基于条件表现的EWMA-Maxwell控制图精确设计  

The Designs of the EWMA-Maxwell Control Charts Based on Conditional Performance via Exact Methods

作　　者：郭宝才[1,2] 吴志超 朱玉梅 何希祥 GUO Bao-cai;WU Zhi-chao;ZHU Yu-mei;HE Xi-xiang(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China;Collaborative Innovation Center of Statistical Data Engineering Technology&Application,Zhejiang Gongshang University,Hangzhou 310018,China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018 [2]浙江工商大学统计数据工程技术与应用协同创新中心,浙江杭州310018

出　　处：《数理统计与管理》2023年第2期278-292,共15页Journal of Applied Statistics and Management

基　　金：国家社会科学基金资助项目(18BTJ037)。

摘　　要：多数控制图设计均基于过程服从正态分布,且受控过程参数已知的假定,然而实际中,过程真实分布常常偏态,且过程参数也经常未知.本文首先设计了等尾和平均链长无偏(无偏)EWMA图用于偏态Maxwell分布的监控,接着从条件视角出发推导出了条件平均链长的精确分布,讨论了参数估计对所提控制图的影响,并基于超越概率准则给出为将参数估计所引致的伪警报率降低到合理水平所需的第Ⅰ阶段最小样本数.为弥补实际应用中第Ⅰ阶段样本数据的不足,提出精确修正方法设计具有理想条件表现的等尾和无偏EWMA图用于早期过程的监控.结果表明,相较于未修正图,修正图发现过程失控的能力略有下降.另外,修正无偏图整体上优于等尾图.最后通过实例说明所设计控制图的实际执行.Most of the control charts are designed based on the assumptions that the distribution to be monitored follows the normal distribution and in-control parameters are known.However,in many practical applications,the underlying distribution is often skewed and the process parameters are often unknown.This paper develops the equal-tailed and average run length-unbiased(unbiased)EWMA charts to monitor the skewed Maxwell distribution.Next the exact distribution of the conditional average run length are derived and the infuence of parameter estimation on the proposed charts is studied from a conditional perspective.Besides,based on exceedance probability criterion,the required minimum number of Phase I samples is given to reduce the false alarm rate caused by parameter estimation to a reasonable level.In order to solve the problem that the limited Phase I data results in more false alarms than expected,an exact method is proposed to adjust the equal-tailed and unbiased EWMA control charts to obtain the desired conditional in-control performance for detecting the problems that may occur during start-up.Comparison results show that,relative to the unadjusted chart,the adjusted chart has a slightly bad out-of-control performance.In addition,the performance of the adjusted limits average run length-unbiased EWMA chart is better than the adjusted limits equal-tailed EWMA chart.Finally,an example is used to illustrate the implementation of the proposed control charts.

关 键 词：控制图 参数估计 条件平均链长 超越概率准则 条件视角 

分 类 号：O212[理学—概率论与数理统计]