Critical Parameter Development & Mgt.

Deriving Capability Indices from “Scratch”

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?

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

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)

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

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

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

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

−=

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

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

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

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

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

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!?!?

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....

MIT OpenCourseWarehttp://ocw.mit.edu

ESD.33 Systems EngineeringSummer 2010

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