基于贝叶斯估计的威布尔更新过程统计控制  

Statistic control of Weibull renewal process based on the Bayesian estimation

作　　者：曹程明 马义中[1] Cao Chengming;Ma Yizhong(School of Economics and Management,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学经济管理学院,江苏南京210094

出　　处：《系统工程学报》2021年第2期240-246,263,共8页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(71871119)。

摘　　要：针对威布尔更新过程,考虑威布尔分布形状参数偏移的探测问题以及实际中样本数据较少的问题,结合贝叶斯理论,设计了Bayesian-Beta控制图,给出了控制图的设计方法、监控程序和参数的贝叶斯估计方法.使用控制图的平均运行链长的均值AARL(average of the average run length)和标准差SDARL(standard deviation of the average run length)分析了参数估计对所设计的控制图性能的影响,结果表明Bayesian-Beta控制图受参数估计的影响小,对过程偏移具有较好的探测能力.A Bayesian-Beta control chart is proposed for the Weibull renewal process by combining Bayesian theory,to alleviate the problem of detecting the shift of the Weibull shape parameter and the problem of lack of enough sample data in practice usually.The design method and the monitoring procedure of the control chart and the Bayesian estimation method of the parameters are given.The effects of parameter estimation on the chart performance are evaluated in terms of the AARL and the SDARL.It is shown that the Bayesian-Beta control chart is less influenced by the parameter estimation and can detect the process shift efficiently.

关 键 词：威布尔分布 更新过程 贝叶斯 参数估计 AARL SDARL 

分 类 号：O213.1[理学—概率论与数理统计]