Quality Progress - October 2017 - 42

F E AT U R E

DESIGN OF EXPERIMENTS

New experimental designs

The classic approach to the design of experiments
(DoE) includes orthogonal arrays and full, fractional
and central composite designs. From George E.P. Box,
William G. Hunter and J. Stuart Hunter's 1978 influential
Statistics for Experimenters2 to Peter Goos and Bradley Jones' Optimal Design of Experiments, 3 industrial
statistics has seen major improvements in experimental
design methods.4
Particularly influential in recent years have been
space-filling computer experiments5 and definitive
screening designs (DSD).⁶
Computer experiments are not limited to the physical
setup of factor-level combinations. They are performed
using electronic input files and consist of run points
filling the experimental space.
DSDs are relatively small designs for experiments with
three-level factors that provide information on main and
quadratic effects. DSD-based mixed-level screening
designs can be used for experiments involving two and
three-level factors.⁷ In this article, we refer to only twolevel designs.
Today, experimental design methods are expected
to be flexible and packaged in software. 8-10 Alternative
designs, generated by various optimal design considerations, can be compared for their performance. The
design evaluation tools presented in this article can
be applied in a more general setup in which data are
generated through observational data or any arbitrary
method. Be cautious in these cases because of possible
self-selection and bias effects.

Optimal designs

Optimal designs are constructed using several
approaches. Their optimality is determined by different
criteria that lead to different solutions.
The D-optimality criterion minimizes the determinant of the covariance matrix of the model coefficient
estimates. D-optimality precisely estimates the main
effects, quadratic effects and interactions in a pre-specified model and is fully determined by the experimental
design before the experiment is conducted.
D-optimal designs are used in experiments conducted
to estimate effects or test for significance. Their main
application is in designs with an experimental goal of
identifying the active factors. A design is A-optimal if
it minimizes the sum of the variances of the regression
coefficients. This is another approach to obtain precise
estimates of the effects.

42 QP

October 2017 ❘ qualityprogress.com

I-optimal designs
minimize the average
Do you want a good
variance of prediction
predictive model of
over the design space. If
piston performance
the primary experimento design an optimal
tal goal is to predict a
control system?
response or determine
regions in the design
space in which the response falls within an acceptable
range, the I-optimality criterion is more appropriate than
the D-optimality criterion. In these cases, precise prediction of the response takes precedence over precise
estimation of the parameters.
A related approach is G-optimal designs, which minimize the maximum prediction variance over the design
region. These designs are calculated using Monte Carlo
experiments of the design space.11-12
The minimum aberration criterion is useful when
selecting good, regular two-level fractional factorial
designs and is used to discriminate among regular
fractional factorial designs with the same resolution.
Minimum aberration compares the frequency of aliases
of regular designs at different levels. Regular designs
with the smallest frequency of worst aliases are considered the best. The minimum G-aberration criterion also
can handle irregular design spaces.13
When considering what method to use to generate
an experimental design, keep in mind that experiments
are conducted to produce information. This requires a
managed transition from problem elicitation to data collection, data analysis, derivation and communication of
findings. Eventually, this roadmap produces information.

InfoQ

Experimental designs are used to generate the data set
used in a study. InfoQ is different from data quality and
analysis quality, though it is dependent on these components and the relationship between them.
A key requirement for determining InfoQ is the nature
of the study goal and whether it is explanatory, predictive or descriptive. An explanatory goal is based on
causal hypotheses or seeks causal answers. A predictive
goal predicts future or new individual observations. A
descriptive goal quantifies an observed effect using a
statistical or other approximation. In designing an experiment, the study goal should be accounted for.
The definition of InfoQ consists of the utility from the
application of a statistical or data analytic model to a
data set (X) given the research goal. The assessment of


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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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