The $overline{x}$ control chart for the process mean and either the R or s control chart for the process dispersion have been used together to monitor the manufacturing processes. However, it has been pointed out that this procedure is flawed by a fault that makes it difficult to capture the behavior of process condition visually by considering 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 ($overline{x}$, s) control chart has been proposed to enable the process managers to monitor the changes in the process mean, process dispersion, or both. On the one hand, identifying which process parameters are responsible for out-of-control condition of process is one of the important issues in the process management. It is especially important in the ($overline{x}$, 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 to identify the 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.