Quality Progress - December 2016 - 55


DESIGN OF EXPERIMENTS

After a model is validated, analysts have
many options and can continue to
drill down and leverage modern statistical
software capabilities as necessary.
tional confirmatory tests in the optimal region allows

recent evolution of statistical capabilities available

experimenters to check their predictions, ensuring a

to analysts. Cutting-edge techniques in uncertainty

statistical model does, in fact, have predictive capa-

quantification, big data analytics, DoE and Bayes-

bility beyond the original data set and will result in

ian reliability estimation have been implemented

the best-possible process performance.

for practitioners in recent years. Now, the critical

In our example, the prediction obtained from the

path is developing the statistical expertise and capa-

model was a combination of factor-level settings

bilities in the workforce to leverage these powerful

not represented by any of the runs in the 22-run ex-

techniques. QP

periments. The logical choice for confirmatory runs,
therefore, was at the settings that yielded the maximum times to failure, which turned out to be closely
predicted by our model-a testament to the success
of the experimental approach.
After a model is validated, analysts have many
options and can continue to drill down and leverage
modern statistical software capabilities as necessary.
Analysts can perform sensitivity analyses, run simulation-based probabilistic analyses of a scaled-up process to simulate the impact of full-scale manufacturing process tolerance variations, and use a quality by
design approach to minimize defect rate predictions
and develop product specification tolerances.
Robust parameter design via propagation of error
methods can be used to ensure a product is robust
to random variation present in the manufacturing or
operational environment.12 Global optimization approaches can be used, which account not only for
performance of the process variables, but also incorporate-and optimize for-cost, schedule and manufacturing throughput-related effects associated with
each process variable setting.
As warfighter systems continue to become more
complex to achieve battlefield superiority, the Office
of the Secretary of Defense is requiring the integration of statistical rigor into test and evaluation-related
activities to ensure products meet the demands of the
users in the harshest of conditions.13
Advances in computational power have led to a

REFERENCES
1.	Rachel Johnson, Gregory Hutto, James Simpson and Douglas Montgomery, "Designed Experiments for the Defense Community," Quality
Engineering, Vol. 24, No. 1, pp. 60-79.
2.	Christine Anderson-Cook and Connie Borror, "Paving the Way," Quality
Progress, April 2013, pp. 18-29.
3.	Douglas Montgomery, Design and Analysis of Experiments, eighth edition, Wiley, 2009.
4.	David E. Coleman and Douglas C. Montgomery, "A Systematic Approach
to Planning for a Designed Industrial Experiment," Technometrics, Vol.
35, No. 1, 1993, pp. 1-12.
5.	Raymond H. Myers, Douglas C. Montgomery and Christine M. AndersonCook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, third edition, Wiley, 2009.
6.	Jerome Sacks, William J. Welch, Toby J. Mitchell and Henry P. Winn,
"Design and Analysis of Computer Experiments," Statistical Science, Vol.
4, No. 4, 1989, pp. 409-423.
7.	Bradley Jones and Christopher J. Nachtsheim, "Definitive Screening
Designs With Added Two-Level Categorical Factors," Journal of Quality
Technology, Vol. 45, No. 2, 2013, pp. 121-129.
8.	Robert Tibshirani, "Regression Shrinkage and Selection via the Lasso,"
Journal of the Royal Statistical Society, Series B, Vol. 58, No. 1, 1996, pp.
267-288.
9.	Hui Zou and Trevor Hastie, "Regularization and Variable Selection via
the Elastic Net," Journal of the Royal Statistical Society, Series B, Vol. 67,
2005, pp. 301-320.
10. Raymond H. Myers, Douglas C. Montgomery, G. Geoffrey Vining and
Timothy J. Robinson, Generalized Linear Models With Applications in
Engineering and the Sciences, second edition, Wiley, 2010.
11. William O. Meeker and Luis A. Escobar, Statistical Methods for Reliability Data, Wiley-Interscience, 1998.
12. Myers, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, see reference 5.
13. Department of Defense, Scientific Test and Analysis Techniques in Test
and Evaluation Implementation Plan, 2012, http://tinyurl.com/
dod-test-analysis.
DOUGLAS RAY is lead mathematical statistician
of the U.S. Army Armament Research, Development and Engineering Center's (ARDEC) statistical
methods and analysis group in the ARDEC quality
engineering and system assurance directorate's
reliability management branch at Picatinny Arsenal,
NJ. He is an American Statistical Association-accredited graduate statistician, a lean Six Sigma Black
Belt from the ARDEC's Lean Six Sigma Competency Office, an ASQ-certified
reliability engineer and a combat veteran of the U.S. Army.

December 2016 * QP 55


http://www.tinyurl.com/dod-test-analysis

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