Reverse programming the optimal process mean problem to identify a factor space profile

For the manufacturer that intends to reduce the processing costs without sacrificing product quality, the identification of the optimal process mean is a problem frequently revisited. The traditional method to solving this problem involves making assumptions on the process parameter values and then determining the ideal location of the mean based upon various constraints such as cost or the degree of quality loss when a product characteristic deviates from its desired target value. The optimal process mean, however, is affected not only by these settings but also by any shift in the variability of a process, thus making it extremely difficult to predict with any accuracy. In contrast, this paper proposes the use of a reverse programming scheme to determine the relationship between the optimal process mean and the settings within an experimental factor space. By doing so, one may gain increased awareness of the sensitivity and robustness of a process, as well as greater predictive capability in the setting of the optimal process mean. Non-linear optimization programming routines are used from both a univariate and multivariate perspective in order to illustrate the proposed methodology.