Minimum Aberration 2 k–p Designs
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.
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TL;DR: In this article, a general majorization framework for assessing balanced lattice designs is presented, which includes a stringent criterion of majorization via pairwise coincidences and flexible surrogates via convex functions.
Abstract: This paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs, including fractional factorial designs, supersaturated designs and uniform designs. We present a general majorization framework for assessing designs, which includes a stringent criterion of majorization via pairwise coincidences and flexible surrogates via convex functions. Classical orthogonality, aberration and uniformity criteria are unified by choosing combinatorial and exponential kernels. A construction method is also sketched out.
40 citations
TL;DR: This article defines causal factorial effects for treatment components that may be applied sequentially to a patient and proposes experimental designs that can be used to study the treatment components.
Abstract: Dynamic treatment regimes are time-varying treatments that individualize sequences of treatments to the patient. The construction of dynamic treatment regimes is challenging because a patient will be eligible for some treatment components only if he has not responded (or has responded) to other treatment components. In addition, there are usually a number of potentially useful treatment components and combinations thereof. In this article, we propose new methodology for identifying promising components and screening out negligible ones. First, we define causal factorial effects for treatment components that may be applied sequentially to a patient. Second, we propose experimental designs that can be used to study the treatment components. Surprisingly, modifications can be made to (fractional) factorial designs—more commonly found in the engineering statistics literature—for screening in this setting. Furthermore, we provide an analysis model that can be used to screen the factorial effects. We demonstrat...
39 citations
TL;DR: In this paper, the influence of eight emulsion polymerization variables on the final PSA properties of butyl acrylate/vinyl acetate (BA/VAc) emulsion-based PSAs was investigated.
Abstract: Emulsion-based pressure-sensitive adhesives (PSAs) are gaining in importance due to their improved performance as well as the lower environmental impact of the emulsion polymerization process. In this study, the influence of eight emulsion polymerization variables on the final PSA properties of butyl acrylate/vinyl acetate (BA/VAc) emulsion-based PSAs was investigated (i.e., BA/VAc ratio, acrylic acid content, type and concentration of stabilizer, concentration of initiator, concentration of CTA, temperature, solids content). Final performance properties such as peel strength, shear strength, and tack were investigated on two different substrates: stainless steel and high-density polyethylene. A wide range of properties was generated ranging from very good to poor PSA performance. The screening design fulfilled its purpose in that it was used to generate a wide range of final properties. The results obtained here will be used in the decision-making process for further experimentation. However, for severa...
37 citations
TL;DR: In this paper, the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly is studied, which can be interpreted as the balancing of multicriteria optimization.
Abstract: We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multicriteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection and an algebraic algorithm for vectorial matroids. Our work is partly motivated by applications to minimum-aberration model-fitting in experimental design in statistics, which we discuss and demonstrate in detail.
37 citations
TL;DR: In this article, the MaxC2 design with n = N/4+1 is unique up to isomorphism and has general minimum lower order confounding (GMC) design.
36 citations
References
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471 citations
Book•
23 Jun 1976
TL;DR: In conclusion, the size of Industrial Experiments, Fractional Replication--Elementary, and Incomplete Factorials are found to be about the same as that of conventional comparison experiments.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
311 citations
09 Jun 1976
271 citations
TL;DR: Incomplete Factorials, Fractional Replication, Intermediate Factorial, and Nested Designs as discussed by the authors are some of the examples of incomplete Factorial Experiments and incomplete fractional replicates.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.
252 citations