Quality loss functions and performance measures for a mixed bivariate response

Mixed bivariate vectors occur when a sampling unit has two different types of responses. This is a common occurrence in many manufacturing processes. The traditional optimization approach for such a problem is to analyze each response separately and to determine vital factors for that response, then choose optimal factor settings by making trade-off adjustments among all factors. The objective of this paper is to develop a general mixed bivariate model that will consider the correlation between the two responses. A general quality loss function is first developed to evaluate societal losses for a vector response. Then signal-to-noise ratios as performance measures are developed for the three different mixed responses (Smaller the better, Larger the better) (STB, LTB), (Smaller the better, Nominal the best) (STB, NTB), and (Larger the better, Nominal the best) (LTB, NTB). Simulation is introduced to evaluate the efficiency of performance measures that are developed herein.