基于马尔可夫链模型的B&L VP X 控制图统计性能分析

工业工程 ›› 2012, Vol. 15 ›› Issue (3): 87-91.

基于马尔可夫链模型的B&L VP X 控制图统计性能分析

南京理工大学经济管理学院, 江苏南京 210094

出版日期:2012-06-30 发布日期:2012-07-21
作者简介:郭志芳（1983-）女，山西省人，博士研究生，主要研究方向为质量管理与应用统计.
基金资助:
教育部人文社会科学研究规划基金资助项目（10YJA630020）；国家自然科学基金资助项目(11071120)；江苏省社会科学基金资助项目（08SHA001）

Statistical Performance Analysis of a VP X Control Chart with B&L Switching Rule by Using a Markov Chain Model

School of Economics and Management, Nanjing University of Science & Technology, Nanjing 210094, China

Online:2012-06-30 Published:2012-07-21

摘要/Abstract

摘要： 在已有VP X控制图基础上，增加了B&L转换规则，构建了基于马尔可夫链模型的B&L VP X控制图统计性能分析模型，给出了统计性能指标ATS、AATS以及ANSW的表达式。针对2组设计参数，将构建的模型与现有VP X控制图进行了比较分析，结果表明当平均运行时间相同时，本文构建的模型在缩短报警时间和减少转换次数方面，都有着明显的优势，而且随着转换参数L的增大，这种优势会增大。

关键词: 统计过程控制, 控制图, 变量参数X 控制图, 马尔可夫链

Abstract: In statistical process control, variable parameter (VP)X chart is widely used. To improve the performance of the VPXchart, Bai & Lee (B&L) switching rules are applied to design the VPX chart. By this method, a Markov chain model is developed to obtain the expressions of Average Time to Signal (ATS), Adjusted Average Time to Signal (AATS), and average number of switches (ANSW). To evaluate the performance of the proposed method, comparison is done between the chart designed by the proposed method and the existing VPX chart by using two samples. Results show that, with the same average runtime, the proposed method outperforms the existing VPX chart in both shortening the alarm time and in reducing the number of switch times. The larger the parameter L is, the better the performance of the proposed method is.

Key words: statistical process control, control chart, variable parameter X chart, Markov chain

郭志芳，程龙生. 基于马尔可夫链模型的B&L VP X 控制图统计性能分析[J]. 工业工程, 2012, 15(3): 87-91.

Guo Zhifang， Cheng Longsheng. Statistical Performance Analysis of a VP X Control Chart with B&L Switching Rule by Using a Markov Chain Model[J]. Industrial Engineering Journal , 2012, 15(3): 87-91.

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