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 Scope of CP
define clear, specific & measurable CP project results
Activity
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
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
-
CP candidate structure &
Define the relationships between Y, ys & their controlling xs
prioritize for focus areas
o Function Trees & Functional Flow Diagrams
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)
Facts database of CPs &
MSparameter / MStotal
their relationships
-
Cp & Cpk values
Capability Growth Indices (CGI maturation by development process phase)
© 2010 PDSS Inc.
page 1 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
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 + …. + s2n)
verify & validate final design & processing set points
Documented CP 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?
Conduct CP summary
reviews & make
Cpk>>>Cp adjustments
as needed during steady
state mfg.
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
Change Implementation
and Document Ongoing
Control Plan
© 2010 PDSS Inc.
page 2 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
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 Specific Experience, Technical Expertise & Judgment, Prefer
a crossDFLSS trained individuals on the IPT; can be trained and
functional team mentored JIT as required
of experts to
help ID a
thorough set of
CPs
Step 3:
Customer/Stakeholder ID, Interviewing Methods, KJ Method,
Generate /
NUD vs. ECO Classification, Kano Method, Quality Function
Assess
Deployment (QFD) & the Houses of Quality, DOORS Reqts.
Requirement
Software Tool, CP Reqt. Database Documentation, CP
Clarity,
Reqts. Worksheets
Classification &
Flow-down
Documentation
Step 4:
I-O-C Diagramming, P-Diagramming, Noise Diagramming,
Generate I-O­ System Noise Mapping, Boundary & Interface Diagramming,
C Diagrams, P- 1st Principles Modeling & Simulations
Diagrams,
Noise
Diagrams,
Boundary
Diagrams &
Math Models
Step 5:
Functional Diagramming, FAST Diagramming, Tree
Structure a
Diagramming, Flow Diagramming, CocCPit CPM Software
Critical
Tool (Cognition), CP Data Base Construction Module, CP
Characteristics Score Card Structuring Module, CP Reqts. & Measured Y
Flow-down
Worksheets
Tree
Step 6: Identify NUD vs. ECO Classification, Kano Classification, Pareto
unique sub­
Process, QFD Reqts. Ranking & Prioritization, Function
areas of focus; Trees, Noise Diagrams, FMEAs
lean out, rank
& prioritize the
areas to work
Step 7: Prove
Measurement System Analysis, Gage R&R Studies
measurement
systems are
capable
© 2010 PDSS Inc.
page 3 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
Step 8: Design
& conduct
experiments
Step 9:
Analyze data
using ANOVA
& other
statistical
methods that
identify
sensitivities &
level of
capability
Step 10:
Establish &
Verify
tolerance
ranges & %
contribution to
variation of
critical Ys &
sub-ys
Steps 11-12:
Mfg. &
Production
Implementation
Plan
© 2010 PDSS Inc.
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
Descriptive, Graphical & Inferential Statistical Data Analysis
Methods, Confidence Interval Analysis, ANOVA, Regression,
Main Effects & Interaction Plotting, CP Documentation & CP
Scorecards
Screening DOEs (Plackett-Burman Arrays), ANOVA, Taguchi
Loss Function, Additive Variance Modeling, SPC & Capability
Studies, CP Documentation & CP Scorecards
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
page 4 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
Recommendation for linking NUD requirements to CPs for Capability tracking
Cp =
USL − LSL
Cp =
6σ
What is Required?
Customer Level (USL – LSL)
System Level (USL – LSL)
Subsystem Level (USL – LSL)
Subassembly Level (USL – LSL)
Component Level (USL – LSL)
Mfg. Process Level (USL – LSL)
USL − LSL
σ
What is6Measured?
Customer Level (Avg & σ)
System Level (Avg & σ)
Subsystem Level (Avg & σ)
Subassembly Level (Avg & σ)
Component Level (Avg & σ)
Mfg. Process Level (Avg & σ)
From this comparison we can document performance Capability
USL − LSL
Cp =
6σ

X −
LSL USL − X
Cpk = Min
,
3
σ
3σ

P ro c e ss C a p a b ilit y A n a ly s is f o r C2
P ro c e ss D a ta
1 2 .0 00 0
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)
L SL
US L
W it hi n
*
Ov e ral l
8 .0 00 0
9 .9 76 6
10 0
0 .4 4 7 13 4
0 .4 5 8 18 6
P o te nt ial (W ith in) C a pa b ility
Cp
1 .4 9
C PU
C PL
1 .5 1
1 .4 7
C pk
1 .4 7
C pm
*
8
9
O v er a ll C a pa b ility
10
O b s e rv ed P er fo r m a n ce
11
12
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
Pp
P PU
1 .4 6
1 .4 7
PPM < L SL
P P M > US L
0 .0 0
0 .0 0
PP M < L SL
P P M > US L
4. 92
3. 02
PPM < L SL
P P M > US L
P PL
P pk
1 .4 4
1 .4 4
P P M T o t al
0 .0 0
P P M T ot al
7. 94
P P M T ot al
8 .0 1
5 .0 3
1 3 .0 4
P ro c e ss C a p a b ilit y A n a ly s is f o r C2



L SL
P ro c e ss D a ta
U SL
T a r ge t
L SL
M e an
US L
1 2 .0 00 0
*
W it hi n
8 .0 00 0
9 .9 76 6
S am ple N
S tD ev ( W ith in )
10 0
0 .4 4 7 13 4
S tD ev ( O ve ra ll)
0 .4 5 8 18 6
Ov e ral l
P o te nt ial (W ith in) C a pa b ility
Cp
C PU
1 .4 9
1 .5 1
C PL
C pk
1 .4 7
1 .4 7
C pm
*
O v er a ll C a pa b ility
8
9
10
O b s e rv ed P er fo r m a n ce
11
E xp . " W ith in " Pe r fo rm a nc e
12
E xp . "O v er a ll" Pe r fo rm an c e
Pp
P PU
1 .4 6
1 .4 7
PPM < L SL
PPM > US L
0 .0 0
0 .0 0
PP M < L SL
PP M > US L
4. 92
3. 02
PPM < L SL
PPM > US L
P PL
P pk
1 .4 4
1 .4 4
PPM T o t al
0 .0 0
PP M T ot al
7. 94
PPM T ot al
8 .0 1
5 .0 3
1 3 .0 4
Summary of Critical CPM Actions:
CPM Actions
Reliability Actions
Metrics: scalars & vectors; continuous variables
Y=f(x) physics –based models
Metrics: time-based failures; discrete events
Additive / Product Functions; serial / parallel
Time-To-Failure models
Reliability Block Diagrams
FMEA, FMECA & Fault Tree Analysis
Duane Reliability Growth Plots
Normal Reliability Tests
Accelerated Reliability Tests
HALT, HASS & HAST evaluations
P-Diagrams
Noise Diagrams
Function Trees
Functional Flow Diagrams
Form Hypotheses & prioritize evaluations
Screening & Modeling DOEs under nominal
conditions
Robustness experiments under stressful
FRACAS
conditions
Tolerance balancing experiments under nominal
& stressful conditions
© 2010 PDSS Inc.
page 5 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
Problem Prevention Steps:
The 6 Steps for Problem Prevention:
Plan &
Rank
Tasks
Define
Potential
Problems
Evaluate
Causes
Define
Preventive
Actions
Define
Contingent
Actions
Re-Use
Learning
• Design a Diagram of detailed functions in their serial & parallel flows
• These are value-added functions that possess inherent robustness
• Rank & prioritize the value of each function relative to one another
• Define potential problems that can occur within & between the functions
• A statement of the mistakes or errors that characterize the problem
• Identification of Leading Indicators that measure the on-set of a problem
• Evaluate & document the root causes of the potential problems
• Understand the mechanisms behind all impending problems
• Define preventive actions for effectiveness & value
• Finalize, measure & track leading indicators – be proactively efficient
• Define contingency plans if the problem actually occurs
• Finalize, Measure & track leading & lagging indicators – be reactively effective after
indicators reach a trigger point.
• Re-use the lessons learned for future use & reactivity
• Continuously improve the problem prevention process
The P3IMA Table to help with the Problem Prevention Steps
The Potential Problem Prevention & Impact Mitigation Analysis (P3IMA)
(a derivative of FMEA)
Critical
Function
Potential
Problem
© 2010 PDSS Inc.
Likely
Causes
Probability of
Occurrence
Preventive
Action
Ability to
Detect
Onset
Severity of
Impact
Contingency
Action
page 6 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
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:
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
1
2
3
R C hart by O perator
Fre d
Sample Range
0 .2
Jo e
5
6
7
8
9
10
8 .2
U C L =0 .1 4 5 9
0 .1
8 .1
R = 0 .0 5 66 7
0 .0
8 .0
LCL=0
7 .9
Op e ra tor Fre d
0
Xbar Chart by Operator
Jo e
J oe
M ary
Operator*Part Interac tion
O p e ra tor
8 .2
M ary
8 .1
Average
Fre d
8 .2
Sample Mean
4
By Operator
8 .3
M ary
U C L =8 .1 0 2
M e a n= 8. 0 44
8 .0
L C L = 7. 98 6
7 .9
Fre d
J oe
M a ry
8 .1
8 .0
7 .9
Pa rt
0
1
2
3
4
5
6
7
8
9
10
Stability:
Individual Value
I and MR Chart for C2
UCL=5.917
5
0
Mean=-0.03816
-5
Subgroup
LCL=-5.994
0
50
100
Moving Range
10
UCL=7.316
5
R=2.239
0
LCL=0
Tunability:
Main Effects Plot - Data Means for Y plus Noise
ANOVA: Y plus Noise versus A, B, C
A
B
Surface Plot of Cool Tim
C
30
25
P
0.000
0.000
0.000
0.000
0.000
0.969
0.967
Y plus Noise
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
A
1
69.82
69.82 196.14
B
1
401.70
401.70 1128.38
C
1
1620.35
1620.35 4551.60
A*B
1
27.82
27.82
78.14
A*C
1
110.85
110.85 311.38
B*C
1
0.00
0.00
0.00
A*B*C
1
0.00
0.00
0.00
Error
8
2.85
0.36 Total
15
2233.39 20
15
10
-1
1
-1
1
1
-1
6
5
4
Interaction Plot (data means) for Y plus Noise
-1
1
-1
Cool Time (sec)
1
A
30
1
Effect
Sum of Squares
epsilon2
A
69.82
69.82/2233.39=0.031
%epsilon2
3.1% B
401.70
401.70/2233.39=0.18
18%
C
1620.35
1620.35/2233.39=0.72
72%
20
-1
30
1
2
1
27.82
27.82/2233.39=0.012
1.2%
AB
110.85
110.85/2233.39=0.05
5%
Total
AC
2233.39
1
0
-2
-1
Speed
20
-1
2
0
10
B
3
-1
0
1
Temp
-2
2
10
C
Hold values: Vol: 0.0 © 2010 PDSS Inc.
page 7 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
Interactivity:
Main Effects Plot - Data Means for Y plus Noise
ANOVA: Y plus Noise versus A, B, C
Factor
A
B
C
Type Levels Values
fixed
2
-1
fixed
2
-1
fixed
2
-1
1
1
1
A
B
C
30
Analysis of Variance for Y plus N
DF
1
1
1
1
1
1
1
8
15
SS
69.82
401.70
1620.35
27.82
110.85
0.00
0.00
2.85
2233.39
MS
F
69.82 196.14
401.70 1128.38
1620.35 4551.60
27.82
78.14
110.85 311.38
0.00
0.00
0.00
0.00
0.36
Y plus Noise
25
Source
A
B
C
A*B
A*C
B*C
A*B*C
Error
Total
P
0.000
0.000
0.000
0.000
0.000
0.969
0.967
20
15
10
1
-1
1
-1
1
-1
Interaction Plot (data means) for Y plus Noise
-1
1
-1
1
A
30
1
20
-1
10
B
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
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
Effect
30
1
20
-1
10
C
18%
Sensitivity & Statistical Significance:
[36,960/105,227] x [100] = 35%
[29,843/105,227] x [100] = 28%
[14,945 /105,227] x [100]= 14%
[10,764/105,227] x [100]= 10%
[6,281/105,227] x [100]= 6%
[3,335/105,227] x [100]= 3%
[1,580/105,227] x [100]= 1.5%
[716/105,227]
x [100]= 0.68%
40
25
20
Res A
1
3335
3335
3335
24.88 0.002
10
Res B
1
6281
6281
6281
46.85 0.000
5
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
10.26
5.99
3.18
1.5
0.68 0.39
0
Trans. F
Cap C
14.24
15
Voltage L
P
Trans. K
F
Resistor A
Adj MS
Cap. C
Adj SS
Resistor B
Seq SS
Re sistor I
DF
28.44
30
% Contribution
Source
35.23
35
Resistor D
Resistor G
Resistor I
Resistor D
Capacitor C
Resistor B
Resistor A
Transistor C
Transistor F
Resistor G
•
•
•
•
•
•
•
•
105227
Total MS
Capability:
P ro c e s s C a p a b ilit y A n a ly s is fo r C 2
LSL
P roc es s D at a
U SL
T ar get
US L
12. 00 00
*
LS L
8. 00 00
Me an
9. 97 66
S am ple N
S tD ev ( W ith in)
1 00
0 .4 471 34
S tD ev ( O ve rall)
0 .4 581 86
W ith in
O v e ra ll
Po te nt ial (W it hin) C apa bilit y
Cp
1. 49
CP U
1. 51
CP L
Cpk
1. 47
1. 47
Cpm
*
O v era ll C apa bilit y
8
9
10
O bs e rv ed P erf or m a nc e
11
E xp . "W it hin " Pe rf orm an c e
12
Ex p. "O v era ll" Pe rf orm an c e
Pp
P PU
1. 46
1. 47
PP M < L SL
PP M > U S L
0 .0 0
0 .0 0
P P M < L SL
P P M > US L
4 .9 2
3 .0 2
PP M < L SL
PP M > U S L
P PL
1. 44
PP M T ot al
0 .0 0
P P M T ot al
7 .9 4
PP M T ot al
P pk
1. 44
8. 01
5. 03
13. 04
Robustness:
Yavg
A1
Sensitivity to
Noise!
Critical Functional
Robustness
Parameter (CFRP)
A2
Robustness
N1
N2
Compounded
Noise Factors
© 2010 PDSS Inc.
page 8 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
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)
F1
F2
Function Tree Diagram
F3
F4
F5
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.
F2
F1
F3
F4
F5
Functional Flow Diagram
time
Each function is quantified as a y variable and is stated in its physics-based units of measure (a
scalar or vector). We add the y variables and their units of physical measure to the Post It notes.
F1…y1
© 2010 PDSS Inc.
page 9 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
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 σ
X COV shifter = controllable parameter that has a strong ability to move both the mean of y and the
value of σ (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 σ 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, …)
y2 = f(Xa, Xb, …)
y3 = f(Xa, Xb, …)
y4 = f(Xa, Xb, …)
y5 = f(Xa, Xb, …)
Δy1 = f(Δ
ΔXa, ΔXb, …);
Δy2 = f(Δ
ΔXa, ΔXb, …);
Δy3 = f(Δ
ΔXa, ΔXb, …);
Δy4 = f(Δ
ΔXa, ΔXb, …);
Δy5 = f(Δ
ΔXa, ΔXb, …);
σ2 of y1 = f(σ
σ2 from ΔXa, σ2 from ΔXb,…)
2
σ of y2 = f(σ
σ2 from ΔXa, σ2 from ΔXb,…)
σ2 of y3 = f(σ
σ2 from ΔXa, σ2 from ΔXb,…)
σ2 of y4 = f(σ
σ2 from ΔXa, σ2 from ΔXb,…)
2
σ of y5 = f(σ
σ2 from ΔXa, σ2 from ΔXb,…)
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.
© 2010 PDSS Inc.
page 10 of 11
PDSS Critical Parameter Development & Mgt. Process Quick Guide
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-Unit
Noises
External
Noises
Function
Δy = f(Xs)
Mean of
y&σ
Deterioration
Noises
For any X variable that is not a Noise Parameter, what noises cause it to vary? X variations
Unit-Unit
Noises
External
Noises
ΔXn
Mean of
y&σ
Deterioration
Noises
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.
© 2010 PDSS Inc.
page 11 of 11
MIT OpenCourseWare
http://ocw.mit.edu
ESD.33 Systems Engineering
Summer 2010
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