尤度比管理図の経済的運用法とその設計に関する研究

似然比控制图的经济运行研究及其设计

• 批准号: 10680434
• 负责人: ARIZONO Ikuo
• 金额: $ 1.22万
• 依托单位: University of Osaka Prefecture
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680434/
• 关键词: (x, s) Control Chart; Adaptive Control Chart; Double Sampling Control Chart; Taguchi's Loss Function; Economical Operation of Control Chart; Double Sampling管理図; (χ^^-,s)同時管理図

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.

（x, s）控制图是一种基于似然统计量的控制图，用户可以同时监控过程均值的筛选和过程方差的变化。我们考虑了（x, s）控制图中对数似然比统计量的近似分布。因此，可以在规定的第一类误差概率和样本量下确定控制极限，并评估（x, s）控制图的功率。此外，为了提高图的性能，考虑了可变样本量和采样间隔的自适应（x, s）控制图。比较（x, s）控制图与自适应（x, s）控制图的功率，证实变样本量和采样间隔（x, s）控制图的性能优于（x, s）控制图。在此基础上，将双采样方法应用于（x, s）控制图，提出了双采样（x, s）控制图。实验证明，双采样（x, s）控制图对于减小失控状态下的平均运行长度特别有效。另一方面，我们根据（x, s）控制图的抽样成本和批次质量的损失定义了期望总运行成本函数，然后考虑（x, s）控制图的经济运行和批次质量的损失，然后考虑（x, s）控制图的经济运行。因此，既提出了在考虑损失的情况下使预期总运行成本最小化的经济运行，又提出了在任何损失情况下使预期总运行成本最小化的经济运行。

项目成果

青山行宏,渡壁京子,有薗育生: "可変サンプル・サイズと可変サンプリング間隔をもつ(x^^-,s)同時管理図の設計"日本経営工業会論文誌. 49. 374-383 (1999)

Yukihiro Aoyama、Kyoko Watakabe、Ikuo Arizono：“可变样本量和可变采样间隔的 (x^^-,s) 同步控制图的设计” 日本管理协会杂志 49. 374-383 (1999)。

Yukihiro AOYAMA, Kyoko WATAKABE and Ikuo ARIZONO: "Design of an Adaptive (x, s) Simulataneous Control Chart with Variable Sample Size and Sampling Intervals"Journal of Japan Industrial Management Association. Vol.49. 374-383 (1999)

Yukihiro AOYAMA、Kyoko WATAKABE 和 Ikuo ARIZONO：“Design of an Adaptive (x, s) Simulate Control Chart with Variable Sample Size and Sampling Intervals”日本工业管理协会杂志。

Kyoko Watanabe, Ikuo Anzono: "The Power of the (x^^-,s) Control Chart Based on the Log-Likelihood Ratio Statistic"Saval Research Logistics. 46. 928-951 (1999)

Kyoko Watanabe、Ikuo Anzono：“基于对数似然比统计的 (x^^-,s) 控制图的功效”Saval Research Logistics。

Kyoko Watakabe, Ikuo Arizono: "The Power of the (x,s) Control Chart Based on the Log-Likelihood Ratio Statistic"Saval Research Logistics. 46・8. 928-951 (1999)

Kyoko Watakabe，Ikuo Arizon：“基于对数似然比统计的 (x,s) 控制图的功效”Saval Research Logistics 46・8 (1999)。

Kyoko WATAKABE and Ikuo ARIZONO: "The Power of the (x, s) Simulataneous Control Chart Based on the Log-Likelihood Ratio Statistic"Naval Research Logistics. Vol.46. 928-951 (1999)

Kyoko WATAKABE 和 Ikuo ARIZONO：“基于对数似然比统计的 (x, s) 同步控制图的力量”海军研究后勤。