The optimal process mean problem: Integrating predictability and profitability into an experimental factor space

For complex manufacturing systems, process or product optimization can be instrumental in achieving a significant economic advantage. To reduce costs associated with product non‐conformance or excessive waste, engineers often identify the most critical quality characteristics and then use methods to obtain their ideal parameter settings. The optimal process mean problem is one such statistical method; it begins with the assumption of the characteristic parameters, whereby the ideal settings are determined based upon the tradeoff among various processing costs. Unfortunately, however, the ideal parameter settings for a characteristic mean can be unpredictable, as it is directly influenced by changes in the process variability, tolerance, and cost structure. In this paper, a method is proposed that relates the optimal process mean to the ideal settings through experimental design. With the method, one may gain greater predictability of the new optimal process mean when the process conditions are altered. The methodology is illustrated for a process with multiple mixed quality characteristics; such an optimal process mean problem is seldom treated in the literature.