Simultaneous Optimization of Multiple Responses That Involve Correlated Continuous and Ordinal Responses According to the Gaussian Copula Models

Abstract

This study investigates the simultaneous optimization of multiple correlated responses that involve mixed ordinal and continuous responses. The proposed approach is applicable for responses that have either an all ordinal categorical form are continuous but have different marginal distributions, or when standard multivariate distribution of responses is not applicable or does not exist. These multiple responses have rarely been the focus of studies despite their high occurrence during experiments. The copula functions have been used to construct a multivariate model for mixed responses. To resolve the computational problems of estimation under a high dimension of responses, we have estimated parameters of the model according to a pairwise likelihood estimation method. We adapted the generalized distance approach to determine settings of the factors that simultaneously optimized the mean of continuous responses and desired cumulative categories of the ordinal responses. A simulation study was used to evaluate the performance of the estimators from the pairwise likelihood approach. Finally, we presented an application of the proposed method in a real data example of a semiconductor manufacturing process.

Keywords

• Gaussian copula
• Mixed outcomes
• Multivariate distribution
• Simultaneous optimization