独立序列均值与方差变点的累积和估计及应用  

Cumulative sum estimation for change-points in the mean and variance of independent observations and applications

作　　者：袁芳[1] 田铮[1,2] 苏晓丽[1] 陈占寿[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072 [2]中国科学院遥感应用研究所,北京100101

出　　处：《控制理论与应用》2010年第3期395-399,共5页Control Theory & Applications

基　　金：国家自然科学基金资助项目(60375003);国家航空基金基础项目资助项目(03I53059);西北工业大学科技创新基金资助项目(2007KJ01033)

摘　　要：产品生产加工过程中,反映产品质量参数的均值和方差都有可能出现异常波动,及时发现质量异常波动,对于控制产品质量十分重要.在工业生产、通信工程等领域中独立序列有广泛应用背景.本文研究了独立序列中均值和方差都存在变点且变点时刻不相同时的变点估计问题,给出变点时刻的累积和(CUSUM)型估计,并得到变点估计的收敛速度.最后将该方法应用于航空发动机管路生产质量控制中和放射医学研究的扫描仪质量控制问题中,模拟结果和实例分析都说明方法的有效性.In the process of product manufacturing, abnormal fluctuations of the mean and variance, which reflect prod-uct quality parameters, are always possible. It is extremely important to discover the abnormal variation of the quality in time for controlling the quality of products. Besides, independent observations have been applied extensively in industrial production, communication engineering and other fields. The estimation problem of change-points of independent observa-tions whose mean and variance change respectively is studied. The cumulative sum（CUSUM） estimators of change-points are presented and the rate of convergence is established. Finally, the proposed method is applied to the production qual-ity control of aero engine pipelines and the quality control of the scanners in the radiation medicine research. Both the simulation results and instance analysis support the validity of our method.

关 键 词：独立序列 均值与方差变点 CUSUM估计 

分 类 号：F224[经济管理—国民经济] F273.2