Minimum aberration designs for discrete choice experiments

A discrete choice experiment (DCE) is a survey method that givesinsight into individual preferences for particular attributes.Traditionally, methods for constructing DCEs focus on identifyingthe individual effect of each attribute (a main effect). However, aninteraction effect between two attributes (a two-factor interaction)better represents real-life trade-offs, and provides us a better understandingof subjects’ competing preferences. In practice it is oftenunknown which two-factor interactions are significant. To address theuncertainty, we propose the use of minimum aberration blockeddesigns to construct DCEs. Such designs maximize the number ofmodels with estimable two-factor interactions in a DCE with two-levelattributes. We further extend the minimum aberration criteria toDCEs with mixed-level attributes and develop some general theoreticalresults

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Regularities in the Augmentation of Fractional Factorial Designs

Two-level factorial experiments are widely used in experimental design because they are simple to construct and interpret while also being efficient. However, full factorial designs for many factors can quickly become inefficient, time consuming, or expensive and therefore fractional factorial designs are sometimes preferable since they provide information on effects of interest and can be performed in fewer experimental runs. The disadvantage of using these designs is that when using fewer experimental runs, information about effects of interest is sometimes lost. Although there are methods for selecting fractional designs so that the number of runs is minimized while the amount of information provided is maximized, sometimes the design must be augmented with a follow-up experiment to resolve ambiguities. Using a fractional factorial design augmented with an optimal follow-up design allows for many factors to be studied using only a small number of additional experimental runs, compared to the full factorial design, without a loss in the amount of information that can be gained about the effects of interest. This thesis looks at discovering regularities in the number of follow-up runs that are needed to estimate all aliased effects in the model of interest for 4-, 5-, 6-, and 7-factor resolution III and IV fractional factorial experiments. From this research it was determined that for all of the resolution IV designs, four or fewer (typically three) augmented runs would estimate all of the aliased effects in the model of interest. In comparison, all of the resolution III designs required seven or eight follow-up runs to estimate all of the aliased effects of interest. It was determined that D-optimal follow-up experiments were significantly better with respect to run size economy versus fold-over and semi-foldover designs for (i) resolution IV designs and (ii) designs with larger run sizes

Optimal and near-optimal pairs for the estimation of effects in 2-level choice experiments

This paper gives constructions for optimal and near-optimal sets of pairs for the estimation of main effects, and for the estimation of main effects and two factor interactions, in forced choice experiments in which all attributes have two levels. The number of pairs in the sets is much smaller than that in previously constructed optimal 2-level choice experiments. © 2002 Elsevier B.V. All rights reserved

Tailoring the Statistical Experimental Design Process for LVC Experiments

The use of Live, Virtual and Constructive (LVC) Simulation environments are increasingly being examined for potential analytical use particularly in test and evaluation. The LVC simulation environments provide a mechanism for conducting joint mission testing and system of systems testing when scale and resource limitations prevent the accumulation of the necessary density and diversity of assets required for these complex and comprehensive tests. The statistical experimental design process is re-examined for potential application to LVC experiments and several additional considerations are identified to augment the experimental design process for use with LVC. This augmented statistical experimental design process is demonstrated by a case study involving a series of tests on an experimental data link for strike aircraft using LVC simulation for the test environment. The goal of these tests is to assess the usefulness of information being presented to aircrew members via different datalink capabilities. The statistical experimental design process is used to structure the experiment leading to the discovery of faulty assumptions and planning mistakes that could potentially wreck the results of the experiment. Lastly, an aggressive sequential experimentation strategy is presented for LVC experiments when test resources are limited. This strategy depends on a foldover algorithm that we developed for nearly orthogonal arrays to rescue LVC experiments when important factor effects are confounded

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

Discriminating Between Optimal Follow-Up Designs

Sequential experimentation is often employed in process optimization wherein a series of small experiments are run successively in order to determine which experimental factor levels are likely to yield a desirable response. Although there currently exists a framework for identifying optimal follow-up designs after an initial experiment has been run, the accepted methods frequently point to multiple designs leaving the practitioner to choose one arbitrarily. In this thesis, we apply preposterior analysis and Bayesian model-averaging to develop a methodology for further discriminating between optimal follow-up designs while controlling for both parameter and model uncertainty

Economic Trend Resistant2n-(n-k) Designs of Resolutions III and IV Based on Hadamard Matrices

This article utilizes the Normalized Sylvester-Hadamard Matrices  of size 2kx2kand their associated  saturated orthogonal arrays OA(2k, 2k - 1, 2, 2) topropose analgorithmbased on factor projection (Backward/Forward) for the construction of three systematic run-after-run2n-(n-k) fractional factorial designs: (i) minimum cost  trend free 2n-(n-k)designsof resolution III (2k-1≤n≤2k– 1 – k)by backward factor deletion (ii) minimum cost trend free 2n-(n-k) designsof resolution III (k+1≤n≤ 2k-1– 2+k ) by forward factor addition (iii) minimum costtrend free  2n-(n-k) designsof resolution IV (2k-2≤n≤2k-1-2) ,where each 2n-(n-k)design is economic minimizing the number of factor level changes between the 2ksuccessive runs and allows for the estimation of all factor main effects unbiased by the linear time trend,which might be present in the 2ksequentially generated responses. The article gives for each 2n-(n-k)design: (i) the defining contrast displaying the design’s alias structure(ii) the k independent generators for sequencingthe design’s  2n-(n-k) runs  by the Generalized Fold over Scheme and (ii) the minimum total cost of factor level changes between the 2n-(n-k) runs of the design. Proposed designs compete well with existing systematic2n-(n-k)designs (of either resolution) in minimizing the experimental costandin securing factors’ resistance to the non-negligible time trend. Keywords: Sequential fractional factorial experimentation; Time trend free systematic run orders; Generalizedfoldover scheme for sequencing experimentalruns; The total cost of factor level changes between successive runs; The Normalized Sylvester –Hadamard Matrices; Orthogonal Arrays and factor projection; Design resolution and the alias structure. DOI: 10.7176/JEP/11-25-05 Publication date:September 30th 202

(Dt,C) Optimal run orders.

Cost considerations have rarely been taken into account in optimum design theory. A few authors consider measurement costs, i.e. the costs associated with a particular factor level combination. A second cost approach results from the fact that it is often expensive to change factor levels from one observation to another. We refer to these costs as transition costs. In view of cost minimization, one should minimize the number of factor level changes. However, there is a substantial likelihood that there is some time order dependence in the results. Consequently, when considering both time order dependence and transition costs, an optimal ordering is not easy to find. There is precious little in the literature on how to select good time order sequences for arbitrary design problems and up to now, no thorough analysis of both costs is found in the literature. For arbitrary design problems, our proposed design algorithm incorporates cost considerations in optimum design construction and enables one to compute cost-efficient run orders that are optimally balanced for time trends. The results show that cost considerations in the construction of trend-resistant run orders entail considerable reductions in the total cost of an experiment and imply a large increase in the amount of information per unit cost.Optimal; Run orders;