82 research outputs found
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
Complete enumeration of two-Level orthogonal arrays of strength with constraints
Enumerating nonisomorphic orthogonal arrays is an important, yet very
difficult, problem. Although orthogonal arrays with a specified set of
parameters have been enumerated in a number of cases, general results are
extremely rare. In this paper, we provide a complete solution to enumerating
nonisomorphic two-level orthogonal arrays of strength with
constraints for any and any run size . Our results not only
give the number of nonisomorphic orthogonal arrays for given and , but
also provide a systematic way of explicitly constructing these arrays. Our
approach to the problem is to make use of the recently developed theory of
-characteristics for fractional factorial designs. Besides the general
theoretical results, the paper presents some results from applications of the
theory to orthogonal arrays of strength two, three and four.Comment: Published at http://dx.doi.org/10.1214/009053606000001325 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Selection of non-regular fractional factorial designs when some two-factor interactions are important
Introduction: Non-regular two-level fractional factorial designs, such as Placket-Burman designs, are becoming popular choices in many areas of scientific investigation due to their run size economy and flexibility. The run size of non-regular two-level factorial designs is a multiple of 4. They fill the gaps left by the regular two-level fractional factorial designs whose run size is always a power of 2 (4, 8, 16, 32, ...). In non-regular factorial designs each main effect is partially confounded with all the two-factor interactions not involving itself. Because of this complex aliasing structure, non-regular factorial designs had not received sufficient attention until recently. ... In practical applications of non-regular designs, it is often in the case that some of the two-factor interactions are important and need to be estimated in addition to the main effects. In this article, we consider how to select non-regular two-level fractional factorial designs when some of the two-factor interactions are presumably important. We propose and study a method to select the optimal non-regular two-level fractional factorial designs in the situation that some of the two-factor interactions are potentially important. We then discuss how to search for the best designs according to this method and present some results for the Plackett-Burman design of 12 runs.Includes bibliographical references
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
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