尤度比管理図の経済的運用法とその設計に関する研究

(x，S)控制图是一种基于似然统计量的控制图，使用户既能监测过程均值的SIFT，又能监测过程方差的变化。我们考虑了(x，S)控制图中对数似然比统计量的近似分布。结果，可以确定在指定的第一类误差概率和样本量下的控制界限，并可以评估(x，S)控制图的威力。此外，为了改善图的性能，还考虑了样本容量和抽样间隔可变的自适应(x，S)控制图。通过比较(x，S)控制图和自适应(x，S)控制图的性能，证实了变样本容量和抽样间隔(x，S)控制图的性能优于(x，S)控制图。并将双抽样方法应用于(x，S)控制图，提出了双抽样(x，S)控制图。实践证明，双抽样(x，S)控制图对于减少失控状态下的平均行程特别有效。另一方面，基于(x，S)控制图的抽样成本和批次质量损失，定义了期望总运行成本函数，进而考虑了(x，S)控制图的经济运行和批次质量损失，进而考虑了(x，S)控制图的经济运行。在此基础上，给出了在指定损失情况下最小化期望总运行成本的经济运行和最小化任何损失的期望总运行成本的经济运行。

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.