What

1
Whats New inDesign-Expert version 7Pat
WhitcombSeptember 13, 2005
2
Whats New

• General improvements
• Design evaluation
• Diagnostics
• Updated graphics
• Better help
• Miscellaneous Cool New Stuff
• Factorial design and analysis
• Response surface design
• Mixture design and analysis
• Combined design and analysis

3
Design Evaluation

• User specifies what order terms to ignore.
• Can evaluate by design or response.
• New options for more flexibility.
• User specifies D/s ratios for power calculation.
• User specifies what to report.
• User specified options for standard error plots.
• Annotation added to design evaluation report.

4
Design Evaluation Specify Order of Terms to
Ignore
Focus attention on what is most important.
5
Design Evaluation Evaluate by Design or Response
Useful when a response has missing data.
6
Design Evaluation New Options for More
Flexibility

• User specifies D/s ratios for power calculation.
• User specifies what to report.
• User specified options for standard error plots.

7
Design EvaluationAnnotated Design Evaluation
Report
8
Diagnostics

• Diagnostics Tool has two sets of buttons
• Diagnostics and Influence.
• New names and limits.
• Internally studentized residual studentized
  residual v6.
• Externally studentized residual outlier t v6.
• The externally studentized residual has exact
  limits.
• New DFFITS
• New DFBETAS

9
Diagnostics Diagnostics Tool has Two Sets of
Buttons
ei residuali
10
DiagnosticsExact Limits
t(a/n, n-p'-1) p' is the number of model terms
including the interceptn is the total number of
runs
11
Diagnostics DFFITS

• DFFITS measures the influence the ith
  observation has on the predicted value.(See
  Myers, Raymond Classical andModern Regression
  with Applications,1986, Duxbury Press, page
  284.) It isthe studentized difference between
  thepredicted value with observation i andthe
  predicted value without observation i. DFFITS
  is the externally studentized residual magnified
  by high leverage points and shrunk by low
  leverage points. It is a sensitive test for
  influence and points outside the limits are not
  necessarily bad just influential. These runs
  associated with points outside the limits should
  be investigated to for potential problems.
• DFFITS is very sensitive and it is not surprising
  to have a point or two falling outside the
  limits, especially for small designs.

12
Diagnostics DFBETAS
DFBETAS measures the influence the ith
observation has on each regression coefficient.
(See Myers, Raymond Classical and Modern
Regression with Applications, 1986, Duxbury
Press, page 284.) The DFBETASj,i is the number
of standard errors that the jth coefficient
changes if the ith observation is removed.
13
Updated Graphics

• New color by option.
• Full color contour and 3D plots.
• Design points and their projection lines added to
  3D plots.
• Grid lines on contour plots.
• Cross hairs read coordinates on plots.
• Magnification on contour plots.
• User specified detail on contour Flags.
• Choice of LSD Bars, Confidence Bands or
  None on one factor and interaction plots.

14
New Color by Option
15
Full Color Contour and 3D Plots
16
Design Points on 3D Plots
17
Grid lines on contour plots
18
Cross Hairs
19
Magnification on Contour Plots
20
Specify Detail on Contour Flags
21
LSD Bars Confidence Bands
22
Better Help

• Improved help
• Screen tips
• Movies (mini tutorials)

23
Miscellaneous Cool New Stuff

• Graph Columns now has its own node.
• Highlight points in the design layout or on a
  diagnostic graph for easy identification.
• Right click and response cell and ignore it.
• Improved design summary.
• Numerical optimization results now carried over
  to graphical optimization and point prediction.
• Export graph to enhanced metafile (.emf).

24
Graph Columns Node
25
Highlight Points
26
Ignore Response Cells
27
Improved Design Summary

• New in version 7
• Means and standard deviations for factors and
  responses.
• The ratio of maximum to minimum added for
  responses.

28
Numerical optimization results carried over to
graphical optimization and point prediction.
29
Whats New

• General improvements
• Design evaluation
• Diagnostics
• Updated graphics
• Better help
• Miscellaneous Cool New Stuff
• Factorial design and analysis
• Response surface design
• Mixture design and analysis
• Combined design and analysis

30
Two-Level Factorial Designs

• 2k-p factorials for up to 512 runs (256 in v6)
  and 21 factors (15 in v6).
• Design screen now shows resolution and updates
  with blocking choices.
• Generators are hidden by default.
• User can specify base factors for generators.
• Block names are entered during build.
• Minimum run equireplicated resolution V designs
  for6 to 31 factors.
• Minimum run equireplicated resolution IV designs
  for 5 to 50 factors.

31
2k-p Factorial DesignsMore Choices
Need to check box to see factor generators
32
2k-p Factorial DesignsSpecify Base Factors for
Generators
33
MR5 Designs Motivation

• Regular fractions (2k-p fractional factorials) of
  2k designs often contain considerably more runs
  than necessary to estimate the 1kk(k-1)/2
  effects in the 2FI model.
• For example, the smallest regular resolution V
  design for k7 uses 64 runs (27-1) to estimate 29
  coefficients.
• Our balanced minimum run resolution V design for
  k7 has 30 runs, a savings of 34 runs.

Small, Efficient, Equireplicated Resolution V
Fractions of 2k designs and their Application to
Central Composite Designs, Gary Oehlert and Pat
Whitcomb, 46th Annual Fall Technical Conference,
Friday, October 18, 2002. Available as PDF at
http//www.statease.com/pubs/small5.pdf
34
MR5 DesignsConstruction

• Designs have equireplication, so each column
  contains the same number of 1s and -1s.
• Used the columnwise-pairwise of Li and Wu (1997)
  with the D-optimality criterion to find designs.
• Overall our CP-type designs have better
  properties than the algebraically derived
  irregular fractions.
• Efficiencies tend to be higher.
• Correlations among the effects tend be lower.

35
MR5 DesignsProvide Considerable Savings
k 2k-p MR5 k 2k-p MR5
6 32 22 15 256 122
7 64 30 16 256 138
8 64 38 17 256 154
9 128 46 18 512 172
10 128 56 19 512 192
11 128 68 20 512 212
12 256 80 21 512 232
13 256 92 25 1024 326
14 256 106 30 1024 466
36
MR4 DesignsMitigate the use of Resolution III
Designs

• The minimum number of runs for resolution IV
  designs is only two times the number of factors
  (runs 2k). This can offer quite a savings when
  compared to a regular resolution IV 2k-p
  fraction.
• 32 runs are required for 9 through 16 factors to
  obtain a resolution IV regular fraction.
• The minimum-run resolution IV designs require 18
  to 32 runs, depending on the number of factors.
• A savings of (32 18) 14 runs for 9 factors.
• No savings for 16 factors.

Screening Process Factors In The Presence of
Interactions, Mark Anderson and Pat Whitcomb,
presented at AQC 2004 Toronto. May 2004.
Available as PDF at http//www.statease.com/pubs
/aqc2004.pdf.
37
MR4 DesignsSuggest using MR42 Designs

• Problems
• If even 1 run lost, design becomes resolution III
  main effects become badly aliased.
• Reduction in runs causes power loss may miss
  significant effects.
• Evaluate power before doing experiment.
• Solution
• To reduce chance of resolution loss and increase
  power, consider adding some padding
• New Whitcomb Oehlert MR42 designs

38
MR4 DesignsProvide Considerable Savings
k 2k-p MR42 k 2k-p MR42
6 16 14 16 32 34
7 16 16 17 64 36
8 16 18 18 64 38
9 32 20 19 64 40
10 32 22 20 64 42
11 32 24 21 64 44
12 32 26 22 64 46
13 32 28 23 64 48
14 32 30 24 64 50
15 32 32 25 64 52
No savings
39
Two-Level Factorial Analysis

• Effects Tool bar for model section tools.
• Colored positive and negative effects and
  Shapiro-Wilk test statistic add to probability
  plots.
• Select model terms by boxing them.
• Pareto chart of t-effects.
• Select aliased terms for model with right click.
• Better initial estimates of effects in irregular
  factions by using Design Model.
• Recalculate and clear buttons.

40
Two-Level Factorial AnalysisEffects Tool Bar

• New Effects Tool on the factorial effects
  screen makes all the options obvious.
• New Pareto Chart
• New Clear Selection button
• New Recalculate button (discuss later in
  respect to irregular fractions)

41
Two-Level Factorial AnalysisColored Positive and
Negative Effects
42
Two-Level Factorial AnalysisSelect Model Terms
by Boxing Them.
43
Two-Level Factorial AnalysisPareto Chart to
Select Effects

• The Pareto chart is useful for showing the
  relative size of effects, especially to
  non-statisticians.
• Problem If the 2k-p factorial design is not
  orthogonal and balanced the effects have
  differing standard errors, so the size of an
  effect may not reflect its statistical
  significance.
• Solution Plotting the t-values of the effects
  addresses the standard error problems for
  non-orthogonal and/or unbalanced designs.
• Problem The largest effects always look large,
  but what is statistically significant?
• Solution Put the t-value and the Bonferroni
  corrected t-value on the Pareto chart as
  guidelines.

44
Two-Level Factorial AnalysisPareto Chart to
Select Effects
45
Two-Level Factorial AnalysisSelect Aliased terms
via Right Click
46
Two-Level Factorial AnalysisBetter Effect
Estimates in Irregular Factions

• Design-Expert version 6 Design-Expert version 7

47
Two-Level Factorial AnalysisBetter Effect
Estimates in Irregular Factions

• ANOVA for Selected Factorial
  Model Analysis of variance table Partial sum of
  squares
• Sum of Mean F Source Squares DF Square Value
  Prob gt F
• Model 38135.17 4 9533.79 130.22 lt
  0.0001 A 10561.33 1 10561.33 144.25 lt
  0.0001 B 8.17 1 8.17 0.11 0.7482 C 11285.33 1 11
  285.33 154.14 lt 0.0001 AC 14701.50 1 14701.50 200
  .80 lt 0.0001 Residual 512.50 7 73.21 Cor
  Total 38647.67 11

48
Two-Level Factorial AnalysisBetter Effect
Estimates in Irregular Factions

• Main effects only model
• Intercept Intercept - 0.333CD -
  0.333ABC - 0.333ABD
• A A - 0.333BC - 0.333BD - 0.333ACD
• B B - 0.333AC - 0.333AD - 0.333BCD
• C C - 0.5AB
• D D - 0.5AB
• Main effects 2fi model
• Intercept Intercept - 0.5ABC - 0.5ABD
• A A - ACD
• B B - BCD
• C C
• D D
• AB AB
• AC AC - BCD
• AD AD - BCD
• BC BC - ACD
• BD BD - ACD
• CD CD - 0.5ABC - 0.5ABD

49
Two-Level Factorial AnalysisBetter Effect
Estimates in Irregular Factions

• Design-Expert version 6 calculates the initial
  effects using sequential SS via hierarchy.
• Design-Expert version 7 calculates the initial
  effects using partial SS for the Base model for
  the design.
• The recalculate button (next slide) calculates
  the chosen (model) effects using partial SS and
  then remaining effects using sequential SS via
  hierarchy.

50
Two-Level Factorial AnalysisBetter Effect
Estimates in Irregular Fractions

• Irregular fractions Use the Recalculate key
  when selecting effects.

51
General Factorials

• Design
• Bigger designs than possible in v6.
• D-optimal now can force categoric balance (or
  impose a balance penalty).
• Choice of nominal or ordinal factor coding.
• Analysis
• Backward stepwise model reduction.
• Select factor levels for interaction plot.
• 3D response plot.

52
General Factorial DesignD-optimal Categoric
Balance
53
General Factorial DesignChoice of Nominal or
Ordinal Factor Coding
54
Categoric FactorsNominal versus Ordinal

• The choice of nominal or ordinal for coding
  categoric factors has no effect on the ANOVA or
  the model graphs. It only affects the
  coefficients and their interpretation
• Nominal coefficients compare each factor level
  mean to the overall mean.
• Ordinal uses orthogonal polynomials to give
  coefficients for linear, quadratic, cubic, ,
  contributions.

55
Battery LifeInterpreting the coefficients

• Nominal contrasts coefficients compare each
  factor level mean to the overall mean.
• Name A1 A2 A1 1 0 A2 0 1 A3
  -1 -1
• The first coefficient is the difference between
  the overall mean and the mean for the first level
  of the treatment.
• The second coefficient is the difference between
  the overall mean and the mean for the second
  level of the treatment.
• The negative sum of all the coefficients is the
  difference between the overall mean and the mean
  for the last level of the treatment.

56
Battery LifeInterpreting the coefficients
Ordinal contrasts using orthogonal polynomials
the first coefficient gives the linear
contribution and the second the quadratic Name
B1 B2 15 -1 1 70 0 -2 125 1
1 B1 linear B2 quadratic
57
General Factorial AnalysisBackward Stepwise
Model Reduction
58
Select Factor Levels for Interaction Plot
59
General Factorial Analysis3D Response Plot
60
Factorial Design Augmentation

• Semifold Use to augment 2k-p resolution IV
  usually as many additional two-factor
  interactions can be estimated with half the runs
  as required for a full foldover.
• Add Center Points.
• Replicate Design.
• Add Blocks.

61
Whats New

• General improvements
• Design evaluation
• Diagnostics
• Updated graphics
• Better help
• Miscellaneous Cool New Stuff
• Factorial design and analysis
• Response surface design
• Mixture design and analysis
• Combined design and analysis

62
Response Surface Designs

• More canned designs more factors and choices.
• CCDs for 30 factors (v6 10 factors)
• New CCD designs based on MR5 factorials.
• New choices for alpha practical, orthogonal
  quadratic and spherical.
• Box-Behnken for 330 factors (v6 3, 4, 5, 6, 7, 9
  10)
• Odd designs moved to Miscellaneous.
• Improved D-optimal design.
• for 30 factors (v6 10 factors)
• Coordinate exchange

63
MR-5 CCDsResponse Surface Design

• Minimum run resolution V (MR-5) CCDs
• Add six center points to the MR-5 factorial
  design.
• Add 2(k) axial points.
• For k10 the quadratic model has 66 coefficients.
  The number of runs for various CCDs
• Regular (210-3) 158
• MR-5 82
• Small (Draper-Lin) 71

64
MR-5 CCDs (k 6 to 30)Number of runs closer to
small CCD
65
MR-5 CCDs (k10, a 1.778)Regular, MR-5 and
Small CCDs
210-3 CCD 158 runs MR-5 CCD 82 runs Small CCD 71 runs
Model 65 65 65
Residuals 92 16 5
Lack of Fit 83 11 1
Pure Error 9 5 4
Corr Total 157 81 70
66
MR-5 CCDs (k10, a 1.778)Properties of
Regular, MR-5 and Small CCDs
210-3 CCD 158 runs MR-5 CCD 82 runs Small CCD 71 runs
Max coefficient SE 0.214 0.227 16.514
Max VIF 1.543 2.892 12,529
Max leverage 0.498 0.991 1.000
Ave leverage 0.418 0.805 0.930
Scaled D-optimality 1.568 2.076 3.824
67
MR-5 CCDs (k10, a 1.778)Properties closer to
regular CCD
A-B slice
210-3 CCD MR-5 CCD Small CCD 158 runs 82
runs 71 runs different y-axis scale
68
MR-5 CCDs (k10, a 1.778)Properties closer to
regular CCD
A-C slice
210-3 CCD MR-5 CCD Small CCD 158 runs 82
runs 71 runs all on the same y-axis scale
69
MR-5 CCDsConclusion

• Best of both worlds
• The number of runs are closer to the number in
  the small than in the regular CCDs.
• Properties of the MR-5 designs are closer to
  those of the regular than the small CCDs.
• The standard errors of prediction are higher than
  regular CCDs, but not extremely so.
• Blocking options are limited to 1 or 2 blocks.

70
Practical alphaChoosing an alpha value for your
CCD

• Problems arise as the number of factors increase
• The standard error of prediction for the face
  centered CCD (alpha 1) increases rapidly. We
  feel that an alpha gt 1 should be used when k gt 5.
• The rotatable and spherical alpha values become
  too large to be practical.
• Solution
• Use an in between value for alpha, i.e. use a
  practical alpha value.
• practical alpha (k)¼

71
Standard Error Plots 26-1 CCDSlice with the
other four factors 0
Face Centered Practical Spherical a 1.000 a
1.565 a 2.449
72
Standard Error Plots 26-1 CCDSlice with two
factors 1 and two 0
Face Centered Practical Spherical a 1.000 a
1.565 a 2.449
73
Standard Error Plots MR-5 CCD (k30) Slice with
the other 28 factors 0
Face Centered Practical Spherical a 1.000 a
2.340 a 5.477
74
Standard Error Plots MR-5 CCD (k30) Slice with
14 factors 1 and 14 0
Face Centered Practical Spherical a 1.000 a
2.340 a 5.477
75
Choosing an alpha value for your CCD
76
D-optimal Coordinate Exchange

• Cyclic Coordinate Exchange Algorithm
• Start with a nonsingular set of model points.
• Step through the coordinates of each design point
  determining if replacing the current value
  increases the optimality criterion. If the
  criterion is improved, the new coordinate
  replaces the old. (The default number of steps
  is twelve. Therefore 13 levels are tested
  between the low and high factor constraints
  usually 1.)
• The exchanges continue and cycle through the
  model points until there is no further
  improvement in the optimality criterion.
• R.K. Meyer, C.J. Nachtsheim (1995), The
  Coordinate-Exchange Algorithm for Constructing
  Exact Optimal Experimental Designs,
  Technometrics, 37, 60-69.

77
Whats New

• General improvements
• Design evaluation
• Diagnostics
• Updated graphics
• Better help
• Miscellaneous Cool New Stuff
• Factorial design and analysis
• Response surface design
• Mixture design and analysis
• Combined design and analysis

78
Mixture Design

• More components
• Simplex lattice 2 to 30 components (v6 2 to 24)
• Screening 6 to 40 components (v6 6 to 24)
• Detect inverted simplex
• Upper bounded pseudo values U_Pseudo and
  L_Pseudo
• New mixture design Historical Data
• Coordinate exchange

79
Inverted Simplex

• When component proportions are restricted by
  upper bounds it can lead to an inverted simplex.
• For example
• x1 0.4
• x2 0.6
• x3 0.3

80
Inverted Simplex3 component L_Pseudo

• Using lower bounded L_Pseudo values leads to the
  following inverted simplex.
• Open I-simplex L_P.dx7 andmodel the response.

0.50 in L_Pseudo
81
Inverted Simplex3 component U_Pseudo (page 1 of
2)

1. Build a new design and say Yes to Use previous
   design info.
2. Change User-Defined to Simplex Centroid.
3. When asked say Yes to switch to upper bounded
   pseudo values U_Pseudo.

82
Inverted Simplex3 component U_Pseudo (page 1 of
3)

• Change the replicates from 4 to 6 and
• Right click on the Blockcolumn header
  andDisplay Point Type

83
Inverted SimplexUpper Bounded Pseudo Values

• The high value becomes 0 and the low value
  becomes 1!

84
Inverted SimplexUpper Bounded Pseudo Values

• The upper value becomes 0 and the lower value 1!
• U_Pseudo values

Real Real Pseudo Pseudo
Li Ui Li Ui
x1 0.1 0.4 1 0
x2 0.3 0.6 1 0
x3 0.0 0.3 1 0
85
Inverted Simplex3 component U_Pseudo

• Go to the Evaluation and view the design space

86
Inverted SimplexNote the Improved Values

• Coding is U_Pseudo. Term StdErr VIF Ri-Sq
• A 0.69 1.74 0.4255 B 0.69 1.74 0.4255
  C 0.69 1.74 0.4255 AB 3.45 1.94 0.4844
  AC 3.45 1.94 0.4844 BC 3.45 1.94 0.4844
  ABC 27.03 1.75 0.4300
• Basis Std. Dev. 1.0

Coding is L_Pseudo. Term StdErr VIF Ri-Sq A 26
.33 1550.78 0.9994 B 26.33 1550.78 0.9994 C 26.3
3 1550.78 0.9994 AB 104.19 2686.10 0.9996 AC 104
.19 2686.10 0.9996 BC 104.19 2686.10 0.9996 ABC
216.27 455.72 0.9978 Basis Std. Dev. 1.0
87
Inverted Simplex 3 component U_Pseudo

1. Simulate the response using I-simplex U_P.sim
2. Model the response.

88
Inverted Simplex Upper vs Lower Bounded Pseudo
Values

• Low becomes high and high becomes low
• U_Pseudo L_Psuedo

89
Mixture DesignHistorical Data
90
D-optimal DesignCoordinate versus Point Exchange

• There are two algorithms to select optimal
  points for estimating model coefficients
• Coordinate exchange
• Point exchange

91
D-optimal Coordinate Exchange

• Cyclic Coordinate Exchange Algorithm
• Start with a nonsingular set of model points.
• Step through the coordinates of each design point
  determining if replacing the current value
  increases the optimality criterion. If the
  criterion is improved, the new coordinate
  replaces the old. (The default number of steps
  is twelve. Therefore 13 levels are tested
  between the low and high factor constraints
  usually 1.)
• The exchanges continue and cycle through the
  model points until there is no further
  improvement in the optimality criterion.
• R.K. Meyer, C.J. Nachtsheim (1995), The
  Coordinate-Exchange Algorithm for Constructing
  Exact Optimal Experimental Designs,
  Technometrics, 37, 60-69.

92
Mixture Analysis

• Cox Model a new mixture parameterization
• New screening tools for linear models
• Constraint Region Bounded Component Effects for
  Piepel Direction
• Constraint Region Bounded Component Effects for
  Cox Direction
• Constraint Region Bounded Component Effects for
  Orthogonal Direction
• Range Adjusted Component Effects for Orthogonal
  Direction (this is the only measure in v6)

93
Mixture Analysis Cox Model

• Cox model option for mixtures May be more
  informative for formulators when they are
  interested in a particular composition.

94
Screening DesignsComponent Effects Concepts

• Basis for screening is a linear model
• In a mixture it is impossible to change one
  component while holding the others fixed.
• Changes in the component of interest must be
  offset by changes in the other components (so the
  components still sum to their total).
• Choosing a direction through the mixture space to
  vary to component of interest defines how the
  offsetting changes are made.

95
Screening DesignsComponent Effect Directions

• Three directions in which component effects are
  assessed
• Orthogonal
• Cox
• Piepel
• The most meaningful direction (or directions) to
  use for computing effects for a particular
  mixture DOE depends on the shape of the mixture
  region.
• In an unconstrained simplex theCox and Piepel
  directions are the same.
• In a constrained simplex theyre not!(Remember
  the ABS Pipe example.)

96
Screening DesignsComponent Effect Directions

• Example (equation in actuals)

97
Screening DesignsOrthogonal Direction Component
Effect
X
1
X
X
2
3

98
Orthogonal Component EffectsRange Adjusted
versus Constraint Bounded

• Bounded Adjusted Component Effect Effect
• A-X1 0.60 1.80
• B-X2 0.00 0.00
• C-X3 -0.30 -0.30
• In constrained mixtures the Adjusted
• effect is almost never realized.

99
Orthogonal Component GradientsConstraint Bounded

• Gradient Component at Base Pt.
• A-X1 3.00
• B-X2 0.00
• C-X3 -3.00
• A has a positive slope
• B has no slope
• C has a negative slope

Slope 3.0
100
Screening DesignsCox Direction Component Effect
101
Cox Component EffectsConstraint Bounded

• Gradient Component at Base Pt.
• A-X1 2.50
• B-X2 -0.91
• C-X3 -2.94
• Component Component Effect
• A-X1 1.00
• B-X2 -0.33
• C-X3 -0.29

Slope 2.5
102
Screening DesignsPiepel Direction Component
Effect
103
Piepel Component EffectsConstraint Bounded

• Gradient Component at Base Pt.
• A-X1 2.25
• B-X2 -1.43
• C-X3 -2.92
• Component Component Effect
• A-X1 1.35
• B-X2 -1.00
• C-X3 -0.29

Slope 2.25
104
SummaryComponent Effect Directions

1. Orthogonal The direction for the ith component
   along a line that is orthogonal to space spanned
   by the other q-1 components. Appropriate only
   for simplex regions.
2. Cox The direction for the ith component along a
   line joining the reference blend to the ith
   vertex (in real values). The line is also
   extended in the opposite direction to its end
   point. Appropriate for all regions.
3. Piepel The same as the Cox direction after
   applying the pseudo component transformation.
   Appropriate for all regions.

105
Whats New

• General improvements
• Design evaluation
• Diagnostics
• Updated graphics
• Better help
• Miscellaneous Cool New Stuff
• Factorial design and analysis
• Response surface design
• Mixture design and analysis
• Combined design and analysis

106
Combined Design

• Design
• Big new feature combine two mixture designs!
• Analysis
• New fit summary layout.
• New model graphs
• Mix-Process contour plot
• Mix-Process 3D plot

107
Combined Design
108
Combined Design Analysis New Fit Summary Layout

• Order Abbreviations in Fit Summary Table
• M Mean L Linear Q Quadratic
  SC Special Cubic C Cubic
• Combined Model Mixture Process Fit Summary
  Table
• Sequential p-value Summary
  Statistics
• Mix Process Mix Process Lack of
  Fit Adjusted Predicted
• Order Order R-Squared R-Squared
• M M
• M L lt 0.0001 0.0027 0.3929 0.3393
• M 2FI 0.9550 0.0024 0.3630 0.2678
• M Q 0.0024 0.3630 0.2678 Aliased
• M C 0.6965 0.0023 0.3528 0.2418 Aliased
• M M L M lt 0.0001 0.0032 0.4350 0.3825
• L L lt 0.0001 lt 0.0001 0.1534 0.9042 0.8715
• L 2FI lt 0.0001 0.5856 0.1415 0.9013 0.8142
• L Q lt 0.0001 0.1415 0.9013 0.8142 Aliased
• L C lt 0.0001 0.7605 0.1280 0.8966 0.7536 Alia
  sed

109
Combined Design Analysis Mix-Process Contour
Plot
110
Combined Design Analysis Mix-Process 3D Plot