Open AccessDissertation
Optimal factorial designs with robust properties
TLDR
In this article, the authors introduce the concept of partially clear interactions which leads to a richer class of robust designs when specific interactions are known to be negligible a priori, and develop several methods to construct designs that allow for additional factors to be studied in comparison to designs with clear two-factor interactions.Abstract:
Fractional factorial designs are used in a wide variety of disciplines as a means of studying how changes in the settings of a set of factors influence a response variable. Two important considerations in choosing a fractional factorial design are identifying which effects can be jointly estimated and how the effects not estimated influence the estimation. Orthogonal arrays with clear two-factor interactions provide a class of designs robust to nonnegligible effects. In the first part of this thesis, we introduce the concept of partially clear interactions which leads to a richer class of robust designs when specific interactions are known to be negligible a priori. We develop several methods to construct designs that allow for additional factors to be studied in comparison to designs with clear two-factor interactions. When used in conjunction with non-regular designs, the results become even more powerful as they provide additional flexibility and retain the robust properties. In some situations, the experimenter would like to study factors at more than two levels, such as when curvature has the potential to occur within the experimental region. The second part of this thesis focuses on the estimation of main effects and specified interactions for designs with more than two levels. As designs with more than two levels have additional complications, results are provided that aid in the search for efficient designs that also have robust properties. For two-level designs, the criteria of $G$ and G2-aberration are based on Jcharacteristics and they provide measures of the projection properties of a design. For multilevel designs, extension to G2 was previously done without the use of J-characteristics.read more
Citations
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Journal ArticleDOI
Experiments: Planning, Analysis, and Parameter Design Optimization
TL;DR: This work discusses the practice of problem solving, testing hypotheses about statistical parameters, calculating and interpreting confidence limits, tolerance limits and prediction limits, and setting up and interpreting control charts.
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Supplement to Simulated Annealing Model Search for Subset Selection in Screening Experiments
Mark A. Wolters,Derek Bingham +1 more
TL;DR: This work proposes a new approach particularly well suited to screening, which uses an intentionally nonconvergent stochastic search to generate a large set of well-fitting models, each with the same number of variables.
Posted Content
Finding the Dimension of a Non-empty Orthogonal Array Polytope
TL;DR: In this article, a sufficient condition for the convex hull of all feasible points polytope of an OA defining integer linear program (ILP) to be full dimensional within the LP relaxation affine space when it is not empty was established.
Bulutoglu, Dursun A. Finding the dimension of a non-empty orthogonal array
TL;DR: Appa et al. as discussed by the authors showed that if a polytope is non-empty, then it is full-dimensional within the affine space where all the feasible points of the ILD relaxation lie.
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Enumeration of Strength Three Orthogonal Arrays and Their Implementation in Parameter Design
Julio Romero,Scott H. Murray +1 more
TL;DR: In this paper, the authors describe the construction and enumeration of mixed orthogonal arrays (MOA) to produce optimal experimental designs, which is a multiset whose rows are the different combinations of factor levels.
References
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Book ChapterDOI
On the Experimental Attainment of Optimum Conditions
George E. P. Box,K. B. Wilson +1 more
TL;DR: The work described in this article is the result of a study extending over the past few years by a chemist and a statistician, which has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but they believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.
Journal ArticleDOI
The design of optimum multifactorial experiments
R. L. Plackett,J. P. Burman +1 more
Journal ArticleDOI
Some New Three Level Designs for the Study of Quantitative Variables
George E. P. Box,D. W. Behnken +1 more
TL;DR: In this paper, a class of incomplete three level factorial designs useful for estimating the coefficients in a second degree graduating polynomial are described and the designs either meet, or approximately meet, the criterion of rotatability and for the most part can be orthogonally blocked.
Book
Experiments: Planning, Analysis, and Parameter Design Optimization
C. F. Jeff Wu,Michael S. Hamada +1 more
TL;DR: This book discusses Factorial and Fractional Factorial Experiments at Three Levels, Robust Parameter Design for Signal-Response Systems, and other Design and Analysis Techniques for Experiments for Improving Reliability.