Optimal Designs for Multi-Response Experiments

Designed experiments can be a powerful tool for gaining a fundamental understanding of systems and processes or maintaining or optimizing systems and processes. There are usually multiple performance and quality metrics that are of interest in an experiment, and these multiple responses may include data from nonnormal distributions, such as binary or count data. A design that is optimal for a normal response can be very different from a design that is optimal for a nonnormal response. This work presents a two-phase method that helps experimenters identify a hybrid design for a multi-response problem. Mixture and optimal design methods are used with a weighted optimality criterion for a three-response problem that includes a normal, binomial, and Poisson model but could be generalized to an arbitrary number and combination of responses belonging to the exponential family. A mixture design is used to identify the optimal weights in the criterion presented.