15 research outputs found
Quarter-fraction factorial designs constructed via quaternary codes
The research of developing a general methodology for the construction of good
nonregular designs has been very active in the last decade. Recent research by
Xu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class of
nonregular designs constructed from quaternary codes. This paper explores the
properties and uses of quaternary codes toward the construction of
quarter-fraction nonregular designs. Some theoretical results are obtained
regarding the aliasing structure of such designs. Optimal designs are
constructed under the maximum resolution, minimum aberration and maximum
projectivity criteria. These designs often have larger generalized resolution
and larger projectivity than regular designs of the same size. It is further
shown that some of these designs have generalized minimum aberration and
maximum projectivity among all possible designs.Comment: Published in at http://dx.doi.org/10.1214/08-AOS656 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
The study of good nonregular fractional factorial designs has received
significant attention over the last two decades. Recent research indicates that
designs constructed from quaternary codes (QC) are very promising in this
regard. The present paper shows how a trigonometric approach can facilitate a
systematic understanding of such QC designs and lead to new theoretical results
covering hitherto unexplored situations. We focus attention on one-eighth and
one-sixteenth fractions of two-level factorials and show that optimal QC
designs often have larger generalized resolution and projectivity than
comparable regular designs. Moreover, some of these designs are found to have
maximum projectivity among all designs.Comment: Published in at http://dx.doi.org/10.1214/10-AOS815 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Recent Developments in Nonregular Fractional Factorial Designs
Nonregular fractional factorial designs such as Plackett-Burman designs and
other orthogonal arrays are widely used in various screening experiments for
their run size economy and flexibility. The traditional analysis focuses on
main effects only. Hamada and Wu (1992) went beyond the traditional approach
and proposed an analysis strategy to demonstrate that some interactions could
be entertained and estimated beyond a few significant main effects. Their
groundbreaking work stimulated much of the recent developments in design
criterion creation, construction and analysis of nonregular designs. This paper
reviews important developments in optimality criteria and comparison, including
projection properties, generalized resolution, various generalized minimum
aberration criteria, optimality results, construction methods and analysis
strategies for nonregular designs.Comment: Submitted to the Statistics Surveys (http://www.i-journals.org/ss/)
by the Institute of Mathematical Statistics (http://www.imstat.org
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The Need of Considering the Interactions in the Analysis of Screening Designs
Fractional factorial designs are widely used experimental plans for identifying important factors in screening studies where many factors are involved. Traditionally, Plackett-Burman (PB) and related designs are employed for in such studies because of their cost efficiencies. The caveat with the use of PB designs is that interactions among factors are implicitly assumed to be non-existent. However, there are many practical situations where some interactions are significant and ignoring them can result in wrong statistical inferences, including biased estimates, missing out on important factors and detection of spurious factors. We reanalyze data for three chemical experiments using the Hamada and Wu’s method and show that we are able to identify significant interactions in each of these chemical experiments and improve the overall fit of the model. In addition, we analyze the data using a Bayesian approach that confirms our findings. In both approaches, graphical tools are employed along with easily available software for analysis
The Use of Nonregular Fractional Factorial Designs in Combination Toxicity Studies
When there is interest to study n chemicals using x dose levels each, factorial designs that require xn treatment groups have been put forward as one of the valuable statistical approaches for hazard assessment of chemical mixtures. Exemplary applications and cost-eciency comparisons of full factorial designs and regular fractional factorial designs in toxicity studies can be found in Nesnow et al. (1995), Narotsky et al. (1995), and Groten et al. (1996,1997). We introduce nonregular fractional factorial designs and show their bene�ts using two studies reported in Groten et al. (1996). Study 1 shows nonregular designs can provide the same amount of information using 75% of the experimental costs required in a regular design. Study 2 demonstrates nonregular designs can additionally estimate some partially aliased e�ects, which cannot be done using regular designs. We also provide a statistical method to evaluate the quality of an assumption made by experts in Study 2 of Groten et al. (1996)
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