Estimating Multiple Step Shifts in a Gaussian Process Mean with an Application to Phase I Control Chart Analysis

Abstract

In preliminary analysis of control charts, one may encounter multiple shifts and/or outliers especially with a large number of observations. The following paper addresses this problem. A statistical model for detecting and estimating multiple change points in a finite batch of retrospective (phase I)data is proposed based on likelihood ratio test. We consider a univariate normal distribution with multiple step shifts occurred in predefined locations of process mean. A numerical example is performed to illustrate the efficiency of our method. Finally, performance comparisons, based on accuracy measures and precision measures, are explored through simulation studies.