| Research Abstract |
The (x, s) control chart which is a kind of the control chart based on the likelihood statistic enables the user to monitor both the sift in process mean and the change in process variance. We have considered the approximate distributions of the log-likelihood ratio statistic in the (x, s) control chart. As a result, it has been possible to decide the control limit under the specified probability of the first kind of error and sample size and to evaluate the power of the (x, s) control chart. Further, the adaptive (x, s) control chart with variable sample size and sampling intervals has been considered for the purpose of improving chart performance. Comparing the powers between the (x, s) control chart and the adaptive (x, s) control chart, it has been confirmed that the performance of the variable sample size and sampling interval (x, s) Control Chart is superior to the (x, s) control chart. Furthermore, the double sampling procedure has been applied to the (x, s) control chart, then the double sampling (x, s) control chart has been proposed. It has been proved that the double sampling (x, s) control chart is particularly effective for decreasing the average run length under the out-of-control state. On the other hand, we defined the expected total operating cost function based on the sampling cost for the (x, s) control chart and the loss derived on the lot quality, then the economical operations of the (x, s) control chart and the loss derived on the lot quality, then the economical operations of the (x, s) control chart have been considered. Consequently, both of the economical operation minimizing the expected total operating cost in the situation that the loss to be considered is specified and the economical, operation minimizing the expected total operating cost for any loss have been presented.
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