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 Range
Cp =
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 specification
LSL 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
0.2
Cpk 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 USL
Lower Specification Limit Upper Specification Limit
Without a mean shift from the center
72666054484236
Potential (Within) C apability( ) p y
C p 0,96
C PL 0,95
C PU 0,97
C 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 0,96
p ,% Total 2,00 % Total 0,39
3 Sigma - Process
LSL USL
with a mean shift of 1,5 StDev
Lower Specification Limit Upper Specification Limit
72666054484236
Potential (Within) C apabilityPotential (Within) C apability
C p 0,89
C PL 1,34
C PU 0,44
C pk 0,44
% < LSL 0,00
% > USL 10,00
% Total 10,00
% < LSL 0,00
% > USL 9,43
% Total 9,44
C C pk 0,89
p ,, ,

6 Sigma - Process
without / with a mean shift of 1,5 StDev
LSL USL LSL USL
C 2 07E P fOb d
Cp 1,97
CPL 2 43E P fOb d
6460565248444036 6460565248444036
Cp 2,07
CPL 2,07
CPU 2,07
Cpk 2,07
Exp.Performance
% < LSL 0,00
% > USL 0,00
% Total 0,00
Observed
% < LSL 0,00
% > USL 0,00
% Total 0,00
CPL 2,43
CPU 1,51
Cpk 1,51
CCpk 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 variationg p p
between 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
Outpu
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
Outpu
11
10
30272421181512963
10
9
Total variability
Mean shift Pooled within
= +Total variability
variability groups variability= +
Total Between Within
Capability PrecisionAccuracy

17
17
16
15
14
ut
13
12
Outpu
11
10
30272421181512963
10
9
2
g ng
22
g n
)X(X)X-X(n)XX( ∑ ∑∑∑ ∑ −+=−
Total variability
Mean shift Pooled within
= +
1j 1=i
jij
1j=1j= 1=i
ij )X(X)X-X(n)XX( ∑ ∑∑∑ ∑ =
+=
Total variability
variability groups variability= +
Short & Long Term Observations
Sample Size:(X Xij j
i=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=
2
j )X-X(n
are required for long
term investigations
Between Variation
1j
Overall Variation
(X X)ij
i 1
n
j 1
g
2
−∑∑
The number of data points
defining long- or short term is
Overall Variationi=1j=1
very process dependent

Definitions of Process Capability
Instantaneous 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 forp pp y p g
the 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 0,69
P-V alue 0,063
Mean 0,079697
StDev 0,014681
Summary for Moisture
File: Capability.mtw
0,110,100,090,080,070,060,05
V ariance 0,000216
Skewness 0,244654
Kurtosis -0,288605
N 33
Minimum 0,050000
1st Q uartile 0,070000
Median 0,080000
3rd Q uartile 0,090000
Maximum 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 0,019418
95% 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
IndividualValue
0,10
0,08
0 06
_
X=0,0797
Control Charts
I
3330272421181512963
0,06
0,04
0,02
LCL=0,0307
Observation
3330272421181512963
Calculation of the Process Capability
Stat
>Quality Tool
>Capability Analysis
File: Capability.mtw
>Capability Analysis
>Normal…
Short and long term measurementsg
of ashes and moisture content in
injection molding materials.
Enter Specification limits for
moisture,
lower limit 0, upper limit 0,15
In 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 0
Process Data Within
O ll
LB 0
Target *
USL 0,15
Sample Mean 0,079697
Sample N 33
StDev (Within) 0 0162803
C p *
C PL *
C PU 1,44
Potential (Within) C apability
Overall
StDev (Within) 0,0162803
StDev (O v erall) 0,014681
,
C pk 1,44
Pp *
PPL *
PPU 1 60
O v erall C apability
PPU 1,60
Ppk 1,60
C pm *
0,140,120,100,080,060,040,020,00
PPM < LB 0 00
PPM < LB *
PPM < LB *
Exp. O v erall Performance
PPM < LB 0,00
PPM > USL 0,00
PPM Total 0,00
PPM < LB
PPM > USL 7,86
PPM Total 7,86
PPM < LB
PPM > USL 0,84
PPM Total 0,84
Subgroups with the Box Plot
Boxplot of Moisture vs Charge
Graph
>Boxplot…
>One Y
0,11
0,10
>One Y
With Groups
isture
0,09
0,08
Mo
0,07
0,06
Cha e
7654321
,
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 Capability
Stat
>Quality Tool
>Capability Analysis>Capability Analysis
>Normal…
>Options…
LB USL
LB 0
Target *
USL 0 15
Process Data
Pp *
PPL *
PPU 1 60
USL 0,15
Sample N 33
PPU 1,60
Ppk 1,60
C pm *
0,140,120,100,080,060,040,020,00
PPM < LB 0,00
PPM > USL 0 00
PPM < LB *
PPM > USL 0 84
PPM > USL 0,00
PPM Total 0,00
PPM > USL 0,84
PPM Total 0,84
Capability Calculation for Subgroups
Stat
>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 1,247
Cpm *
0,1450,1150,0850,0550,025-0,005
0,6
0,3
0,0
Ppk 2,333
Cpm *
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 1,461
Ppk 1,461
Cpm *
0 1450 1150 0850 0550 0250 005
0,50
0,25
0,00
PPU 1,248
Ppk 1,248
Cpm *
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 1,905
Ppk 1 905
Overall 3
2
LB USL
Pp *
PPL *
PPU 1,841
Ppk 1 841
Overall
0,1450,1150,0850,0550,025-0,005
0,5
0,0
Ppk 1,905
Cpm *
0,1450,1150,0850,0550,025-0,005
1
0
Ppk 1,841
Cpm *
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 1,211
Ppk 1,211
Cpm *
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 Cpk
value. Pay attention to this example, the sample size is very small!
Pp and Ppk the accurate Calculation
The 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 c4
2 0 797850
the StDev (Overall) in order to consider the possible change.
!1
n ⎞
⎜
⎛ 2 0.797850
3 0.871530
4 0.905763
5 0.925222
( USL - LSL)
6 Stotal / C4
Pp =
!1
1-n
!1
2
n
1
2
c4
⎞
⎜
⎛
−
⎠
⎞
⎜
⎝
⎛
−
−
=
n
5 0.925222
6 0.937892
7 0.946837
8 0.953503
Thi dj t t f t C4 ill b d l f th l l ti f
total !1
2 ⎠
⎜
⎝
9 0.958669
10 0.962793
15 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 0.981305
25 0.985009
30 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 0
Target *
USL 0 15
Process Data
Within
Overall
Process Capability of Moisture LT
The variation from charge to charge
(between groups) is small in thisUSL 0,15
Sample N 132
StDev (Within) 0,019711
C p *
C PL *
C PU 1,19
C 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
PPU 1,28
Ppk 1,28
C pm *
p y
based on the overall variation only.
The overall variation defines the
process capability,,,,,,,,
PPM < LB 0,00
PPM > USL 0,00
PPM Total 0,00
PPM < LB *
PPM > USL 170,45
PPM Total 170,45
PPM < LB *
PPM > USL 60,04
PPM Total 60,04
Process Capability of Moisture LT
process capability
LB USL
LB 0
Target *
USL 0,15
Sample N 132
StD (O ll) 0 0183585
Process Data
Pp *
PPL *
PPU 1,28
Ppk 1,28
C pm *
0,140,120,100,080,060,040,02-0,00
PPM < LB 0,00
PPM < LB *
PPM > USL 0,00
PPM Total 0,00
PPM > USL 60,04
PPM Total 60,04
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 the
Capability
Short term
In this example we don‘t have the
possibility for improvements by the factor
charge!
Cp
Pp 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.
Cpk
Ppk 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 values
Stat
>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
Specifications
1
1
Process Capability Sixpack of Ash
Xbar Chart Capability Histogram
7654321
31
30
29
SampleMea
__
X=30,615
UCL=30,986
LCL=30,244
LSL 28
USL 32
Specifications
1
1
1,0
Range
_
R 0 643
UCL=1,360
3231302928Tests performed with unequal sample sizes
R Chart Normal Prob Plot
A D: 0,493, P: 0,202
7654321
0,5
0,0
Sample
R=0,643
LCL=0
34323028Tests performed with unequal sample sizes
32,5
31,0
29,5
Values
Within
O v erall
StDev 0,276554
C p 2,41
C pk 1,67
Within
StDev 0,888862
Pp 0,75
Ppk 0,52
C pm *
O v erall
Last 7 Subgroups Capability Plot
642
29,5
Sample
Specs
C 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%
Capability
Short term Long term
CCp
Pp
StDev withinStDev within
CpkCpk
Ppk
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?

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

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