Optimum target value for multivariate processes with unequal non-conforming costs

In quality control charts, the problem of determining the optimum process mean arises when the deviation of a quality characteristic in one direction is more harmful than in the opposite direction. The failure mode in these two directions is usually different. A great majority of researches in this area have considered asymmetric cost function for processes with single quality characteristics. In this paper, we consider processes in which there are more than one quality characteristics to monitor. The quality characteristics themselves may or may not be independent. Based upon the specification limits and the costs associated with the deviations we derive a formula to determine the optimum process mean. To illustrate the proposed formula and to estimate the costs associated with the optimum process mean we present four numerical examples by simulation. The results of the simulation studies show that considerable amount of savings can be obtained by applying the proposed process means.