Quality Progress - October 2017 - 44

F E AT U R E

DESIGN OF EXPERIMENTS
InfoQ is performed by considering eight dimensions:
1. Data resolution.
2. Data structure.
3. Data integration.
4. Temporal relevance.
5. Chronology of data and goal.
6. Generalizability.
7. Operationalization.
8. Communication.
These eight dimensions can be considered when
designing an experiment.14 InfoQ is affected by the
pre-study planning phase. In seeking high InfoQ with
experimental designs, clarify the goal of the experiments and evaluate a proposed set of experiments with
a range of criteria.

Designing experiments for high InfoQ

Consider a piston operating in an engine. The performance of the piston is measured by the cycle time of a
full revolution in seconds. The seven factors that affect
cycle time are:
1. X1: M-piston weight (30-60 Kg).
2. X2: S-piston surface area (0.005-0.2 m²).
3. X3: V0-initial gas volume (0.002-0.01 m3).
4. X4: K-spring coefficient (1,000-5,000 N/m).
5. X5: P0-atmospheric pressure (90,000-110,000 N/
m²).
6. X6: T-ambient temperature (290-296 ⁰K).
7. X7: T0-gas temperature (340-360 ⁰K).
The levels of these factors shown in parentheses
represent extremes on the operating range that cannot
be exceeded without affecting the smooth operation of
the engine.15
When designing experiments to investigate the
performance of the piston, consider various options. For
example:
+ Do you want to accurately estimate the effect of the
seven factors to derive engineering insights on the
system's design?
+ Do you want a good predictive model of piston performance to design an optimal control system?
+ Do you want to compare different models of the piston to assess the effect of engineering modifications?
+ What can you achieve with an experimental budget of
14 experimental runs? What about 16 runs? Is there a
difference?
When answering these questions, consider four
two-level experimental designs representing two 14
and two 16-factor level combinations. For concreteness,
consider experiments on the seven factors of the piston.

44 QP

October 2017 ❘ qualityprogress.com

Remember, this is the experimental design stage before
actual experimental data are collected, so how to set up
the seven factors to meet the stated objectives must be
considered.
To further make the point, we expanded on Christine
Anderson-Cook and Lu Lu's two-part QP columns "Best
Bang for Your Buck," 16-17 which compared four designs in
response to an engineer looking for the best approach
to run an experiment of size 14. Anderson-Cook and Lu
considered the following criteria:
+ Cost (size of the experiment).
+ Parameter estimation (D-efficiency).
+ Prediction capabilities (I-efficiency).
+ Power.
+ Average correlation between estimates of main
effects and interactions.
+ Prediction precision throughout design space (fraction of design space plot).
+ Ability to assess curvature from quadratic terms.
These criteria provide a broad perspective of experimental design capabilities that is partially adopted in our
piston example. Specifically, four designs are compared
with factors considered at two levels. These designs
identify active factors and their interactions by considering the seven factors of the piston at their lowest and
highest values, for example.¹⁸ The low and high levels
typically are coded as -1 and +1, respectively. The specific
designs considered are presented in Figure 1 (p. 43).1⁹
Figure 1 includes two D-optimal designs for 14 runs
and 16 runs (both using the main effects only model)
and two minimum G-aberration designs for 14 runs and
16 runs. The main effects of the 16-run D-optimal and
16-run minimum G-aberration designs are orthogonal
to each other. The main effects of the 14-run and 16-run
minimum G-aberration designs are orthogonal to the
two-factor interactions. This is not the case with the
14-run and 16-run D-optimal designs.
Figure 2 shows an evaluation of the four two-level
designs with the seven factors listed in Figure 1. The
four designs are compared using correlation color plots
and design diagnostics. The correlation color plots
show correlations between estimates of main effects
and interactions. A correlation of one (in red) indicates
full aliasing so that these paired estimates are indistinguishable. Independence of estimates is indicated by
a correlation of zero (dark blue). The design diagnostics compare the designs to orthogonal 100% optimal
designs, such as the 16-run minimum G-aberration.
The four designs were evaluated against a model
including main effects and four two-factor interactions


http://www.qualityprogress.com

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
https://www.nxtbook.com/naylor/ASQM/ASQM0719
https://www.nxtbook.com/naylor/ASQM/ASQM0619
https://www.nxtbook.com/naylor/ASQM/ASQM0519
https://www.nxtbook.com/naylor/ASQM/ASQM0419
https://www.nxtbook.com/naylor/ASQM/ASQM0319
https://www.nxtbook.com/naylor/ASQM/ASQM0219
https://www.nxtbook.com/naylor/ASQM/ASQM0119
https://www.nxtbook.com/naylor/ASQM/ASQM1218
https://www.nxtbook.com/naylor/ASQM/ASQM1118
https://www.nxtbook.com/naylor/ASQM/ASQM1018
https://www.nxtbook.com/naylor/ASQM/ASQM0918
https://www.nxtbook.com/naylor/ASQM/ASQM0818
https://www.nxtbook.com/naylor/ASQM/ASQM0718
https://www.nxtbook.com/naylor/ASQM/ASQM0618
https://www.nxtbook.com/naylor/ASQM/ASQM0518
https://www.nxtbook.com/naylor/ASQM/ASQM0418
https://www.nxtbook.com/naylor/ASQM/ASQM0318
https://www.nxtbook.com/naylor/ASQM/ASQM0218
https://www.nxtbook.com/naylor/ASQM/ASQM0118
https://www.nxtbook.com/naylor/ASQM/ASQM1217
https://www.nxtbook.com/naylor/ASQM/ASQM1117
https://www.nxtbook.com/naylor/ASQM/ASQM1017
https://www.nxtbook.com/naylor/ASQM/ASQM0917
https://www.nxtbook.com/naylor/ASQM/ASQM0817
https://www.nxtbook.com/naylor/ASQM/ASQM0717
https://www.nxtbook.com/naylor/ASQM/ASQM0617
https://www.nxtbook.com/naylor/ASQM/ASQM0517
https://www.nxtbook.com/naylor/ASQM/ASQM0417
https://www.nxtbook.com/naylor/ASQM/ASQC12518
https://www.nxtbook.com/naylor/ASQM/ASQM0317
https://www.nxtbook.com/naylor/ASQM/ASQM0217
https://www.nxtbook.com/naylor/ASQM/ASQM0117
https://www.nxtbook.com/naylor/ASQM/ASQM1216
https://www.nxtbook.com/naylor/ASQM/ASQM1116
https://www.nxtbook.com/naylor/ASQM/ASQM1016
https://www.nxtbook.com/naylor/ASQM/ASAC0016
https://www.nxtbook.com/naylor/ASQM/ASQM0916
https://www.nxtbook.com/naylor/ASQM/ASQA0016
https://www.nxtbook.com/naylor/ASQM/ASQM0816
https://www.nxtbook.com/naylor/ASQM/ASQM0716
https://www.nxtbook.com/naylor/ASQM/ASQM0616
https://www.nxtbook.com/naylor/ASQM/ASQM0516
https://www.nxtbook.com/naylor/ASQM/ASQM0416
https://www.nxtbook.com/naylor/ASQM/ASQM0316
https://www.nxtbook.com/naylor/ASQM/ASQM0216
https://www.nxtbook.com/naylor/ASQM/ASQM0116
https://www.nxtbook.com/naylor/ASQM/ASQM1215
https://www.nxtbook.com/naylor/ASQM/ASQM1115
https://www.nxtbook.com/naylor/ASQM/ASQM1015
https://www.nxtbook.com/naylor/ASQM/ASQM0915
https://www.nxtbook.com/naylor/ASQM/ASQM0815
https://www.nxtbook.com/naylor/ASQM/ASQM0715
https://www.nxtbook.com/naylor/ASQM/ASQM0615
https://www.nxtbook.com/naylor/ASQM/ASQM0515
https://www.nxtbook.com/naylor/ASQM/ASQM0315
https://www.nxtbook.com/naylor/ASQM/ASQM0215
https://www.nxtbook.com/naylor/ASQM/ASQM0115
https://www.nxtbook.com/naylor/ASQM/ASQM1214
https://www.nxtbook.com/naylor/ASQM/ASQM1114
https://www.nxtbook.com/naylor/ASQM/ASQM1014
https://www.nxtbook.com/naylor/ASQM/ASQM0914
https://www.nxtbook.com/naylor/ASQM/ASQM0814
https://www.nxtbook.com/naylor/ASQM/ASQM0714
https://www.nxtbook.com/naylor/ASQM/ASQM0614
https://www.nxtbook.com/naylor/ASQM/ASQM0514
https://www.nxtbook.com/naylor/ASQM/ASQM0414
https://www.nxtbook.com/naylor/ASQM/ASQM0314
https://www.nxtbook.com/naylor/ASQM/ASQM0214
https://www.nxtbook.com/naylor/ASQM/ASQM0114
https://www.nxtbook.com/naylor/ASQM/ASQM1213
https://www.nxtbook.com/naylor/ASQM/ASQM1113
https://www.nxtbook.com/naylor/ASQM/ASQM1013
https://www.nxtbook.com/naylor/ASQM/ASQM0913
https://www.nxtbook.com/naylor/ASQM/ASQM0813
https://www.nxtbook.com/naylor/ASQM/ASQM0713
https://www.nxtbook.com/naylor/ASQM/ASQM0613
https://www.nxtbook.com/naylor/ASQM/ASQM0513
https://www.nxtbook.com/naylor/ASQM/ASQM0413
https://www.nxtbook.com/naylor/ASQM/ASQM0313
https://www.nxtbook.com/nxtbooks/naylor/ASQM0213
https://www.nxtbook.com/nxtbooks/naylor/ASQM0113
https://www.nxtbook.com/nxtbooks/naylor/ASQM1212
https://www.nxtbook.com/nxtbooks/naylor/ASQM1112
https://www.nxtbook.com/nxtbooks/naylor/ASQM1012
https://www.nxtbook.com/nxtbooks/naylor/ASQM0912
https://www.nxtbookmedia.com