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Critical Parameter Development & Mgt.
Deriving Capability Indices from “Scratch”
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Design Capability Studies, Copyright 2006, PDSS Inc. 2
Agenda
�Demonstrate the 4 simple steps for deriving a Cp Index from Sample Data
�How it impacts the 7 Checks for Criticality!� Measurable?
� Stable?
� Adjustable?
� Interactive?
� Sensitive?
� Robust?
� Capable?
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Design Capability Studies, Copyright 2006, PDSS Inc. 3
Step 1: Measurement of samples of functions
�Measure the function by taking data as random, independent, stable samples of a function within the design…
During a Design Functional Capability Study we gather design Functional Response data
Function’s Distribution
3020100
35
25
15
5Observation
Indi
vidu
als
MU=20.39
UCL=32.89
LCL=7.887
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Step 2: Assign Natural Tolerance Limits
to the Function’s Distribution…
Design Capability Studies, Copyright 2006, PDSS Inc. 4
Lower Control
Limit
Function’s Distribution
Upper Control
Limit
-3s +3s
Y99.73% of the FR’s data fall within the Control Lim its (+/- 3 Std. Devs. = Natural Tolerances of the Functi on)
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Step 3: Assign Customer-based Tolerance
Limits to the Function’s Distribution…
Design Capability Studies, Copyright 2006, PDSS Inc. 5
Lower Specification
Limit
Function’s Distribution
Upper Specification
Limit
-3s +3s
Y99.9999998% of the FR’s data fall within the Spec. Limits
(+/- 6 Std. Devs. = Customer-based Tolerances of the Function)
-6s +6s
LCL UCL
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Step 4: Recognize the design latitude between the Control & Spec. Limits…
Design Capability Studies, Copyright 2006, PDSS Inc. 6
Lower Specification
Limit
Function’s Distribution
Upper Specification
Limit
-3s +3s
YEach side of the Function’s distribution has 3s of latitude between the Control Limits & Spec. Limits, when the mean is centered on
the VOC Target Value…
-6s +6s
LCL UCL
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What is Cp?
Design Capability Studies, Copyright 2006, PDSS Inc. 7
Cp is the ratio of….
Function’s Distribution
Lower Specification
Limit
Upper Specification
Limit
Y
-6s +6s
6 x σσσσ
Mean is centered on the desired Target.
Desired Target
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Design Capability Studies, Copyright 2006, PDSS Inc. 8
LSL USL
Y = Target
-6σ +6σ
+3σ-3σ
Measured Design Performance
Natural Tolerances
Mean stays on target in the absence of assignable causes of “noise”
This is what you develop & measure in the Design Phase…
Short Term Capability Performance
6σ
LSLUSLCp
−=
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Mean shifts
Desired Target
What is Cpk?
Design Capability Studies, Copyright 2006, PDSS Inc. 9
Cpk is the ratio of….
Function’s Distribution Function’s Distribution
3 x σ 3 x σ
Mean - LSL USL - Mean
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Design Capability Studies, Copyright 2006, PDSS Inc. 10
Long Term Capability Performance
LSL USLY is 1.5s off-Target-6σ +6σ
+3σ-3σ
Shifted Design Performance
1.5σ
Natural Tolerances
+ & - Mean Shifts are caused by assignable
causes of “noise”
This is what you intentionally create & measure in the Optimize Phase…
−−=3σ
YUSL,
3σ
LSLYMinCpk
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Intro to CPD&M, Copyright 2010, PDSS Inc. 11
Forcing Cpk = Cp: Adjustability!
Function Adjustment Parameters are FR Mean Shifters… driving k = 0!
Cp: Mean Adjusted to VOC Target
Cpk : Off-Target Performance due to Unwanted Variation
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Intro to CPD&M, Copyright 2010, PDSS Inc. 12
Maximizing Cp: Linking Robustness & Adjustability!
FAPs are CFR Mean Shifters
Functional Robustness Parameters are FR Variance Reducers
Mean Adjusted to VOC Target
Robust against
Variation
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Required KP Mgt. Data for any form of Capability Assessment
Intro to CPD&M, Copyright 2010, PDSS Inc. 13
� All FRs or Functional Spec.s must have a capable measurement processdocumented & in use
� Gage R&R Study
� Each FR or Functional Spec. is placed under stable SPC so the Cp can be routinely quantified for Phase-by-Phase growth & Life Cycle stability characterization
� All FRs & Functional Spec.s are Capable -typically w/ target of Cp = 2 & Cpk of 1.5 8 9 10 11 12
L SL U SL
Proc es s Ca p a b il ity A na lys is fo r C2
US L
T arg e t
L S L
M e an
S a m ple N
S t De v (W ith in)
S t De v (O ve ra ll)
C p
C P U
C P L
C p k
C p m
P p
P P U
P P L
P p k
P PM < L S L
P PM > US L
P PM T ot al
P P M < LS L
P P M > US L
P P M To ta l
P P M < LS L
P P M > US L
P P M To ta l
1 2 .0 00 0
*
8 .0 00 0
9 .9 76 6
10 0
0 . 44 7 13 4
0 . 45 8 18 6
1 .4 9
1 .5 1
1 .4 7
1 .4 7
*
1 .4 6
1 .4 7
1 .4 4
1 .4 4
0 .0 0
0 .0 0
0 .0 0
4 . 92
3 . 02
7 . 94
8 .0 1
5 .0 3
1 3 .0 4
P ro c es s D at a
Po te n tia l (W it hin ) C ap a bility
O v era ll Ca p ab ilit y O b se rve d P e rfo rm a n ce E xp. "W ith in " P e rfo rm an c e Ex p. "O ve rall" P e rfo rm a n c e
W ith in
O ve ra l l
Misc :To lera nce:R eported by :D ate of s tudy:Gage name :
0
8 .2
8 .1
8 .0
7 .9
M aryJoeFred
Xbar Chart by Operator
Sam
ple
Mea
n
Mean=8.044
UCL=8 .102
LCL=7.986
0
0 .2
0 .1
0 .0
M aryJoeFred
R Chart by O perator
Sam
ple
Ran
ge
R=0 .05667
UCL=0 .1459
LCL=0
10 9 8 7 6 5 4 3 2 1
8 .2
8 .1
8 .0
7 .9
Part
OperatorOperator*Part Interac tion
Ave
rage
Fred J oe Mary
MaryJ oeFred
8 .3
8 .2
8 .1
8 .0
7 .9
Operator
By Operator10 9 8 7 6 5 4 3 2 1
8 .3
8 .2
8 .1
8 .0
7 .9
Part
B y Part
%Cont ribution %S tudy Var %To le rance
P art-t o-P artRep rodRepea tGage R& R
100
50
0
Com ponents of Variat ion
Per
cent
Gage R&R (ANOVA) for Thickness
10050Subgroup 0
5
0
-5
Indi
vidu
al V
alue
Mean=-0.03816
UCL=5.917
LCL=-5.994
10
5
0
Mov
ing
Ran
ge
R=2.239
UCL=7.316
LCL=0
I and MR Chart for C2
Gage R&R
I & MR Chart
Capability Study
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Y as a Function of Controlling Xs
Design Capability Studies, Copyright 2006, PDSS Inc. 14
For a given Y there can be numerous controlling Xs….
There can be 3 ways for a controlling X to influence Y:Xi dominates the Mean… for AdjustingXj dominates the Standard Deviation… for RobustnessXk co-contributes to both the Mean & σ... You pick!
The question CPD&M asks is “do you know how Xs affect Ys in light of the 7 Checks???
- Which ones are out of control!?!?
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Design Capability Studies, Copyright 2006, PDSS Inc. 15
Summary
� You should be able to repeat this explanation
� It is important for you to be able to do this for anyone you work with.
� An organization practicing CPD&M must understand Capability
� How it degrades....
� how it grows & matures due to intentional investment in KP development tasks....
� How it is calculated....
� What it means in the context of CPD&M....
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MIT OpenCourseWarehttp://ocw.mit.edu
ESD.33 Systems EngineeringSummer 2010
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