Critical Parameter
Development & Mgt.
Deriving Capability Indices from “Scratch”
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?
Design Capability Studies, Copyright 2006, PDSS Inc.
2
Step 1: Measurement of samples of
functions
Measure the function by taking data as random,
independent, stable samples of a function within
the design…
Individuals
35
UCL=32.89
25
MU=20.39
15
5
Observation0
LCL=7.887
10
20
30
Function’s Distribution
During a Design Functional Capability Study we
gather design Functional Response data
Design Capability Studies, Copyright 2006, PDSS Inc.
3
Step 2: Assign Natural Tolerance Limits
to the Function’s Distribution…
Upper
Control
Limit
Lower
Control
Limit
Function’s Distribution
+3s
-3s
Y
99.73% of the FR’s data fall within the Control Limits
(+/- 3 Std. Devs. = Natural Tolerances of the Function)
Design Capability Studies, Copyright 2006, PDSS Inc.
4
Step 3: Assign Customer-based Tolerance
Limits to the Function’s Distribution…
Lower
Specification
Limit
LCL
UCL
Upper
Specification
Limit
Function’s Distribution
-6s
+3s
-3s
+6s
Y
99.9999998% of the FR’s data fall within the Spec. Limits
(+/- 6 Std. Devs. = Customer-based Tolerances of the Function)
Design Capability Studies, Copyright 2006, PDSS Inc.
5
Step 4: Recognize the design latitude
between the Control & Spec. Limits…
Lower
Specification
Limit
LCL
UCL
Upper
Specification
Limit
Function’s Distribution
-6s
+3s
-3s
+6s
Y
Each 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…
Design Capability Studies, Copyright 2006, PDSS Inc.
6
What is Cp?
Cp is the ratio of….
Lower
Specification
Limit
Mean is
centered on the
desired Target.
Desired
Target
Upper
Specification
Limit
+6s
-6s
Y
6xσ
Function’s Distribution
Design Capability Studies, Copyright 2006, PDSS Inc.
7
Short Term Capability Performance
LSL
USL
-6σ
+6σ
Measured
Design Performance
Mean stays on target in the
absence of assignable
causes of “noise”
Design Capability Studies, Copyright 2006, PDSS Inc.
USL − LSL
Cp =
6σ
Y = Target
-3σ
+3σ
Natural
Tolerances
This is what you develop
& measure in the Design
Phase…
8
What is Cpk?
Cpk is the ratio of….
Mean - LSL
3xσ
Function’s Distribution
Design Capability Studies, Copyright 2006, PDSS Inc.
Desired
Target
USL - Mean
Mean shifts
3xσ
Function’s Distribution
9
Long Term Capability Performance
Y is 1.5s off-Target USL
+6σ
LSL
-6σ
Shifted Design Performance
 Y − LSL USL − Y 

Cpk = Min
,
3σ 
 3σ
1.5σ
+ & - Mean Shifts are
caused by assignable
causes of “noise”
Design Capability Studies, Copyright 2006, PDSS Inc.
-3σ
+3σ
Natural
Tolerances
This is what you
intentionally create &
measure in the
Optimize Phase…
10
Forcing Cpk = Cp: Adjustability!
Function Adjustment Parameters are
FR Mean Shifters… driving k = 0!
Cpk : Off-Target
Performance due to
Unwanted Variation
Intro to CPD&M, Copyright 2010, PDSS Inc.
Cp: Mean
Adjusted
to VOC
Target
11
Maximizing Cp:
Linking Robustness & Adjustability!
Functional Robustness Parameters
are FR Variance Reducers
FAPs are CFR
Mean Shifters
Robust
against
Variation
Intro to CPD&M, Copyright 2010, PDSS Inc.
Mean
Adjusted
to VOC
Target
12
Required KP Mgt. Data for any form of
Capability Assessment
Gage R&R
All FRs or Functional Spec.s must have a
capable measurement process
documented & in use
G age name :
D ate of s tudy:
R eported by :
To lera nc e:
Mis c :
G ag e R &R (ANO VA) f or Thic kn ess
C om ponents of Variation
B y Part
Percent
1 00
8 .3
%C o nt rib utio n
%S tu dy Var
%To le ra nce
8 .2
8 .1
50
8 .0
7 .9
0
Ga ge R& R
R ep ea t
R e p ro d
Pa rt
P art-t o-P art
Sample Range
Fre d
2
3
5
6
7
8
9
10
8 .3
M ary
8 .2
U C L =0 .1 4 5 9
8 .1
0 .1
R = 0 .0 5 66 7
8 .0
LCL=0
0 .0
7 .9
Op e ra tor Fre d
0
Xbar Chart by Operator
Jo e
J oe
M ary
Operator*Part Interac tion
8 .1
U C L =8 .1 0 2
M e a n= 8. 0 44
8 .0
O p e ra tor
8 .2
M ary
Average
Fre d
8 .2
Sample Mean
4
By Operator
Jo e
L C L = 7. 98 6
7 .9
Fre d
J oe
M a ry
8 .1
8 .0
7 .9
Pa rt
0
Gage R&R Study
1
2
3
4
5
6
7
8
9
10
I & MR Chart
Individual Value
I and MR Chart for C2
UCL=5.917
5
0
Mean=-0.03816
-5
LCL=-5.994
Subgroup
0
50
100
10
Moving Range
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
1
R C hart by O perator
0 .2
UCL=7.316
5
R=2.239
LCL=0
0
Capability Study
P r oc es s C a p a b ilit y A na ly s is fo r C 2
LSL
P ro c es s D at a
US L
All FRs & Functional Spec.s are Capable typically w/ target of Cp = 2 & Cpk of 1.5
Intro to CPD&M, Copyright 2010, PDSS Inc.
U SL
1 2 .0 00 0
T arg e t
W ith in
*
LSL
8 .0 00 0
M e an
9 .9 76 6
S a m ple N
O ve ra l l
10 0
S t D e v (W ith in)
0 . 44 7 13 4
S t D e v (O ve ra ll)
0 . 45 8 18 6
Po te n tia l (W it hin ) C ap a bility
Cp
1 .4 9
C PU
1 .5 1
C PL
1 .4 7
C pk
1 .4 7
C pm
*
O v era ll C a p ab ilit y
8
9
10
O b se rve d P e rfo rm a n ce
11
E xp. "W ith in " P e rfo rm an c e
12
Ex p. "O ve rall" P e rfo rm a n c e
Pp
1 .4 6
P PM < L S L
0 .0 0
P P M < LS L
4 . 92
P P M < LS L
PPU
1 .4 7
P PM > U S L
0 .0 0
P P M > US L
3 . 02
P P M > US L
PPL
1 .4 4
P PM T ot al
0 .0 0
P P M To ta l
7 . 94
P P M To ta l
Ppk
1 .4 4
13
8 .0 1
5 .0 3
1 3 .0 4
Y as a Function of Controlling Xs
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 Adjusting
Xj dominates the Standard Deviation… for Robustness
Xk 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!?!?
Design Capability Studies, Copyright 2006, PDSS Inc.
14
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....
Design Capability Studies, Copyright 2006, PDSS Inc.
15
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ESD.33 Systems Engineering
Summer 2010
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