Calculation of an optimal region of operation for dual response systems fitted from experimental data

While there is abundant literature on Response Surface Methodology about how to seek optimal operating settings for Dual Response Systems (DRS) using various optimisation approaches, the inherent sampling variability of the fitted responses has typically been neglected. That is, the single global optimum settings for the fitted response represent the expected value of the fitted functions since the true response systems are, in general, noisy and unknown in many engineering and scientific experiments. This paper presents an approach for DRS based on Monte Carlo simulation of the system under study. For each simulated set of responses, a new global optimisation algorithm for DRS is utilised to compute the global optimal factor settings. Repetition of this process constructs an optimal region in the control factor space that provides more useful information to a process engineer than a single optimal – expected – solution. It is shown how the optimal region can be used as an indicator of how trustworthy this single solution is, and as a set of alternative solutions from where an engineer can select other process settings in case limitations not considered by the DRS model prevent the adoption of the single expected optimum. Application to Taguchi's Robust Parameter Design problems illustrates the proposed method.