Multi-response optimization considering quality loss and rejection cost

In this paper, a new multi-response optimization (MRO) approach is proposed to find the optimal parameter setting of the controllable factors from an economic point of view. In some cases, rejection costs, like the rework cost and scrap cost, are incurred when outgoing products fall above the upper specification limit or below the lower specification limit. A rejection cost function is established when the output responses fail to meet their specification limits from the viewpoint of customers. In addition, there still exists different quality level when two different responses fall within their corresponding specification limits. A multivariable quality loss function is used to calculate the expected quality loss (i.e., bias, quality of prediction and robustness) when output responses fall within their corresponding specification limits. Finally, an integrated cost function including rejection cost and quality loss is minimized by using a hybrid genetic algorithm with pattern search. The effectiveness of the proposed method is verified through an example from the literature.