Allocating Factors to the Columns of an Orthogonal Array When Certain Interactions are Important

Abstract

Two-level fractional factorial plans are used extensively in many diverse fields, notably in quality control work and industrial experimentation. A fractional factorial plan represented by an orthogonal array of strength two is universally optimal for estimating the mean and all main effects when all interactions are assumed to be absent. An orthogonal array OA (2n, 2n???{1, 2, 2) where n???d2 is an integer, can be constructed by representing the columns of the array by the factorial effects of a 2n factorial experiment, i.e., (1, 2, 12, 3, 13, 23, 123, 4, ?€?, 1234 ?€?). Such an array represents a 2n-run fractional factorial plan for a 2-level experiment involving 2n???{1 factors. Such a plan is optimal for estimating the mean and all main effects in the absence of 2-factor and higher order interactions. However, if the number of factors in the experiment is smaller than 2n???{1, one can entertain some 2-factor interactions in the model, along with the mean and all main effects. The problem is then to allocate the factors to the above ?€?factor representations?€?, so that the user-specified 2-factor interactions, in addition to the mean and the main effects, are optimally estimable. This problem would be discussed in the talk. An algorithm would be presented for the allocation of factors to factor representations that ensures the optimal estimation of the mean, all main effects and some specified 2- factor interactions. Some illustrations will be given for the cases n=3,4.