sigma aware customers to ask use to describe our capability using these measures.

Cp

• Remember a 3 sigma process is 99% good. For many years in high volume manufacturing this was the goal for process capabilities.

• Once you go beyond 3 sigma process capabilities are measured in fractions of percentages – the numbers are valid but clumsy so the sigma (Cp) scale is used. Cp assumes that you have a normal process centered halfway between the specification limits

• When you have a 3 sigma process. (i.e. from the mean to the spec limits = 3 sigma) Cp 1, your yield is 99%

• If your process is more capable, then Cp increases. If you halve the variation in a 3 sigma process it becomes a 6 sigma process & Cp = 2

termshortp s*6

LSLUSLC

Cpk• The difference between Cp and

Cpk is that Cp assumes the voice of the process is centered half way between the sigma limits and Cpk uses the actual voice of the process mean.

• The bigger the difference between Cp and Cpk the greater opportunity there is to improve the process capability by centering. For some simple processes this is valuable information as you only need change an offset to increase capability

Short -Term Capability Indices

termshortp s*6

LSLUSLC

termshortpk(USL) s*3

)X(USLC

termshortpk(LSL) s*3

LSL)X(C

)pk(LSL)pk(USL)pk C , (C minC

Cpk(USL) & Cpk(LSL)

• Notice we used Cpk USL and Cpk LSL to identify Cpk

• These figures should be quoted instead of Cp when you do not have both upper and lower specification limits .

Short -Term Capability Indices

termshortp s*6

LSLUSLC

termshortpk(USL) s*3

)X(USLC

termshortpk(LSL) s*3

LSL)X(C

)pk(LSL)pk(USL)pk C , (C minC

Cpm

• You are almost never going to use this, but for completeness…..

• In some processes you will not target the center point.

• Example cutting impellers you want to cut an impeller diameter between 196 and 200 mm

• It may be cheaper to bias the target cut towards say 199mm instead of 198mm

• So in this case if we target 199mm we want to measure the process against the target instead of the center point

Short and Long Term Sigma • Remember from modules 1 and 2

over a long period we expect the capability of a process to deteriorate

• Also we estimate that the difference between the short term capability and long term capability will be 1.5 sigma

• So if a project team achieves a process that is 99% capable (ST) we expect it to be 80% capable (LT) and to create a process that is 50% good (LT) we aim for 93% (ST)

Short Term Sigma

Long Term Sigma Yield

Long term yield

6.0 4.5 99.9997% 99.865%5.5 4 99.9968% 99.379%

5.0 3.5 99.9767% 97.725%4.5 3 99.865% 93.319%

4.0 2.5 99.3790% 84%3.5 2 97.72% 69%

3.0 1.5 93% 50%2.5 1 84% 31%

2.0 0.5 69% 16%1.5 0 50% 7%

Short and Long Term Sigma

• What does short term and long term mean? ‘’It depends!’’ as a guide:

– Long term is more likely to include special causes

– Long term is likely to include mixtures of batches, parts and include changing personnel

– Long term capability does not get worse.

Short Term Sigma

Long Term Sigma Yield

Long term yield

6.0 4.5 99.9997% 99.865%5.5 4 99.9968% 99.379%

5.0 3.5 99.9767% 97.725%4.5 3 99.865% 93.319%

4.0 2.5 99.3790% 84%3.5 2 97.72% 69%

3.0 1.5 93% 50%2.5 1 84% 31%

2.0 0.5 69% 16%1.5 0 50% 7%

Pk, Ppk, Ppk(usl), Ppk(lsl)

• The only difference between calculating the C… and P… is that you use the short term sigma level for C.. And the long term sigma level for P….

• Remember long term capability = short term capability + 1.5

Normal Capability – Within Cp Between Pp

• This is another more sophisticated technique for calculating short and long term sigma levels.

• It relies on your ability to group data. For example you collect the shipments per day. However you know that there is a pattern of shipments during the week so you group the shipments into weeks. You can now calculate the average for each week and the standard deviation for each week. The overall variation is made up of two components – the variation within each week and the variation between each week.

• Next the assumption that the variation within each week corresponds to short term and the variation between the weeks is long term. By taking these two variations in turn you derive the standard deviation and hence Cp, Pp etc

Normal Capability – Within Cp Between Pp

In Minitab you would In Minitab you would select these two select these two variations in turn you variations in turn you derive the standard derive the standard deviation and hence Cp, deviation and hence Cp, Pp etcPp etc

Overall variation = short Overall variation = short term variation + long term term variation + long term variationvariation

A large difference A large difference between the Overall and between the Overall and Within Capability indices Within Capability indices may indicate the process may indicate the process is out of control.is out of control.

In Minitab you would In Minitab you would select these two select these two variations in turn you variations in turn you derive the standard derive the standard deviation and hence Cp, deviation and hence Cp, Pp etcPp etc

Overall variation = short Overall variation = short term variation + long term term variation + long term variationvariation

A large difference A large difference between the Overall and between the Overall and Within Capability indices Within Capability indices may indicate the process may indicate the process is out of control.is out of control.

12840-4

LB USLProcess Data

Sample N 27StDev(Within) 2.18221StDev(Overall) 3.77818

LB 0Target *USL 5Sample Mean 4.81481

Potential (Within) Capability

Overall Capability

Pp *PPL *PPU 0.02Ppk 0.02Cpm

Cp

*

*CPL *CPU 0.03Cpk 0.03

Observed PerformancePPM < LB 0.00PPM > USL 518518.52PPM Total 518518.52

Exp. Within PerformancePPM < LB *PPM > USL 466185.90PPM Total 466185.90

Exp. Overall PerformancePPM < LB *PPM > USL 480453.93PPM Total 480453.93

WithinOverall

Process Capability of Y=Shipped

PPM parts per million defects

• The bottom of the capability diagram shows predicted ppm defect rates. The figures are not measured but calculated assuming that the VoP will be normal and using the observed average, standard deviation, sample size and the spec limits.

• Information is presented as number of ppm exceeding each spec limit.

• You will probably wish to simplify into percentages

12840-4

LB USLProcess Data




Overall Capability


Cp

*





WithinOverall

Process Capability of Y=Shipped

What to share with Champions and teams?

• Unless you are confident that your Champion understands CPk, Within variation and parts per million, please edit the graph and delete that information

• Also please make the title legible

• It is often best to print the pictures for sharing with non Minitab users rather than asking them to look at your screen

250240230220210200

LSLProcess Data


LSL 200Target *USL *Sample Mean 226.976


Overall Capability

Pp *PPL 0.81PPU *Ppk 0.81Cpm

Cp

*

*CPL 2.95CPU *Cpk 2.95

Observed PerformancePPM < LSL 0.00PPM > USL *PPM Total 0.00

Exp. Within PerformancePPM < LSL 0.00PPM > USL *PPM Total 0.00

Exp. Overall PerformancePPM < LSL 7637.71PPM > USL *PPM Total 7637.71

WithinOverall

Process Capability of Lead Time

240230220210200

Lower Specification Limit

Process Capability of Lead Time

Summary

• Capability can be shown as a picture

• For GB start with observed capability

• In the long term capability gets worse

• To predict the long term capability You could describe the capability using - % good, parts per million, sigma level, Cp, Pp

• The one you use will depend on your audience

Exercise

• Over the telephone you are told that lead time is a problem, customers want lead times less than 25 days and here are the lead times of the last 20 orders

• 29,15,21,16,30,25,20,28, 21,22,28,30,24,23,45,25, 42,23,27,19

• What is the capability?• How do you interpret the EDA

output?• Create a PowerPoint slide

which you would use to explain the capability to your champion?

Wrong Answer

403020100

LB USLProcess Data




Overall Capability

Pp *PPL *PPU -0.03Ppk -0.03Cpm

Cp

*

*CPL *CPU -0.03Cpk -0.03




WithinOverall

Process Capability of C1

Better Answer• Shape is not normal

• Which may mean that we are looking at –

– Granularity – perhaps there is a reason that there is a gap around orders taking 30-40 days

– Or perhaps we have two catastrophic failures

– or perhaps there is a mixture of more than one type of order.

– Next step is to investigate these two orders with the team.

– With the two values to the right excluded the remaining data is normal. 75% of orders are shipped in 28 days or less and we can expect an average lead time between 21 and 26 days std deviation 7 days….. continued

Descriptive Statistics for: C1

5040302010

95% Confidence I nterval for Mu

5040302010

95% Confidence I nterval for Median

21.2352

5.6818

22.1534

Maximum3rd Quartile

Median1st QuartileMinimum

n of dataKurtosis

SkewnessVarianceStd DevMean

p-value:A-Squared:

28.0000

10.9122

29.1466

45.000028.750024.500021.000015.0000

20.0000 1.9857 1.258355.8184 7.471225.6500

0.0439 0.7439

95% Confidence Interval for Median

95% Confidence Interval for Sigma

95% Confidence Interval for Mu

Anderson-Darling Normality Test

35302520151050

LB USLProcess Data




Overall Capability


Cp

*





WithinOverall

Process Capability outliers removed

• Remaining system is stable and shows long term Capability 61%

Descriptive Statistics for orders less outliers

30252015

95% Confidence I nterval for Mu

30252015

95% Confidence I nterval for Median

21.0000

3.3951

21.4167

Maximum3rd Quartile

Median1st QuartileMinimum

n of dataKurtosis

SkewnessVarianceStd DevMean

p-value:A-Squared:

27.4820

6.7828

25.9166

30.0000 28.0000 23.5000 20.7500 15.0000

18.0000 -0.6675 -0.3082 20.4706 4.5244 23.6667

0.7800 0.2279

95% Confidence Interval for Median

95% Confidence Interval for Sigma

95% Confidence Interval for Mu

Anderson-Darling Normality Test

Even Better Answer

• Having investigated with the team there is a reason that there is a gap around orders taking 30-40 days as we pull orders into this month if possible. The two orders later than this were delayed by the customer

• Unless we have more customer delays we can expect around 66% of orders to be within customer expectations

• To achieve 90% or better we need to make significant process changes to reduce the average lead time by around 5 days

302520151050

LB USL

Capability outliers removed - 66% of lead times within cust expectations

Practice

• Using data from a project you or your Green Belt are working on create power point slides to describe the Capability

Quantitative Capability Assessment

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