Optimal Design of Experiments for Dual-Response Systems with Normal, Binary, and Poisson Distributions

Many experiments on a system or process have multiple responses of interest, each with potentially different data types and hence underlying distributions. However, traditionally, designing the experiment typically has been based on only one type of response, usually a continuous response, often assumed to come from a normal distribution. This can lead to suboptimal design choices for the other types of responses, since the underlying distribution has an impact on what the ideal design should be. In the Department of Defense, tests with multiple responses are common with many tests having continuous responses, binary responses, and count responses that must be shown to have met a specified requirement. This work extends a new approach to design of experiments for dual-response systems. Dual-response systems with combinations of normal, binomial, or Poisson distributions are considered. The method utilizes a weighted criterion that combines the D-criterion for the linear model and the Bayesian D-criterion for the binary and Poisson models. A coordinate exchange algorithm is used to find a set of designs using the weighted D-criteria for the relative prioritization of the design performance for each of the two responses as the design criterion. Several designs are created and compared across different weights for different dual-response systems. Sensitivity of the priors supplied for the Bayesian D-criterion for the Poisson response is also discussed. The methods are illustrated with a case study for an experiment to evaluate a missile defense warning system.