An Optimality Probability Index for Correlated Multiple Responses

Abstract

In the real problems, there are many cases which have correlated quality characteristics so multiple response optimization can be more realistic if we can consider correlation structure of responses. In this study we propose a new method which uses multivariate normal probability to find the optimal treatment in an experimental design. Moreover, a heuristic method is used to find better factors’ level in all possible combinations in the designs with large number of controllable factors and their levels. Some simulated numerical examples and a real case were studied by the proposed approach and the comparison of the results with previous methods show efficiency of the proposed method.

Keywords:

• Multiple response optimization
• Correlation
• Design of experiments
• Multivariate normal probability

Mathematics Subject Classification:

• 62K99
• 65C60