12 steps for a critical parameter development project steps for a critical parameter development...

PDSS Critical Parameter Development & Mgt. Process Quick Guide

12 Steps for a Critical Parameter Development Project (incl. 6 Check Points)

Step 1: Create a CP Project Charter - establish goal, objectives, team members, roles & responsibilities, time line & scope - define clear, specific & measurable CP project results

Step 2: Create a cross-functional team of experts to help ID a thorough set of CPs - make sure they are well balanced, right mix of people (experience & judgment) - good at mistake-proofing the list of parameters (methods for mistake-proofing)

Step 3: Generate / Assess Requirement Clarity, Classification & Flow-down - define Critical System level functional Reqts & their tolerance limits (USL & LSL) - define NUD (Critical) & ECO (non-Critical) requirements as they flow down to subsystems,

subassemblies, parts, materials and mfg. /assy./ packaging processes

Scope of CP Activity

Step 4: Generate I-O-C Diagrams, P – Diagram, Noise Diagrams & the Boundary Diagram - identify high level mass, energy & information flows into and out of the system, subsystems & subassemblies - identify candidate Critical functions, inputs, outputs, controllable parameters & noises - Define leading and lagging indicators & their units of measure - identify unit-to-unit, external / environmental & deteriorative noise parameters - preliminary documentation of required measurement systems

Step 5: Structure a Critical Parameter Flow-down Tree - Define the relationships between Y, ys & their controlling xs

o Function Trees & Functional Flow Diagrams

CP candidate structure & prioritize for focus areas

o Math Models - Define macro-relationships aligned with Critical noise parameters; which are NUD?

- Plan to separate which xs dominate & control the mean & which control σ for each Y & sub-y - Conduct Potential Problem Prevention & Impact Mitigation Analysis (P3IMA Table aka FMEA)

o Laws of Unintended Consequences (unwanted functions)

Step 6: Identify unique sub-areas of focus; lean out, rank & prioritize the areas to work on - Group prioritized CP flows with the biggest impact on the reqts; apply 6 Step Prevention Process - Select the appropriate groups of flows that matter the most; again – which are NUD? - Align critical noise parameters with the appropriate sub-groups

Step 7: Prove measurement systems are capable - MSA & Gage R&R Studies for Critical Ys, sub-ys & controlling Xs (for both leading & lagging indicators)

Step 8: Design & conduct experiments (problem ID & prevention!) - screening experiments (separate signal from random noise)- modeling experiments (linear & non-linear effects plus interactivity)- noise parameter strength experiments (what shifts the mean or spreads the variance?)- robustness experiments- tolerance sensitivity experiments

Step 9: Analyze data using ANOVA & other statistical methods that identify sensitivities & level of capability

- define statistical significance (p values)- MSparameter / MStotal

- Cp & Cpk values- Capability Growth Indices (CGI maturation by development process phase)

Facts database of CPs & their relationships

© 2010 PDSS Inc. page 1 of 11


Step 10: Establish & Verify tolerance ranges & % contribution to variation of critical Ys & sub-ys

- USL & LSL for both nominal conditions & stressful conditions (robust tolerances) - establish variance role-up model (s2 total = s21 + s22 + …. + s2 n) - verify & validate final design & processing set points

Step 11: Mfg. & Production Implementation Plan for Critical Parameters - Establish production & assembly data requirements & data utilization plan o Agreement on what constitutes a production or assembly CP

� In-process CPs on the process itself � Within-process or post-process CPs (on parts, sub-assy, sub-system

or system during mfg., assembly, packaging or upon receipt) o Requirements/Specifications to measure production & assembly CPs against o SPC & Cp/Cpk Study requirements & procedures

� Frequency of measurements & action based upon data � Critical Cpk>>>Cp Adjustment parameters (mean shifters)

o Measurement system requirements & acceptable signal/noise resolution o Contingency & Corrective Action plans

� Alternative action plan � Process specific LSS-based corrective action process plan

• Kaizen event or 6σ Project?

Step 12: Evaluate Quality and Implement Changes in a Control plan - Develop and submit alternate acceptance plans that maintain or improve functional

quality with reduced acceptance costs o Select acceptance plan that meets overall program needs o Verify performance of selected plan o Implement changes as supported by data per the control plan

Documented CP set points

Conduct CP summary reviews & make Cpk>>>Cp adjustments as needed during steady state mfg.

Change Implementation and Document Ongoing Control Plan



CP Step Enabling Tools, Methods or Best Practices Step 1: Create a CP Project Charter

Project Planning tools (MS Project); Monte Carlo Simulations of Critical the Path of Task Flows (@Risk Software Tool; Palisades), Cost Estimation, SMART Problem & Goal Identification, Intro. to CP Module

Step 2: Create a cross-functional team of experts to help ID a thorough set of CPs

Specific Experience, Technical Expertise & Judgment, Prefer DFLSS trained individuals on the IPT; can be trained and mentored JIT as required

Step 3: Generate / Assess Requirement Clarity, Classification & Flow-down Documentation

Customer/Stakeholder ID, Interviewing Methods, KJ Method, NUD vs. ECO Classification, Kano Method, Quality Function Deployment (QFD) & the Houses of Quality, DOORS Reqts. Software Tool, CP Reqt. Database Documentation, CP Reqts. Worksheets

Step 4: Generate I-OC Diagrams, P-Diagrams, Noise Diagrams, Boundary Diagrams & Math Models

I-O-C Diagramming, P-Diagramming, Noise Diagramming, System Noise Mapping, Boundary & Interface Diagramming, 1st Principles Modeling & Simulations

Step 5: Structure a Critical Characteristics Flow-down Tree

Functional Diagramming, FAST Diagramming, Tree Diagramming, Flow Diagramming, CocCPit CPM Software Tool (Cognition), CP Data Base Construction Module, CP Score Card Structuring Module, CP Reqts. & Measured Y Worksheets

Step 6: Identify unique subareas of focus; lean out, rank & prioritize the areas to work

NUD vs. ECO Classification, Kano Classification, Pareto Process, QFD Reqts. Ranking & Prioritization, Function Trees, Noise Diagrams, FMEAs

Step 7: Prove measurement systems are capable

Measurement System Analysis, Gage R&R Studies



Step 8: Design & conduct experiments

SPC Studies, Capability Studies, Sample-size Determination, Sample Data Parameter & Distribution Characterization Studies, Multi-vari Correlation Studies, t-Tests for 2 Way Comparisons, DOE Methods: Full & Fractional Factorial Designs, Screening Experiments, Modeling Experiments, Optimization Experiments, Mixture Experiments, Robustness Development Experiments, System Integration Sensitivity Experiments, Tolerance Balancing Experiments, ALT, HALT & HAST, Duane Plotting

Step 9: Analyze data using ANOVA & other statistical methods that identify sensitivities & level of capability

Descriptive, Graphical & Inferential Statistical Data Analysis Methods, Confidence Interval Analysis, ANOVA, Regression, Main Effects & Interaction Plotting, CP Documentation & CP Scorecards

Step 10: Establish & Verify tolerance ranges & % contribution to variation of critical Ys & sub-ys

Screening DOEs (Plackett-Burman Arrays), ANOVA, Taguchi Loss Function, Additive Variance Modeling, SPC & Capability Studies, CP Documentation & CP Scorecards

Steps 11-12: Mfg. & Production Implementation Plan

Control Planning, Quality Planning, SPC Studies, Capability Studies, CP Allocation for Production & Assembly Processes, CP Documentation & CP Scorecards, CP Deployment in Production & Supply Chain Environments Module


σ6

LSLUSLCp

−σ6

LSLUSLCp

−


Recommendation for linking NUD requirements to CPs for Capability tracking

= = What is Required? What is Measured?

Customer Level (USL – LSL) Customer Level (Avg & σ) System Level (USL – LSL) System Level (Avg & σ)

Subsystem Level (USL – LSL) Subsystem Level (Avg & σ) Subassembly Level (USL – LSL) Subassembly Level (Avg & σ) Component Level (USL – LSL) Component Level (Avg & σ)

Mfg. Process Level (USL – LSL) Mfg. Process Level (Avg & σ)

From this comparison we can document performance Capability

− σ3

, XUSLLSL

8 9 1 0 1 1 1 2

L SL U S L

P ro c e ss C a p a b ilit y A n a ly s is f o r C2

U S L

T a r ge t

L S L

M e an

S am ple N

S tD ev ( W ith in )

S tD ev ( 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 pk

P P M < L S L

P P M > US L

P P M T o t al

P P M < L S L

P P M > US L

P P M T ot al

P P M < L S L

P P M > US L

P P M T ot al

1 2 .0 00 0

*

8 .0 00 0

9 .9 76 6

10 0

0 .4 4 7 13 4

0 .4 5 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 e ss D a ta

P o te nt ial (W ith in) C a pa b ility

O v er a ll C a pa b ility O b s e rv ed P er fo r m a n ce E xp . " W ith in " P e r fo rm a nc e E xp . "O v er a ll" P e r fo rm an c e

W ithi n

Ove ral l

8 9 1 0 1 1 1 2

L SL U S L

P ro c e ss C a p a b ilit y A n a ly s is f o r C2

U SL

T a r ge t

L SL

M e an

S am ple N

S tD ev ( W ith in )

S tD ev ( O ve ra ll)

C p

C PU

C PL

C p k

C p m

P p

P PU

P PL

P pk

PPM < L SL

PPM > US L

PPM T o t al

PP M < L SL

PP M > US L

PP M T ot al

PPM < L SL

PPM > US L

PPM T ot al

1 2 .0 00 0

*

8 .0 00 0

9 .9 76 6

10 0

0 .4 4 7 13 4

0 .4 5 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 e ss D a ta

P o te nt ial (W ith in) C a pa b ility

O v er a ll C a pa b ility O b s e rv ed P er fo r m a n ce E xp . " W ith in " Pe r fo rm a nc e E xp . "O v er a ll" Pe r fo rm an c e

W ithi n

Ove ral l

USL − LSLCp =

6σ

X −Cpk = Min

3σ

Summary of Critical CPM Actions:

CPM Actions Reliability Actions Metrics: scalars & vectors; continuous variables Metrics: time-based failures; discrete events Y=f(x) physics –based models Additive / Product Functions; serial / parallel

Time-To-Failure models P-Diagrams Reliability Block Diagrams

Noise Diagrams FMEA, FMECA & Fault Tree Analysis Function Trees Duane Reliability Growth Plots

Functional Flow Diagrams Normal Reliability Tests Form Hypotheses & prioritize evaluations Accelerated Reliability Tests

Screening & Modeling DOEs under nominal conditions

HALT, HASS & HAST evaluations

Robustness experiments under stressful conditions

FRACAS

Tolerance balancing experiments under nominal & stressful conditions


-


Problem Prevention Steps: The 6 Steps for Problem Prevention:

• Design a Diagram of detailed functions in their serial & parallel flowsPlan & • These are value-addedfunctions that possess inherent robustnessRank • Rank& prioritize the value of each function relative to one anotherTasks

• Define potential problems that can occur within & between the functions Define • A statement of the mistakes or errors that characterize the problem

Potential • Identification of Leading Indicatorsthat measure the on-set of a problemProblems

• Evaluate & document the root causes of the potential problemsEvaluate • Understand the mechanisms behind all impending problemsCauses

• Define preventive actions for effectiveness & value Define

Preventive • Finalize, measure & track leading indicators – be proactively efficientActions

• Define contingencyplans if the problem actually occurs Define • Finalize, Measure & track leading & lagging indicators – be reactively effectiveafter

Contingent indicators reach a trigger point. Actions

• Re-use the lessons learned for future use & reactivityRe Use • Continuously improve the problem prevention processLearning

The P3IMA Table to help with the Problem Prevention StepsThe Potential Problem Prevention & Impact Mitigation Analysis (P3IMA)(a derivative of FMEA)

Critical Potential Likely Probabilityof Preventive Ability to Severity of Contingency Function Problem Causes Occurrence Action Detect Impact Action

Onset


0

5

10

-1 1 -1 1 -1 1

-1 1 -1 1


What do I keep track of? & how do I do it? 7 Things to prove you are ok!

Measure How? Measurability MSA: Gage R&R Study

Stability SPC Chart: I & MR Tunability DOE, RSM, Regression Y=F(CAPs)

Sensitivity & Stat. Significance DOE, p-Value, ANOVA:DY/DX Interactivity DOE, ANOVA: Xa * Xb

Capability Capability Indices: Cp & Cpk Robustness DOE, S/n: COV, std. deviation

If these items are problematic and not in control then these are NUD parameters that are very good candidates for Critical Parameter status… until proven under control and able to be re-classified as Easy, Common & Old. Measurability:

Gage name : D ate of s tudy:

Gage R&R (ANOVA) for Thickness R eported by :

Mis c : To lera nc e:

1 00

C om ponents of Variat ion

%C o nt rib utio n %S tu dy Var

8 .3

8 .2

B y Part

Sam

ple

Mea

nSa

mpl

e R

ange

P

erce

nt

%To le ra nce 50 8 .1

8 .0

0 7 .9

Gage R& R Repea t Rep rod P art-t o-P art Part 1 2 3 4 5 6 7 8 9 10

R Chart by O perator By Operator 0 .2 Fred Joe M ary 8 .3

UCL =0 .1459 8 .2

0 .1 8 .1

R = 0 .0 5 66 7 8 .0

0 .0 LCL =0 7 .9

0 Operator Fred J oe Mary

Xbar Chart by Operator Operator*Part Interac tion Operator

Fred J oe

8 .2 Fred Joe M ary 8 .2

8 .1 UCL =8 .102

M e a n= 8. 0 44 8 .0 L C L = 7. 98 6 A

vera

ge

8 .1

8 .0

M a ry

7 .9 7 .9

Part 1 2 3 4 5 6 7 8 9 10 Stability:

I and MR Chart for C2

UCL=5.917

Indi

vidu

al V

alue

0 Mean=-0.03816

-5 LCL=-5.994

Subgroup 0 50 100

Mov

ing

Ra

nge

UCL=7.316

5

R=2.239

0 LCL=0

Tunability:

ANOVA: Y plus Noise versus A, B, C Main Effects Plot - Data Means for Yplus Noise

Factor Type Levels Values A fixed 2 -1 1 B fixed 2 -1 1 C fixed 2 -1 1 30

Surface Plot of Cool Tim A B C

Analysis of Variance for Y plus N

25 Source DF SS MS F P A 1 69.82 69.82 196.14 0.000 B 1 401.70 401.70 1128.38 0.000 C 1 1620.35 1620.35 4551.60 0.000 Y

plus

Noi

se

20

15

A*B 1 27.82 27.82 78.14 0.000 A*C 1 110.85 110.85 311.38 0.000 B*C 1 0.00 0.00 0.00 0.969 10

6A*B*C 1 0.00 0.00 0.00 0.967 Error 8 2.85 0.36 Total 15 2233.39 5

4

Interaction Plot (data means) for Y plus Noise 3Cool Time (sec)

2

1

A 30 Effect Sum of Squares epsilon2 %epsilon2

1 20

A 69.82 69.82/2233.39=0.031 3.1% 2 10 0 1

B 401.70 401.70/2233.39=0.18 18% 0B 30 -2 -1 Temp

C 1620.35 1620.35/2233.39=0.72 72% -1 0 -2

1 20 AC 27.82 27.82/2233.39=0.012 1.2% Speed 1

2 -1 10

AB 110.85 110.85/2233.39=0.05 5%

C Total 2233.39

Hold values: Vol: 0.0


-1


Interactivity: ANOVA: Y plus Noise versus A, B, C Factor Type Levels Values A fixed 2 -1 1 B fixed 2 -1 1 C fixed 2 -1 1

Analysis of Variance for Y plus N

Source DF SS MS F P A 1 69.82 69.82 196.14 0.000 B 1 401.70 401.70 1128.38 0.000 C 1 1620.35 1620.35 4551.60 0.000 A*B 1 27.82 27.82 78.14 0.000 A*C 1 110.85 110.85 311.38 0.000 B*C 1 0.00 0.00 0.00 0.969 A*B*C 1 0.00 0.00 0.00 0.967 Error 8 2.85 0.36 Total 15 2233.39

A B C

-1 1 -1

1 -1 1

10

15

20

25

30

Y p

lus

Noi

se

Main Effects Plot - Data Means for Y plus Noise

-1 1 -1 1

10

20

30

10

20

30 A

B

C

-1

1

-1

1

Interaction Plot (data means) for Y plus Noise

Effect Sum of Squares epsilon2 %epsilon2

A 69.82 69.82/2233. 39=0.031 3. 1%

B 401. 70 401.70/2233.39=0.18 18%

C 1620.35 1620. 35/2233.39=0.72 72%

AC 27.82 27.82/2233. 39=0.012 1. 2%

AB 110. 85 110.85/2233.39=0.05 5%

Total 2233.39

Sensitivity & Statistical Significance:• Resistor G [36,960/105,227] x [100] = 35% • Resistor I [29,843/105,227] x [100] = 28% • Resistor D [14,945 /105,227] x [100]= 14% • Capacitor C [10,764/105,227] x [100]= 10% • Resistor B [6,281/105,227] x [100]= 6% • Resistor A [3,335/105,227] x [100]= 3% • Transistor C [1,580/105,227] x [100]= 1.5% • Transistor F [716/105,227] x [100]= 0.68%

Source DF Seq SS Adj SS Adj MS F P

Res A 1 3335 3335 3335 24.88 0.002

Res B 1 6281 6281 6281 46.85 0.000

Cap C 1 10764 10764 10764 80.29 0.000

Res D 1 14945 14945 14945 111.48 0.000

Trans F 1 716 716 716 5.34 0.054

Res G 1 36960 36960 36960 275.69 0.000

Res I 1 29843 29843 29843 222.60 0.000

Trans K 1 1580 1580 1580 11.79 0.011

Error 7 938 938 134

Total 15 105361 105227

Total MS

28.44

14.24

10.26

5.99 3.18

1.5 0.68 0.39

35.23

0

5

10

15

20

25

30

35

40

Re

sis

tor

G

Re

sis

tor

I

Re

sis

tor

D

Cap

. C

Re

sis

tor

B

Re

sis

tor

A

Tra

ns

. K

Tra

ns

. F

Vo

ltag

e L

% Contribution

Capability:

8 9 1 0 1 1 1 2

L S L US L

P ro c e s s C a p a b ilit y A n a ly s is fo r C 2

U SL

T ar get

LS L

Me an

S am ple N

S tD ev ( W ith in)

S tD ev ( O ve rall)

C p

C P U

C P L

C p k

C p m

P p

P PU

P PL

P pk

PP M < L SL

PP M > U S L

PP M T ot al

P P M < L SL

P P M > U S L

P P M T ot al

PP M < L SL

PP M > U S L

PP M T ot al

12. 00 00

*

8. 00 00

9. 97 66

1 00

0 .4 471 34

0 .4 581 86

1. 49

1. 51

1. 47

1. 47

*

1. 46

1. 47

1. 44

1. 44

0 .0 0

0 .0 0

0 .0 0

4 .9 2

3 .0 2

7 .9 4

8. 01

5. 03

13. 04

P roc es s D at a

Po te nt ial (W it hin) C apa bilit y

O v era ll C apa bilit y O bs e rv ed P erf or m a nc e E xp . "W it hin " Pe rf orm an c e Ex p. "O v era ll" Pe rf orm an c e

W ith in

O ve ra ll

Robustness:

Yavg Sensitivity to Noise!

A1 Critical Functional

RobustnessParameter (CFRP)

A2 Robustness

N1 N2

CompoundedNoise Factors



Example of getting Functions right and driving your CP development methodology:

If I have 5 Functions, then I have at least 5 measurable ys. Each y variable is dependent on one or more X variables.

First, we define all 5 functions verbally using verb-noun pairs on Post It notes. This results in vertical branches of lists of functions called Function Trees. The top of the tree is a big Y, which is your business or VOC based requirement. This is usually not stated in physics terms but rather quality, financial or some other non-physics form of units of measure. We MUST state our functions in fundamental units of physical measure. You can have multiple branches of functions coming from multiple Voice of Business (VOB) goals or Voice of Customer (VOC) requirements…

Y = Business Goal 1 (VOB) or Customer Reqt. 1 (VOC)

Function Tree Diagram

F1

F2

F3

F4

F5

F1

F2

F3

F4

F5

time

Functional Flow Diagram

Next, we rearrange the Post It notes containing the Functions into their horizontal flow relationships over time. This will result in a serial-parallel flow diagram of exactly how the functions occur over time.

Each function is quantified as a y variable and is stated in its physics-based units of measure (ascalar or vector). We add the y variables and their units of physical measure to the Post It notes.

F1…y1



Next we must define each X variable that controls or influences each y…

X variables come in 4 varieties:

X mean shifter = controllable parameter that has a strong ability to move the mean of y

X std. dev. shifter = controllable parameter that has a strong ability to move the value of σσσσX COV shifter = controllable parameter that has a strong ability to move both the mean of y and the

value of σσσσ (a coupled affect on both statistical parameters! Called the Coefficient of Variation: COV

= (σ/mean) X noise inducer = an uncontrollable parameter that has a strong ability to either move the mean of y,

the value of σσσσ or the COV. They come from either External, Unit-Unit or Deteriorative sources.

So for each X we can create a Post It note to align with each y…

Xa = … Xb = … Xn = …

To define the candidate critical parameter ys & Xs; we lay out the functional relationships

F1…y1 Xa = … Xb = … Xn = …

For each function you develop a Y = f(X…) model. This is a set of “hypotheses” that must be proven to be complete and true. DOEs will answer the following questions…

y1 = f(Xa, Xb, …) ΔΔΔΔy1 = f(ΔΔΔΔXa, ΔΔΔΔXb, …); σσσσ2 of y1 = f(σσσσ2 from ΔΔΔΔXa, σσσσ2 from ΔΔΔΔXb,…)





We will know the model is complete by developing both analytical & empirical models. If our correlation coefficient (R2) for the empirical model is high, then we know very little of the data is attributable to missing Xs and in fact the error on the model is due to random effects and not missed X parameters. If random error is small, then our model is good and our data acquisition system is too. If random error is high and our GR&R is over 10-20% we have a measurement system problem to correct!

We will know the model is true because the terms, coefficients, linearity or curvature in the analytical and empirical models are in agreement and that the X parameters are all statistically significant – a parsimonius or efficient model! Assumptions will have been proven or corrected.



What about Noise and its affect of the Functions (ys) and the relationship of (X * Noise)interactions.

The Noise Diagrams:

For the Function, what noises cause it to vary?

Unit-UnitNoises

Function Δy = f(Xs)

External Noises

Mean of y & σ

DeteriorationNoises

For any X variable that is not a Noise Parameter, what noises cause it to vary? X variations

ΔXn

Unit-Unit Noises

External Noises

Mean of y & σ

DeteriorationNoises

We must know what noise parameters really affect our Xs & Ys so we can conduct robust design experiments to assess interactivity between the Xs & the Noises. These noises will also impact k in Cpk assessment because they are able to cause both mean shifts and variance growth.


MIT OpenCourseWarehttp://ocw.mit.edu

ESD.33 Systems Engineering Summer 2010

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

http://ocw.mit.edu

http://ocw.mit.edu/terms

12 steps for a critical parameter development project steps for a critical parameter development...

Documents