一种可用于检测过程尺度参数的非参数控制图  

A Distribution-free Control Chart for Monitoring Variability

作　　者：宋贽 何川[3] 张久军[1] SONG Zhi;HE Chuan;ZHANG Jiu-jun(Department of Mathematics, Liaoning University, Liaoning Shenyang 110036, China;College of Science, Shenyang Agricultural University, Liaoning Shenyang 110866, China;Department of Mathematics, Northeastern University, Liaoning Shenyang 118019, China)

机构地区：[1]辽宁大学数学院,辽宁沈阳110036 [2]沈阳农业大学理学院,辽宁沈阳110866 [3]东北大学数学系,辽宁沈阳118019

出　　处：《数理统计与管理》2019年第4期652-660,共9页Journal of Applied Statistics and Management

基　　金：国家自然科学基金资助项目(11571191,11431006,11371202);河北省高等学校科学技术研究青年基金项目(QN2017328);河北经贸大学科研基金青年项目(2017KYQ09)

摘　　要：传统的控制图多数是在已知过程分布的假设下构建的,这种控制图被称为参数控制图.然而,在实际应用中,大多数过程因为其数据的复杂性导致他们的精确分布往往难以确定.当预先指定的参数分布无效时,参数控制图的结果将不再可靠.为了解决这个问题,通常考虑非参数控制图,因为非参数控制图比参数控制图更加稳健.近年来对非参数控制图的研究越来越多,但大多数现有的控制图主要是用于检测位置参数的变化.本文提出一个新的非参数Shewhart控制图(称为LOG图),可用来检测未知连续过程分布的尺度参数.文中依据运行长度分布的均值,方差和分位数,分析了LOG图在过程受控和失控时的性能表现,并与其他非参数控制图进行比较.模拟结果表明,LOG图在不同过程分布下对检测尺度参数的漂移都具有很好的性能.最后用一个实例来说明LOG图在实际中的应用.Traditional control charts are constructed under the assumption of known process distribution.Such control charts are known as the parametric control charts.In various applications,most of the data streams follow complex processes and their exact distributions are often untraceable.When a parametric distribution specified beforehand is invalid,some articles argue that results from such conventional parametric monitoring schemes would no longer be reliable.To address this problem,the nonparametric control chart is often considered,since a nonparametric control chart is more robust than a parametric one.Although research on nonparametric control charts has increased in recent years,the majority of existing charts focus only on detecting process location shifts.In this paper,we propose a new Shewhart-type distribution-free control chart(named as LOG chart)for monitoring of unknown scale parameter of continuous distributions.The in-control and out-of-control performance properties and a comparison with some other distribution-free control charts are presented in terms of the average,the standard deviation and some percentiles of the run length distribution.Numerical results based on Monte Carlo analysis show that the proposed LOG chart provides quite a satisfactory performance for a class of location-scale models.The application of our proposed LOG chart is illustrated by a real data example.

关 键 词：非参数 方差 平均运行长度 统计过程控制 

分 类 号：O212[理学—概率论与数理统计]