Economical Operation of the (x^^-, s) Simultaneous Control Chart Indexed by Taguchi's Loss Function

Abstract

Assume that lot quality characteristics obey a normal distribution. Kanagawa et al. have proposed the (x^^-, s) simultaneous control chart, based on the estimator of Kullback-Leibler information, which is designed in conformity with the probability limit method and enables the user to monitor both changes of the mean and variance simultaneously. Further, based on the results derived by Arizono et al., we can evaluate the power characteristics for out-of-control state when using the (x^^-, s) simultaneous control chart. In this paper, we define the expected total operation cost function based on the sampling cost for the (x^^-, s) simultaneous control chart and the loss derived from lot quality, and consider economical operation of the (x^^-, s) simultaneous control chart minimizing the expected total operation cost.