Combinatorics and Statistical Inferencing D-Optimal Experimental Designs with Covering Array Attributes
While D-Optimal experimental designs are used with great frequency in surface response analysis they also offer a mechanism to screen factors and factor interactions in experiments involving categorical factors. Covering arrays are widely used to test interactions in factors, but have not been used quantitatively to offer insight into the variance contributions of factors and interactions or estimating coefficients as optimal designs can. As with optimal designs the role of covering arrays is to produce the fewest possible experimental runs with the objective of obtaining the most information, in the case of covering arrays this has historically been qualitative detection of interactions, and with optimal designs quantitative detection. A covering array, CAλ(N; t, k, v), is an N×k array for which every N×t subarray has the property that every t-tuple appears at least λ times. In this application, t is the strength, k is the number of factors (degree), and v is the number of symbols for each factor (order). A D-Optimal design, OD(model, k, v) utilizes a model identifying main effects and interactions and in a similar manner to a covering array is based on k factors with v levels. The strength of a covering array dictates the level of coverage much as a model does for a D-Optimal design.A hybrid covering array / D-Optimal design generator has been constructed that enhances D-Optimal designs that estimate main effects plus two-factor interactions while including full covering to strength t = 3. The benefit of this hybrid design is that it (1) maintains high D-effciencies with a full strength 3 covering, allowing quantitative estimation of main effects and two-factor interactions, (2) offers the ability to qualitatively see three factor interactions, and (3) has the added benefit of providing a closer estimation of full factorial results than a D-optimal design does alone.
Dean S. Hoskins
Department of Computer Science and Engineering, Arizona State University,Tempe, Arizona 85287
国际会议
2006 International Conference on Design of Experiments and Its Applications(2006实验设计及其应用国际会议)
天津
英文
2006-07-09（万方平台首次上网日期，不代表论文的发表时间）