The objective of parameter design is to determine settings of the design parameters of a product or a process such that the performance characteristic becomes robust against manufacturing variation or environmental noise. Most existing parameter design techniques are concerned with the case of only one performance characteristic, although in product and process design, the case of multiple performance characteristics is more common. A critical problem in dealing with multiple performance characteristics is how to compromise the conflict among the selected levels of the design parameters for each individual performance characteristic. The existing methods for compromising the conflict do not consider the robustness against manufacturing variation or environmental noise, or do not sufficiently reflect the basic idea of parameter design.
This thesis shows that the loss function proposed by Dong and Pignatiello for a multiple performance characteristics is contradictory in that a point which is farther from the target might have the same loss with the one which is closer to the target. We develop a new loss function of multiple performance characteristics which is free from this contradiction. We then derive the expected loss function as well as the expected loss function after adjustment, and investigate the relation between the correlation of the characteristics and the quality loss. We also develop a method for compromising the conflict using the expected loss function after adjustment for the various cases.
