Cumulative sum estimation for change-points in the mean and variance of independent observations and applications
独立序列均值与方差变点的累积和估计及应用

In the process of product manufacturing, abnormal fluctuations of the mean and variance, which reflect product 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 observations 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 quality 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.