(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;

Trend-resistant design of experiments under budget constraints.

When experiments are to be performed in a time sequence, the observed responses are affected by a time trend. The construction of trend-resistant run orders is extensively described in the literature. However, run orders that are optimally balanced for time trends usually involve huge costs and they are often of low practical value in view of economical considerations. This paper presents a design algorithm for the construction of trend-resistant run orders under budget constraints. The algorithm offers the experimenter a general method for solving a wide range of practical design problems.