The decision of type and direction of process change Based on Akaike information criterion in (x‾,s) Simultaneous Control Chart

Abstract

Traditionally, a x_bar control chart has been used together with s or R control chart to monitor a state of the production process. But there is such a fault that it is hard to interpret the connection of behavior between mean and dispersion in the process because respective characteristics are monitored by an individual method in parallel. A (x_bar,s) simultaneous control chart has been proposed in order to enable the process manager to monitor the change in the process mean, process dispersion, or both. Also, identifying which of the process parameters is responsible for the out-of-control condition of the process is one of the important issues in the process management. Especially, it is an important task in the (x_bar,s) simultaneous control chart because the observations of some parameters are connected. In the traditional literature, the multiple decision method based on the statistical hypothesis tests and the decomposition method of the statistic by the perspective of Kullback-Leibler information are proposed for the purpose of identifying the parameter responsible for the out-of-control condition. In this paper, we propose how to identify the parameter responsible for the out-of-control condition using Akaike information criterion. Then, the validity of the proposed technique is shown through the numerical experiment.