Solving the optimal process target problem using response surface designs in heteroscedastic conditions

The contemporary industrial environment continues to rely on the identification of the optimal process target as a means to minimise the product defect rate and ultimately reduce manufacturing costs. Within the context of the optimal process target problem, this paper will offer three distinct contributions. First, a review of literature associated with the process target problem indicates that most research work assumes a known process distribution mean and variance prior to the identification of optimal settings. In contrast, this paper will incorporate the use of response surface designs into solving the process target problem, thus removing the need to make assumptions regarding the process parameters. Second, most research regarding the development of response surface designs either assumes that the same number of observations are made on a quality characteristic of interest, or model error always exhibits a uniform pattern of constant variance. This paper, however, will incorporate alternative modelling techniques to investigate instances when these assumptions are not present, thus broadening the scope of the process target problem. Finally, most research in this area focuses on the determination of the optimal process mean; in this paper, however, we propose a model for simultaneously determining the optimal process mean and variance.