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 f actors. The objective of this paper is to develop a general mixed bivariate model that will consider the correlation between the two responses. A gene ral quality loss function is first developed to evaluate societal losses fo r a vector response. Then signal-to-noise ratios as performance measures ar e developed for the three different mixed responses (Smaller the better, La rger the better) (STB, LTB), (Smaller the better, Nominal the best) (STB, N TB), and (Larger the better, Nominal the best) (LTB, NTB). Simulation is in troduced to evaluate the efficiency of performance measures that are develo ped herein.