Javier Garcia - Verdugo Sanchez - Six Sigma Training - W1 Process Capability

Process CapabilityProcess Capability

USLUSL

Week 1

Knorr-Bremse Group

About this Module

P bilit d th t i•Process capability and other metrics

Calc lations ith Minitab•Calculations with Minitab

•Short term and long term observations•Short term and long term observations

•Proceeding with improvements•Proceeding with improvements

Knorr-Bremse Group 12 BB W1 Process Capability 08, D. Szemkus/H. Winkler Page 2/34

The Process Capability Ratio Cp

• The bigger the maximal allowable range (specification range) of the design, the better the Rolled Throughput Yield (RTY).

• The Process Capability Ratio Cp measures the allowable design range

Specification RangeCp = P V i ti+3s-3s

Cp Process Variation

( USL - LSL)

Process Width

( USL - LSL)Cp =

6 StDev.

Cp x 3 = X TLSL USL

Specification=> X Sigma Process


Process Capability Metrics Cp

Customer specificationLSL USL LSL USL

Customer specification

0.4

0.3

0.4

0.3

0.2

0.1

0.2

0.1

Process variation

43210-1-2-3-4

0.0

86420-2-4-6-8

0.0

Process variation

Process centeredCp= 1 Cp= 2


Process Capability Metrics Cp & Cpk

Process not centered

C 1 33

0.4

LSL USLCustomer Specification

Cp = 1.33

Cpk = 1.33

0.3

0.2

01

5.334.02.671.33-1.33-2.67-4.0-5.33 0

0.1

0.0

LSL USLCustomer Specification

Cp = 1.33

C k = 0 83

0.4

0.3

0.2Cpk 0.83

0

0.1

0.0

5 334 02 671 331 332 674 05 33


0 5.334.02.671.33-1.33-2.67-4.0-5.33

The Process Capability Ratio Cpk

)X-USLLSL-X

Mi (C ),S3S3

Min(Cpk =

This process capability index accounts for the statistical mean shift in the processmean shift in the process.

It reflects the expected, dynamic mean shift in the process.It reflects the expected, dynamic mean shift in the process.

Wh i l t ?When is cp equal to cpk ?

Is it possible that c is bigger than c ?Is it possible that cpk is bigger than cp?

Is it possible that c or c will be negative?


Is it possible that cp or cpk will be negative?

3 Sigma - Process

LSL USLLower Specification Limit Upper Specification Limit

Without a mean shift from the center

72666054484236Potential (Within) C apability( ) p y

C p 0,96C PL 0,95C PU 0,97C pk 0,95

O bserv ed Performance% < LSL 1,00% > USL 1,00% Total 2 00

Exp. Within Performance% < LSL 0,22% > USL 0,18% Total 0 39


C C pk 0,96p ,% Total 2,00 % Total 0,39

3 Sigma - Process

LSL USL

with a mean shift of 1,5 StDevLower Specification Limit Upper Specification Limit

72666054484236Potential (Within) C apabilityPotential (Within) C apability

C p 0,89C PL 1,34C PU 0,44C pk 0,44

O bserv ed Performance% < LSL 0,00% > USL 10,00% Total 10,00

Exp. Within Performance% < LSL 0,00% > USL 9,43% Total 9,44


C C pk 0,89p ,, ,

6 Sigma - Processwithout / with a mean shift of 1,5 StDev

LSL USL LSL USL

C 2 07E P fOb dCp 1,97CPL 2 43E P fOb d

6460565248444036 6460565248444036

Cp 2,07CPL 2,07CPU 2,07Cpk 2,07

Exp.Performance% < LSL 0,00% > USL 0,00% Total 0,00

Observed % < LSL 0,00% > USL 0,00% Total 0,00

CPL 2,43CPU 1,51Cpk 1,51CCpk 1,97

Exp. Performance% < LSL 0,00% > USL 0,00% Total 0,00

Observed% < LSL 0,00% > USL 0,00% Total 0,00


Rational Subgroups

• The goal is the identification of rational subgroups (important input) to establish a sample window, which is ( p p ) p ,small enough to exclude systematic and not by chance caused effects.

• The intended result will be that we see common cause variation within the group and special cause variation g p pbetween the group, if they exist.

• If done with an input which has a signal averaged (pooled)If done with an input which has a signal, averaged (pooled) Stdev. from the subgroups estimate best case or possible process capability based of the current process.p p y p

• If there is a big difference between the pooled standard deviation and the total standard deviation then either wedeviation and the total standard deviation, then either we have a shift of the process mean, or the process Stdev is changing over time.


g g

Example for Subgroups

17

Demonstration of Rational Subgroups Shift is the Grouping Variable

17

16

Shift 1 Shift 2 Shift 1 Shift 2

15

14

ut

13

12

Ou

tpu

11

10

30272421181512963

10

9

The arrangement of the groups can h t i t th lt

The variation within the group is ll th b t th


have a strong impact on the resultssmaller than between the groups


17


17

16


15

14

ut

13

12

Ou

tpu

11

10

30272421181512963

10

9

Total variabilityMean shift Pooled within = +Total variabilityvariability groups variability= +

Total Between Within


Capability PrecisionAccuracy


17


17

16


15

14

ut

13

12

Ou

tpu

11

10

30272421181512963

10

9

2g ng

22g n

)X(X)X-X(n)XX( ∑ ∑∑∑ ∑ −+=−

Total variabilityMean shift Pooled within = +

1j 1=ijij

1j=1j= 1=iij )X(X)X-X(n)XX( ∑ ∑∑∑ ∑

=

+=


Total variabilityvariability groups variability= +

Short & Long Term Observations

Sample Size:(X Xij ji=1

n

j 1

g

−∑∑=

)2

Within Variation

30 to 50 values are USLLSL

Within Variation

required for short term investigations

100 values minimum ∑g

1j=

2j )X-X(n

are required for long term investigations

Between Variation

1j

Overall Variation(X X)ij

i 1

n

j 1

g2−∑∑

The number of data points defining long- or short term is

Overall Variationi=1j=1


very process dependent

Definitions of Process CapabilityInstantaneous capability:

− Process capability over a very short period of time.

− It should display the best possible performance of a process over a short period of time.

− It should be the best estimation of the maximum process performanceIt should be the best estimation of the maximum process performance capability.

− Minimal effects due to noise variables

Short term capability:− Capability study based on 30-50 data points.

− Usually equal or better than the long term capability.

− Includes effects of short term noise variables

Long term capability:− Capability study based on high number of data points.

− Best estimation of the true process capability.

− Includes effects of long term noise variables

P l i b d thi t f d t


− Process analysis based on this set of data.

Steps to Build a Capability Study• Use the standard set up for the process and record the values of all key

process input variables.

Id tif t ti l i bl t f ti l b i• Identify potential variable to use for rational sub grouping.

• Run the process and measure the output variable for study over a short period of time. Approximately 30 data points is a reasonable target for p pp y p gthe data collection.

• Observe the process during the measurement phase. Make notes, i ll f th i t t i t i bl i d tespecially focus on the important input variable in accordance to your

process map.

• Measure and record the values for the key output variables.Measure and record the values for the key output variables.

• Apply the capability analysis (eventually “Sixpack”) and check the following issues: probability plot and the for process diagnostics:

– Normal distribution (Normal Probability Plot )

– Stability (SPC Diagram)

– Mean shift and variation

– Long term capability

D l ti l b d th di ti


• Develop an action plan based on the diagnostics.

Pooled and Overall Standard Deviation During the measurement phase in the DMAIC cycle a short term process capability study is required in order to establish a process baseline (as is performance of the process)performance of the process)

The Minitab macros for process capability gives us the possibility to calculate the potential Cp/Cpk values beside the actual Pp/Ppk Values:calculate the potential Cp/Cpk values beside the actual Pp/Ppk Values:

Cp/Cpk values are based on the Pooled Standard Deviation:

This option will be applied for the calculation of the potential (best case)This option will be applied for the calculation of the potential (best case) capability, but only if rational subgroups can be used. The uncritical application of these results in this option may be misleading in respect to the

bilit D i thi l i tt ti th t th bprocess capability. During this analysis, pay attention that the subgroups are accordingly sorted. This option is a good method to estimate the potential capability. This option has to be deactivated for the evaluation of individual values if the order of the data is not known!

Pp/Ppk values are based on the Overall Standard Deviation:

This option should be used to determine the true process capability. This calculation is based on the complete set of data without consideration of influences of the subgroups


influences of the subgroups.

Evaluation and Interpretation

If we use the capability six pack in Minitab, we can realize the dynamic of the process. In every process we can find a minimum of four common sources of change.

1. Chronic mean shift: If the mean shifts and remains shifted.

2. Acute mean shift: If the mean shifts over the subgroups in short periods of timeof time.

3. Acute change of the variability: If the variation changes within a subgroup over a determined period of timesubgroup over a determined period of time.

4. Chronic change of the variability: If the variation is getting gradually smaller or bigger within a subgroup over a determined period of time.gg g

We can see these patterns from the investigation of the different Cp’s and Cpk’s, if we use the overall standard deviation. We also can see pattern between and within subgroup, if we use the graphics of the capability six pack analysis


of the capability six pack analysis.

Start with Basic Statistics and a Graphic

A nderson-Darling Normality Test

A -Squared 0,69P-V alue 0,063

Mean 0,079697StDev 0,014681

Summary for Moisture

File: Capability.mtw

0,110,100,090,080,070,060,05

V ariance 0,000216Skewness 0,244654Kurtosis -0,288605N 33

Minimum 0,0500001st Q uartile 0,070000Median 0,0800003rd Q uartile 0,090000Maximum 0 110000

Two questions first:

1 What type of distribution?0,110,100,090,080,070,060,05

Mean

Maximum 0,110000

95% C onfidence Interv al for Mean

0,074491 0,084903

95% C onfidence Interv al for Median

0,070000 0,085026

95% C onfidence Interv al for StDev

0,011806 0,01941895% Confidence Intervals

1. What type of distribution?

2. Is the process stable?

Median

Mean

0,08500,08250,08000,07750,07500,07250,0700

I Ch t f M i t

Graphical Summary from

0,14

0,12

UCL=0,1287

I Chart of Moisture

Graphical Summary from Basic Statistic and Individual Chart under

Ind

ivid

ua

l Va

lue 0,10

0,08

0 06

_X=0,0797

Control Charts

I

3330272421181512963

0,06

0,04

0,02

LCL=0,0307


Observation3330272421181512963

Calculation of the Process CapabilityStat

>Quality Tool

>Capability Analysis

File: Capability.mtw

>Capability Analysis

>Normal…

Short and long term measurements gof ashes and moisture content in injection molding materials.

Enter Specification limits for moisture,lower limit 0, upper limit 0,15In this case we have to check the boundary box, there is no practical value below 0!


Short Term Study for Moisture, 33 values

Process Capability of Moisture

LB USL

LB 0Process Data Within

O ll


LB 0Target *USL 0,15Sample Mean 0,079697Sample N 33StDev (Within) 0 0162803

C p *C PL *C PU 1,44

Potential (Within) C apability

Overall

StDev (Within) 0,0162803StDev (O v erall) 0,014681

,C pk 1,44

Pp *PPL *PPU 1 60

O v erall C apability

PPU 1,60Ppk 1,60C pm *

0,140,120,100,080,060,040,020,00

PPM < LB 0 00O bserv ed Performance

PPM < LB *Exp. Within Performance

PPM < LB *Exp. O v erall Performance

PPM < LB 0,00PPM > USL 0,00PPM Total 0,00

PPM < LBPPM > USL 7,86PPM Total 7,86

PPM < LBPPM > USL 0,84PPM Total 0,84


Subgroups with the Box Plot

Boxplot of Moisture vs Charge

Graph

>Boxplot…

>One Y0,11

0,10

>One Y

With Groups

istu

re

0,09

0,08

Mo

0,07

0,06

Cha e7654321

,

0,05

There are small differences only between the single charges

Charge

There are small differences only between the single charges

What factors (subgroups) could show bigger differentiation? Vacuum, Inspector, shift, …


Inspector, shift, …

Deactivating of the Potential CapabilityStat

>Quality Tool

>Capability Analysis>Capability Analysis

>Normal…

>Options…


LB USL

LB 0Target *USL 0 15

Process DataPp *PPL *PPU 1 60


USL 0,15Sample Mean 0,079697Sample N 33StDev (O v erall) 0,014681


0,140,120,100,080,060,040,020,00

PPM < LB 0,00PPM > USL 0 00

O bserv ed PerformancePPM < LB *PPM > USL 0 84

Exp. O v erall Performance


PPM > USL 0,00PPM Total 0,00


Capability Calculation for SubgroupsStat

>Quality Tool

>Capability Analysis>Capability Analysis

>Multiple Variables (normal)

Capability Histograms of Moisture by Charge

Charge = 1 Charge = 2

2,0

1,5

1,0

LB USL

Pp *PPL *PPU 1,247

Overall 1,2

0,9

0,6

LB USL

Pp *PPL *PPU 2,333

Overall

0,1450,1150,0850,0550,025-0,005

1,0

0,5

0,0

Ppk 1,247Cpm *

0,1450,1150,0850,0550,025-0,005

0,6

0,3

0,0

Ppk 2,333Cpm *

3

2

LB USL

Pp *PPL *

Overall 1,00

0,75

LB USL

Pp *PPL *

Overall


0 1450 1150 0850 0550 0250 005

2

1

0

PPU 1,461Ppk 1,461Cpm *

0 1450 1150 0850 0550 0250 005

0,50

0,25

0,00

PPU 1,248Ppk 1,248Cpm *


0,1450,1150,0850,0550,025-0,005 0,1450,1150,0850,0550,025-0,005

Capability Calculation for Subgroups

LB USL LB USL

Capability Histograms of Moisture by Charge


2,0

1,5

1,0

LB USL

Pp *PPL *PPU 1,905Ppk 1 905

Overall 3

2

LB USL

Pp *PPL *PPU 1,841Ppk 1 841

Overall

0,1450,1150,0850,0550,025-0,005

0,5

0,0

Ppk 1,905Cpm *

0,1450,1150,0850,0550,025-0,005

1

0

Ppk 1,841Cpm *

Ch 7

2,0

1,5

LB USL

Pp *PPL *PPU 1 211

Overall

Charge = 7

0,1450,1150,0850,0550,025-0,005

1,0

0,5

0,0

PPU 1,211Ppk 1,211Cpm *

Interpretation: Minitab supports also the capability calculation of subgroups. Th b t bilit ill b hi d t h 2 D d t f thThe best capability will be achieved at charge 2. Dependent of the

arrangement of the data, this is a better way for the evaluation of the Cpkvalue. Pay attention to this example, the sample size is very small!


Pp and Ppk the accurate CalculationThe Pp and Ppk calculation is of course dependent from the sample size. A factor C4, dependent from the sample size, will be used for the calculation of the StDev (Overall) in order to consider the possible change.

N c42 0 797850

the StDev (Overall) in order to consider the possible change.

!1n ⎞

⎜⎛ 2 0.797850

3 0.8715304 0.9057635 0.925222

( USL - LSL)6 Stotal / C4

Pp =!1

1-n

!12

n

1

2c4

⎞⎜⎛ −

⎠⎞

⎜⎝⎛ −

−=

n5 0.9252226 0.9378927 0.9468378 0.953503

Thi dj t t f t C4 ill b d l f th l l ti f

total !12 ⎠

⎜⎝

9 0.95866910 0.96279315 0.975137

This adjustment factor C4 will be used also for the calculation of the potential capability Cp and Cpk.

In Minitab 15 the adjustment factor is activated for the StDev 20 0.98130525 0.98500930 0.987480

j(Within).

The factor is deactivated for the StDev (Overall). It can be activated under > Estimate > Use unbiasing constant to calculate 40 0.990571

50 0.992427

activated under > Estimate > Use unbiasing constant to calculate overall standard deviation”.


Literatur: Wheeler; Statistical Process Control

Long Term Study for Moisture, 132 values

LB USL

LB 0Target *USL 0 15

Process Data


WithinOverall

Process Capability of Moisture LT

The variation from charge to charge (between groups) is small in this

USL 0,15Sample Mean 0,0793939Sample N 132StDev (Within) 0,019711StDev (O v erall) 0,0183585

C p *C PL *C PU 1,19C pk 1,19

Pp *PPL *



case, based on the Cpk and Ppk values . Therefore it makes more sense to calculate the capability

0,140,120,100,080,060,040,02-0,00


p ybased on the overall variation only.

The overall variation defines the process capability,,,,,,,,

PPM < LB 0,00PPM > USL 0,00PPM Total 0,00

O bserv ed PerformancePPM < LB *PPM > USL 170,45PPM Total 170,45

Exp. Within PerformancePPM < LB *PPM > USL 60,04PPM Total 60,04

Exp. O v erall Performance

Process Capability of Moisture LT

process capability

LB USL

LB 0Target *USL 0,15Sample Mean 0,0793939Sample N 132StD (O ll) 0 0183585

Process DataPp *PPL *PPU 1,28Ppk 1,28C pm *


StDev (O v erall) 0,0183585

0,140,120,100,080,060,040,02-0,00

PPM < LB 0,00O bserv ed Performance

PPM < LB *Exp. O v erall Performance




Short Term and Long Term Investigations

Potential for the capability

Minitab helps us with the Cp and Pp differentiation to make improvements step by stepthe capability

Goal

to make improvements step by step.

In this example we don‘t have theCapability

Short term

In this example we don‘t have the possibility for improvements by the factor

charge!

CpPp 1,44

StD ithi 0 0163

If we compare the Ppk values for the long to short term observation we see an

improvement from 1 28 to 1 6StDev within 0,0163

Cpk A t l

improvement from 1,28 to 1,6.

CpkPpk 1,28

StDev overall 0,0147

Actual Capability

Experience: Center the process on the target first, then minimize the variability


minimize the variability

Short Term Study for Ash 33 valuesStat

>Quality Tool

>Capability Sixpack

This time we calculate the capability of ash content with the „Sixpack“>Capability Sixpack

>Normal…

p

The specification for the ash content is 28 – 32 %

The subgroups are in the column ChargeThe subgroups are in the column Charge.


Short Term Study for Ash 33 values

an

LSL USL

Specifications1

1

Process Capability Sixpack of AshXbar Chart Capability Histogram

7654321

31

30

29

Sa

mp

le M

ea __

X=30,615UCL=30,986

LCL=30,244LSL 28USL 32

Specifications

1

1

1,0

Ra

ng

e

_R 0 643

UCL=1,360

3231302928Tests performed with unequal sample sizes

R Chart Normal Prob PlotA D: 0,493, P: 0,202

7654321

0,5

0,0Sa

mp

le

R=0,643

LCL=0

34323028Tests performed with unequal sample sizes

32,5

31,0

29,5

Va

lue

s

Within

O v erall

StDev 0,276554C p 2,41C pk 1,67

WithinStDev 0,888862Pp 0,75Ppk 0,52C pm *

O v erall

Last 7 Subgroups Capability Plot

642

29,5

Sample

SpecsC pm *

The variation from charge to charge (between groups) has a strong effect on the capability. Cpk and Ppk values are different. In this case the capability

within the charge is much better than between the charges.


g g

Exercise 1

Analyze the ashes content with Minitab

LSL 28%----USL = 32%

CapabilityShort term Long term

CCpPp

StDev withinStDev within

CpkCpkPpk

StDev overall

Comment your results!


y

Exercise 2

Process parameter “total friction torque” (GESRM) at anProcess parameter total friction torque (GESRM) at an assembly line.

LSL = 1 65 Nm; USL = 3 5 NmLSL = 1,65 Nm; USL = 3,5 Nm

Background information:File:

Friction Torque MTW

Background information:

122 measurements (100%-inspection during the assembly process)Friction Torque.MTW during the assembly process)

Within one shop order

Analyze the process capability:y p p y- Short term capability?

- Long term capability?


g p y

Exercise 3

Parameter “diaphragm diameter” inspected at goods receivingParameter diaphragm diameter inspected at goods receiving

LSL 157,6 mm; USL = 158,5 mm

Background information :File:

Diaphragm diameter xls

Background information :

225 measurements recorded (Sampling inspection)Diaphragm diameter.xls inspection)

Charge information not available

Analyze the process capability:y p p y- Short term capability?

- Long term capability?


g p y

Important Questions in Respect to the Process Capability

Is the measurement system capable?

For a critical output variableFor a critical output variable

− The target value better?

A higher al e better− A higher value better

− A Lower value better?

The focus is on

− The process center?

− The process deviation?

− Or on both?

Is the output currently under statistical control?

Does the output change over time?p g

Are they results which are important for you?

− Where do we have priority?


Where do we have priority?

Engineering

Javier Garcia - Verdugo Sanchez - Six Sigma Training - W1 Process Capability