A strategy of robust parameter design for multiple responses

In this article, we provide a strategy for the simultaneous optimization of multiple responses. Cases are covered where a set of response variables has finite target values and depends on easy to control as well as on hard to control variables. Our approach is based on loss functions, without the need for a predefined cost matrix. For each element of a sequence of possible weights assigned to the individual responses, settings of the easy to control parameters are determined, which minimize the estimated mean of a multivariate loss function. The estimation is based on statistical models, which depend only on the easy to control variables. The loss function itself takes the value zero, if all responses are on target with zero variances. In each case, the derived parameter settings are connected to a specific compromise of the responses, which is graphically displayed to the engineer by so called joint optimization plots. The expert can thereby gain valuable insight into the production process and then decide on the most sensible parameter setting. The proposed strategy is illustrated with a data set from the literature and new data from an up to date application.