Quality Progress - October 2017 - 46

F E AT U R E

DESIGN OF EXPERIMENTS

FIGURE 3

Power for the four two-level designs
Power analysis
Significance level
Anticipated RMSE

0.05
1.00

Anticipated
coefficient

Term
Intercept
X1
X2
X3
X4
X5
X6
X7
X1*X2
X1*X3
X1*X4
X1*X5

1
1
1
1
1
1
1
1
1
-1
1
-1

Significance level
Anticipated RMSE

Power

Term

0.491
0.481
0.326
0.344
0.306
0.311
0.362
0.227
0.280
0.344
0.208
0.230

Intercept
X1
X2
X3
X4
X5
X6
X7
X1*X2
X1*X3
X1*X4
X1*X5

D-optimal, 14 runs

Power analysis

Power analysis

Power analysis
0.05
1.00

Anticipated
coefficient
1
1
1
1
1
1
1
1
1
-1
1
-1

Significance level
Anticipated RMSE
Anticipated
coefficient

Power

Term

0.471
0.357
0.357
0.357
0.357
0.357
0.357
0.357
0.471
0.471
0.471
0.471

Intercept
X1
X2
X3
X4
X5
X6
X7
X1*X2
X1*X3
X1*X4
X1*X5

Significance level
Anticipated RMSE

0.05
1.00

1
1
1
1
1
1
1
1
1
-1
1
-1

Anticipated
coefficient

Power

Term

0.843
0.843
0.336
0.646
0.422
0.486
0.646
0.486
0.463
0.572
0.243
0.463

Intercept
X1
X2
X3
X4
X5
X6
X7
X1*X2
X1*X3
X1*X4
X1*X5

1
1
1
1
1
1
1
1
1
-1
1
-1

Power
0.843
0.843
0.843
0.843
0.843
0.843
0.843
0.843
0.843
0.843
0.843
0.843

Minimum G-aberration, 16 runs

D-optimal, 16 runs

Minimum G-aberration, 14 runs

0.05
1.00

RMSE = root-mean-square error

46 QP

October 2017 ❘ qualityprogress.com

to the choice of various models for different designs.
They are constructed by sampling many values-n,
for example-from throughout the design space and
FIGURE 4

Fraction of design space plot for
all four two-level designs
1.0

Prediction variance

(X1*X2, X1*X3, X1*X4 and X2*X3). The D-optimal
designs seem inferior to the corresponding two-level
minimum G-aberration designs in the sense that these
four two-factor interactions of the D-optimal designs
are correlated (or partially confounded) with the main
effects. In general, it is difficult for the experimenter to
know at the design stage which two-factor interactions
to account for in the model to fit to the data. To include
all two-factor interactions in the model, the D-optimal
design requires at least 29 runs.
The power for the four designs is compared in Figure
3. Figure 4 shows, on one plot, the fraction of design
space plot for all four designs. 20
The power represents the probability of detecting,
with statistical significance, the anticipated effect
in Figure 1. Specifically, the power for detecting the
interaction X1*X2 is 28% and 46% for the 14 and 16-run
D-optimal designs, respectively. The corresponding 14
and 16-run minimum G-aberration designs provide a
power of 47% and 83%, respectively, for detecting this
same interaction. In fact, the 14-run minimum G-aberration design provides the same power as the 16-run
D-optimal design.
The fraction of design space (FDS) plot in Figure 4
shows the proportion of the design space for which the
scaled prediction variance (SPV) falls below a specific
value. FDS plots are used to examine design robustness

Minimum G-aberration, 14 runs

0.5
D-optimal, 16 runs

D-optimal, 14 runs

Minimum G-aberration, 16 runs

0.0
0.0

0.2

0.4

0.6

Fraction of space

0.8

1.0


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Table of Contents for the Digital Edition of Quality Progress - October 2017

Seen and Heard
Progress Report
Mr. Pareto Head
Expert Answers
Career Coach
In Focus
The Results Are In
Visual Aid
Experimental Learning
Statistics Spotlight
Standard Issues
Marketplace
Footnotes
Try This Today
STANDARDS AND AUDITING GUIDE
Quality Progress - October 2017 - intro
Quality Progress - October 2017 - cover1
Quality Progress - October 2017 - cover2
Quality Progress - October 2017 - 1
Quality Progress - October 2017 - 2
Quality Progress - October 2017 - 3
Quality Progress - October 2017 - 4
Quality Progress - October 2017 - 5
Quality Progress - October 2017 - Seen and Heard
Quality Progress - October 2017 - 7
Quality Progress - October 2017 - Progress Report
Quality Progress - October 2017 - Mr. Pareto Head
Quality Progress - October 2017 - 10
Quality Progress - October 2017 - 11
Quality Progress - October 2017 - Expert Answers
Quality Progress - October 2017 - 13
Quality Progress - October 2017 - Career Coach
Quality Progress - October 2017 - 15
Quality Progress - October 2017 - 16
Quality Progress - October 2017 - 17
Quality Progress - October 2017 - In Focus
Quality Progress - October 2017 - 19
Quality Progress - October 2017 - 20
Quality Progress - October 2017 - 21
Quality Progress - October 2017 - 22
Quality Progress - October 2017 - 23
Quality Progress - October 2017 - 24
Quality Progress - October 2017 - 25
Quality Progress - October 2017 - The Results Are In
Quality Progress - October 2017 - 27
Quality Progress - October 2017 - 28
Quality Progress - October 2017 - 29
Quality Progress - October 2017 - 30
Quality Progress - October 2017 - 31
Quality Progress - October 2017 - 32
Quality Progress - October 2017 - 33
Quality Progress - October 2017 - Visual Aid
Quality Progress - October 2017 - 35
Quality Progress - October 2017 - 36
Quality Progress - October 2017 - 37
Quality Progress - October 2017 - 38
Quality Progress - October 2017 - 39
Quality Progress - October 2017 - Experimental Learning
Quality Progress - October 2017 - 41
Quality Progress - October 2017 - 42
Quality Progress - October 2017 - 43
Quality Progress - October 2017 - 44
Quality Progress - October 2017 - 45
Quality Progress - October 2017 - 46
Quality Progress - October 2017 - 47
Quality Progress - October 2017 - Statistics Spotlight
Quality Progress - October 2017 - 49
Quality Progress - October 2017 - Standard Issues
Quality Progress - October 2017 - 51
Quality Progress - October 2017 - 52
Quality Progress - October 2017 - 53
Quality Progress - October 2017 - 54
Quality Progress - October 2017 - 55
Quality Progress - October 2017 - STANDARDS AND AUDITING GUIDE
Quality Progress - October 2017 - 57
Quality Progress - October 2017 - Marketplace
Quality Progress - October 2017 - 59
Quality Progress - October 2017 - Footnotes
Quality Progress - October 2017 - 61
Quality Progress - October 2017 - 62
Quality Progress - October 2017 - 63
Quality Progress - October 2017 - Try This Today
Quality Progress - October 2017 - cover3
Quality Progress - October 2017 - cover4
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