面向多变量生产过程的动态TBE控制图设计与分析

Control charts have been widely used to monitor and determine whether a production process is in-control or not. In the recent years,Time Between Events (TBE) control charts have been proven to be very effective in the monitoring high quality processes and in reliability and maintenance management. In this proposed research, we will develop and investigate some advanced control charts for TBE data, which are adaptive and targeted at more generalized applications, with a focus on multivariate situations. First, in this research we will expand the current studies on TBE chart to adaptive TBE control charts and investigate issues regarding their properties and applications. Necessary modifications and implementation procedures will also be proposed and investigated. Besides a time variable modelled by exponential, we will extend it to Weibull, Gamma or extreme-value distribution. This will lead to a category of charts that will encompass wide application areas. Another focus in our research is the estimation errors and uncertainty in the modelling. This is an important issue because the process stability and the amount of data available for the estimation are of serious concern. We will not be able to assume that past data parameters are known or estimated accurately. Hence, statistical confidence level is a concept that needs emphasis, in research and in applications. This allows us to tailor the development and applications of statistical process control approaches to better suit decision makers. Furthermore, in this study, we will also investigate the statistical and economic design problems for multivariate adaptive TBE control charts. Economic design is another important design approach of control charts from a managerial point of view. It takes into account uncertainty from an economic perspective. This research will improve the application of control chart for multivariate process, promote theoretical research, and provide the technical support for the production quality control and in reliability and maintenance management.

TBE（事件发生间隔时间）控制图可以实时监测两个连续缺陷之间产生的产品数量，在高质量过程控制及可靠性监测中很有潜力的一直过程控制图。目前大部分研究假设事件发生间隔时间服从指数分布，并且研究主要集中在单变量问题。但是，复杂产品的设计技术、制造工艺复杂程度使其具有多因素影响、多质量特性等特点，因此，针对多元质量控制和多分布特征的动态TBE控制图研究能更好地完善多指标、多工序复杂制造系统，对进一步提高产品质量与可靠性有很大帮助。 本项目拟针对多种动态TBE控制图，重点研究其对多变量生产过程的性能特征，包括其在不同分布、生产过程参数未知等情况下的性能分析，以及经济设计。拟解决的关键科学问题包括：动态TBE控制图新的设计方法、性能定量分析、性能比较特征值求解。其预期研究成果将完善统计过程控制理论，推动其基本理论研究，为复杂生产过程质量监控提供支撑。

本项目面向高质量生产过程控制及可靠性监测的问题，研究了一类新的TBE（事件发生间隔时间）控制图的设计方法。充分考虑过程监控的时间间隔和检测次数，分别采用ARL（平均链长）/ATS（平均报警时间）作为控制图设计指标，开展了参数已知情形下的多种无偏控制图设计，在此基础上研究了生产过程分布参数未知情形下的无偏控制图设计，提出了基于序贯抽样检验的动态多阶段TBE控制图设计方法、多阶段截尾数据动态TBE控制图设计方法，提高了过程监控的效果，增强了TBE控制图的实际使用价值，扩展了TBE控制图的适用范围。针对同时监控事件发生间隔和事件幅度、同时监控过程均值和离散度、同时监控多种分类数据的多变量联合监控的问题，本项目开展了在不同分布情形下多变量联合监控控制图的研究，提出了多元伽马控制图、多元非参控制图、综合CUSUM控制图等设计方法，提高了联合监控的监控效率，增强了多变量联合监控控制图的适用性。此外，本项目还开展了针对控制图的经济性设计研究，综合考虑监控成本和监控效率，给出了在分布情形已知和未知情形下，多种控制图的经济性设计方法，降低了过程监控的成本，具有很高的实际使用价值。本项目完成了预期任务。