A D-optimal design approach to constrained multiresponse robust design with prioritized mean and variance considerations

The traditional measures of ensuring quality, derived from viewing quality as simply conforming to specifications, does not adequately address today's global markets and value-driven customers. Consequently, process improvement projects are often performed to improve operational performance in order to increase customer satisfaction. Therefore, process improvement methods, such as robust design, are important to industrial quality improvement initiatives. Yet, little of the work in the area of robust design has specifically addressed problems involving physical processing constraints that create an irregularly shape experimental region and the simultaneous consideration of multiple quality characteristics. To address these issues, we propose a new approach to robust design that utilizes D-optimal experimental designs in the context of multiresponse optimization problems in order to overcome the limitations of standard experimental approaches often used in robust design studies. Specifically, we formulate our optimization models as a preemptive nonlinear goal programming problem that focuses on consideration of the mean and variance. We also investigate the extension of optimization models traditionally used in robust design investigations to address multiple responses and compare the outcomes of our proposed approaches using a numerical example.