Simultaneous Optimization of Multiple Correlated Responses with Application to a Thermal Spraying Process

In industrial applications, it is often desired to find settings of process parameters, which lead to pre‐specified target values of multiple quality characteristics with minimal variance. One approach to solve this problem is to minimize an estimated risk function depending on a cost matrix. The joint optimization (JOP) method follows this general strategy using a sequence of diagonal cost matrices and requires estimated models for the expectation and the variance of the responses. However, if the quality characteristics might be correlated, this should be considered at the model or optimization stage in order to find a realistic solution. In this contribution, we extend the JOP method to the simultaneous optimization of correlated multiple responses. We also introduce a new approach for the choice of non‐diagonal cost matrices. The resulting JOP method for correlated responses is illustrated on an application arising in the field of thermal spraying.