Determining the optimum process mean under the bivariate quality characteristics

Wen and Mergen (1999) have addressed the problems of a product having specification limits but the manufacturing process not being capable of meeting the specifications in the short term. They select the process mean based on balancing the cost of not meeting the upper specification limit and the lower specification limit. However, they have not considered the quality loss for a product within specifications in the model. Their model was formulated on the basis of a single quality characteristic, but the effect of multiple quality characteristics has not been considered in their model. In this paper, we propose a modified Wen and Mergen's cost model with bivariate quality characteristics and with quadratic asymmetrical quality loss, for a product within specifications, for determining the optimum process mean.