Process optimization via confidence region: a case study from micro-injection molding

In industrial research, experiments are designed to determine the optimal factor levels of the process parameters. Typically, experimental data are used to fit empirical models (for example, regression models) to derive one set of optimal conditions that maximize (or minimize) the response. Unfortunately, the optimization rarely provides a Confidence Interval for the location of the optimal solution, even though the optimal solution itself is subjected to variability. From a practitioner's point of view, identifying a region of possible optimal values provides high operational flexibility to adjust process parameters online during production. This paper provides a procedure for computing a confidence region for the optimal point based on experimental data, bootstrapping, and data depth. The procedure is validated using a case study from micro-injection molding, where the part weight is maximized under a constraint of the probability of flash formation. The proposed method considers that the objective function (part weight) and the constraint (probability of flash formation) are estimated from experimental data and subjected to sampling variability.