Optimal Design for Experiments with Potentially Failing Trials PETER HACKL Department of Statistics, University of Economics and Business Administration, Augasse 2-6, 1090 Vienna, Austria. Abstract: We discuss the problem of optimal allocation of the design points of an ex- periment for the case where the trials may fail with non-zero probability. Nu- merical results for D-optimal designs are given for estimating the coefficients of a polynomial regression. For small sample sizes these designs may deviate substantially from the corresponding designs in the case of certain response. They can be less efficient, but are less affected by failing trials. 1 Introduction Application of the standard theory of optimal design is based on the assumption that all trials of an experiment result in corresponding observations of the response variable. However, we are never sure that the responses of all trials will really be available when the experiment is actually performed. This leads us to consider designs for potentially failing trials, i.e., designs where the probability for getting a response is less than one for some or all sites in the design space. The problem of potentially failing trials has been treated by Hedayat and Majumdar (1983) and later by Das and Sinha (1994) in the context of redesigning experiments due to shortened resources: Which observation should be dropped given the probabilities that the trials will be failing at the sites of the planned experiment. Our paper discusses a more general question: What is the optimal experiment in the case of possibly failing trials. The paper is organized as follows. In Section 2 we state the problem and present criteria that allows us to assess the optimality of candidate designs. In Section 3 we show on the basis of a quadratic polynomial how D-optimal designs for estimating the model coefficients change due to failing trials. •Kitsos, C.P., and Miiller, W.G., Eds., Proceedings of MODA-4, Physica Verlag, Heidelberg, 1995 C. P. Kitsos et al. (eds.), MODA4 — Advances in Model-Oriented Data Analysis © Springer-Verlag Berlin Heidelberg 1995