Optimal Runs Order for (S,n,x Mixed S,n,) Systematic Factorial Design

Abstract

When factorial experiments suffer from the presence of time trend or need large cost for varying the experimental conditions between the successive runs, random allocation of treatments may no longer be appropriate. Instead, systematic runs orders may have to be used to reduce or eliminate the effects of such a trend and reduce the cost by minimizing the number of factor level changes. The resulting designs are referred to as time trend free and/or minimum cost designs. Also, we consider here that the estimates of main effects and two-factor interactions are time trend free. The generalized fold over scheme (GFS) introduced by Coster and Cheng (1988), is one of runs ordering methods which produce runs orders for these two types of factorial experiments that are both economical and/or resistant to time trend, since there are some experimental situations where it is not possible to move randomly between treatment combinations. We explained by the GFS method how we can obtain the D-optimal design with maximum D-efficiency, and compared between different runs orders in the degree of time resistant by using the D-optimal design criterion . We calculated the number of level changes for each factor alone while Coster and Cheng calculated he total number of factor level changes in the entire design. Building upon the GFS method, we generated the works of Coster and Cheng for systematic symmetric designs to the systematic mixed level factorial designs, so we will give our cost function and our algorithm for construction these designs. Since the estimation of main effects and two-factor interactions are trend freeness, and minimum cost cannot always be achieved simultaneously , we proposed several sequences and catalogs showing runs orders for various symmetric , , , factorial designs , and mixed factorial designs which has minimum cost and/or time trend free .