Quality loss functions and performance measures for a mixed bivariate response

Mixed bivariate vectors occur when a sampling unit has two different types of response. This is a common occurrence in many manufacturing processes. The traditional optimization approach for such a problem is to analyse each response separately and to determine vital factors for that response, then choose optimal factor settings by making trade‐off adjustments among all factors. Develops a general mixed bivariate model that will consider the correlation between the two responses of general quality loss function. First, develops a general quality loss function to evaluate societal losses for a vector response and then develops signal‐to‐noise ratios as performance measures and for the three different mixed responses (smaller‐the‐better, larger‐the‐better), (smaller‐the‐better, nominal‐the‐best) and (larger‐the‐better, nominal‐the‐best). Introduces simulation to evaluate the efficiency of performance measures that are developed herein.