Discrimination of Out-of-Control Condition Using AIC in (x_bar, s) Control Chart

The x control chart for process mean and either the R or s control chart for process dispersion are used together for the purpose of monitoring manufacturing process. However, it has been pointed out that this procedure has such a fault that it is difficult to capture the behavior of process condition visually with taking into consideration the relationship between the shift in the process mean and the change in the process dispersion because the respective characteristics are monitored by an individual control chart in parallel. Then, the ( , ) x s control chart has been proposed in order to enable process managers to monitor the change in the process mean, process dispersion, or both. On one hand, identifying which process parameters are responsible for out-of-control condition of process is one of important issues in the process management. Especially, it is surely important in the ( , ) x s control chart where some parameters are monitored at a single plane. The previous literature has proposed the multiple decision method based on the statistical hypothesis tests for the purpose of identifying parameters responsible for out-of-control condition. In this paper, we propose how to identify parameters responsible for out-of-control condition using the information criterion. Then, the effectiveness of proposed method is shown through some numerical experiments.