Multiresponse robust design: Mean square error (MSE) criterion

Most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers. However, manufactured products are typically characterized by numerous quality characteristics. In this paper we present a general framework for the multivariate problem when data are collected from a combined array. Within the framework, a mean square error (MSE) criterion is utilized and a non-linear multiobjective programming problem based on the individual MSE functions of each response is proposed for quality improvement. We adapted a suitable non-linear optimization algorithm to solve the proposed formulation. The optimization method used in this paper generates a string of solutions, called Pareto optimal solutions, rather than a “one shot” optimum solution to make selections and evaluate the trade-offs. The paper also presents an example and comparative results in order to demonstrate the potentials of the proposed approach.