Economical operation of the C_pm control chart for monitoring process capability index

Process capability indices are widely used to provide evaluation measures of process potential and performance. Especially, the process capability index C_pm, which is defined by the tolerance and deviation from the target, is called the Taguchi index. Boyles investigated the statistical characteristics of the C_pm esti-mator, and also proposed a methodology for the C_pm control chart. Needless to say, since the process capability index C_pm is based on the concept of the quality loss introduced by Taguchi, it basically relates to the concept of cost performance. In this article, we consider the economical operation of the C _pm control chart in conformity with the expected total operation cost function based on the sampling cost, the sample cost and the surplus loss by means of ignoring the out-of-control state. Then, the economical operation of the C_pm control chart minimizing the total operation cost is investigated.