(D _T , C)-Optimal Run Orders

Abstract

Cost considerations have rarely been taken into account in optimum design theory. A few authors consider measurement costs, i.e. the cost 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. Our proposed algorithm incorporates both costs in optimum design construction and enables one to compute cost-efficient and nearly trend-free run orders for arbitrary design problems. 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.