自相关控制图理论及其若干应用

【作者】 赵再强；

【导师】 张嗣瀛； 高齐圣；

【作者基本信息】 青岛大学 ， 系统理论， 2007， 硕士

【摘要】 统计过程控制的目的，就是要建立并保持过程处于可接受的并且稳定的水平，以确保产品和服务符合规定的要求。要做到这一点，所应用的主要统计工具就是控制图。常规控制图的基本假设前提是观测值独立同分布，而在实际生产过程中，质量指标值常表现出自相关现象，违背独立性假定。此时，运用常规控制图对平稳自相关过程进行监控时，会出现大量的虚发警报，对过程做出错误的判断，给质量管理、质量控制工作带来严重的误导，减弱了控制图的使用效果，甚至丧失监控过程的作用。本文系统研究了常规控制图的理论思想并对自相关控制图理论方法进行初步探讨，对自相关过程中各类控制图的应用进行了分析比较，以表明白相关现象对质量过程的影响，同时运用残差控制图对具有自相关性的经济序列进行分析，并对未来宏观经济运行质量进行预警。论文各章节主要内容如下：第一章，阐述了选题的目的意义，并介绍了控制图的发展状况及最新动态。第二章，系统介绍了控制图的原理、设计思想、分类以及判异准则等方面的理论知识。第三章，介绍了三种常规控制图：均值(?)—极差(R)控制图，单值(X)—移动极差(R_s)控制图，EWMA控制图(Exponentially Weighted Moving Average Control Chart，指数加权滑动平均控制图)。第四章，介绍了两种自相关控制图：残差控制图，改进型EWMA控制图。第五章，自相关过程中各类控制图的应用比较。第六章，利用残差控制图对我国1952-2004年GDP进行分析，判断宏观经济的运行质量并对未来进行预测。第七章，对本文工作进行总结，并提出今后努力的方向。更多还原

【Abstract】 The purpose of the statistical process control is to build and maintain the process atan acceptable and stable level, and to ensure that products and services meet therequirements. To achieve this, the main statistical tool is the control chart. A basicassumption of conventional control charts is that observations from the process atdifferent times are independent random variables. But in fact many processes displayinherently auto correlated behavior. As a result, using conventional control charts for asmooth autocorrelation process, there will be false alarms. The process will make a wrongjudgment. The quality management and quality control will be seriously misled, and theeffect of control charts will be diminished, or even the process will be out of control. Thepaper systematically studied the theory of conventional and auto-correlated control chart, and in order to show the influence of auto-correlated phenomenon on the quality control, various related process control charts are analyzed. Using residual chart, theauto-correlated economic time-series is analyzed, and the early warning of futureeconomic running quality is carried on.The main content of this paper is as follows:The first chapter expounds the purpose of this paper, and introduces the history ofthe control chart and the latest developments.The second chapter systematically introduces the principle, design, classification, and abnormality criteria of the control chart.The third chapter introduces three conventional control charts: mean (?) and range(R) chart, individual (X) and moving range (R_s) chart, exponentially weighted movingaverage (EWMA) control chart.The fourth chapter introduces two auto-correlated control charts: residual chart, improved exponentially weighted moving average control chart.The fifth chapter contrasts the application of different control charts in auto-correlated process.The sixth chapter uses residual control chart to monitor the GDP of China from 1952to 2004; and judges the performance of macroeconomic and forecasts it for the future.The seventh chapter summarizes the full paper and proposes the further researchwork.更多还原