Quality Progress - October 2017 - 47

obtaining all corresponding SPVs, which are ordered and
plotted against the quantiles (1/n and 2/n, for example).
The idea is the closer the FDS for an SPV is to the minimum, the better the design. In this example, a high FDS
produces a low prediction variance from models created
after collecting data. Moreover, the flatter the line, the
more stable the SPV distribution for that design. In this
example, the increase of experimental runs from 14 to
16 clearly reduces the SPV. The minimum G-aberration
design provides the best performance.

Evaluating designs

Experimental design evaluation is based on different
criteria, including power, FDS, correlation color plots and
design diagnostics. The obvious criterion is the number
of experimental points or experimental runs. The power
and FDS show what can be gained with two additional
runs and provide a comparison of the D-optimal and
minimal G-aberration designs.
In this example, for an equal number of runs, minimal
G-aberration designs perform better than D-optimal
designs. As mentioned, the difficulty with D-optimal
designs is that they are optimal for a specific model,
which may not be the preferred model after the data are
collected.
Other goals, another context and different constraints
can lead to other types of designs. After all, it is all about
generating InfoQ. These examples and tools provide
methods for ensuring InfoQ at the design stage.
REFERENCES AND NOTES
1. Ron S. Kenett and Galit Shmueli, Information Quality: The
Potential of Data and Analytics to Generate Knowledge, John
Wiley & Sons, 2016.
2. George E.P. Box, William G. Hunter and J. Stuart Hunter,
Statistics for Experimenters: An Introduction to Design, Data
Analysis, and Model Building, John Wiley & Sons, 1978.
3. Peter Goos and Bradley Jones, Optimal Design of Experiments:
A Case Study Approach, John Wiley & Sons, 2011.
4. Ron S. Kenett and Shelemyahu Zacks, Modern Industrial
Statistics: With Applications in R, MINITAB and JMP, second
edition, John Wiley & Sons, 2014.
5. Ron S. Kenett and David M. Steinberg, "New Frontiers in Design
of Experiments," Quality Progress, August 2016, pp. 61-65.
6. Bradley Jones and Christopher J. Nachtsheim, "A Class of
Three-Level Designs for Definitive Screening in the Presence of
Second-Order Effects," Journal of Quality Technology, Vol. 43,
No. 1, 2011, pp. 1-15.
7. Nam-Ky Nguyen and Tung-Dinh Pham, "Small Mixed-Level
Screening Designs with Orthogonal Quadratic Effects," Journal
of Quality Technology, Vol. 48, No. 10, 2016, pp. 405-414.
8. Christine M. Anderson-Cook and Lu Lu, "Statistics Roundtable:
Best Bang for Your Buck-Part 1," Quality Progress, October
2016, pp. 45-48.
9. Christine M. Anderson-Cook and Lu Lu, "Statistics Roundtable:
Best Bang for Your Buck-Part 2," Quality Progress, November

2016, pp. 50-52.
10. Examples of software widely used in setting up and analyzing
designed experiments include Minitab (www.minitab.com), JMP
(www.jmp.com), the mistat R package and the Gendex design
of experiments toolkit (www.designcomputing.net/gendex/).
11. Monte Carlo experiments use repeated random sampling to
generate numerical results.
12. Myrta Rodriguez, Bradley Jones, Connie M. Borror and Douglas
C. Montgomery, "Generating and Assessing Exact G-Optimal
Designs," Journal of Quality Technology, Vol. 42, No. 1, 2010, pp.
3-20.
13. Boxin Tang and Lih-Yuan Deng, "Minimum G2-Aberration for
Nonregular Fractional Factorial Designs," Annals of Statistics,
Vol. 27, No. 6, 1999, pp. 1,914-1,926.
14. Kenett and Shmueli, Information Quality, see reference 1.
15. For more details on the operation of the piston, software
in R and JMP, and running the piston in a simulation mode,
see Kenett and Zacks, Modern Industrial Statistics: With
Applications in R, MINITAB and JMP, reference 4.
16. Anderson-Cook and Lu, "Statistics Roundtable: Best Bang for
Your Buck-Part 1," see reference 8.
17. Anderson-Cook and Lu, "Statistics Roundtable: Best Bang for
Your Buck-Part 2," see reference 9.
18. For more information on the theory behind generating two
and three-level factor designs and an introduction to computer
experiments, see Kenett and Zacks, Modern Industrial Statistics:
With Applications in R, MINITAB and JMP, reference 4.
19. All four designs were generated with the Gendex DoE toolkit.
For more information, visit www.designcomputing.net/
gendex/.
20. Figures 2-4 were derived using the JMP software.

Ron S. Kenett is chairman of
the KPA Group in Ra'anana,
Israel, senior research fellow at
the Neaman Institute in Haifa,
Israel, research professor at
the University of Turin in Italy
and visiting professor at the
Institute of Drug Research at
the Hebrew University of Jerusalem in Israel. Kenett
earned a doctorate in statistics and mathematics at
the Weizmann Institute in Rehovot, Israel. For 15 years,
he edited "World View" in Quality Progress and is an
ASQ senior member and the author of Information
Quality: The Potential of Data and Analytics to Generate
Knowledge (Wiley, 2016).

Nam-Ky Nguyen is a senior
researcher at the Vietnam
Institute for Advanced Study in
Mathematics in Hanoi, Vietnam.
He earned a doctorate in statistics
at the Indian Agricultural Statistics
Research Institute in New Delhi.
He is an ASQ member and a
member of the International Biometrics Society, and the
author of the Gendex DoE toolkit.

qualityprogress.com ❘ October 2017

QP 47


http://www.minitab.com http://www.jmp.com http://www.designcomputing.net/gendex/ http://www.designcomputing.net/gendex 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
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