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

TL;DR

This paper introduces a likelihood ratio test-based statistical model for detecting and estimating multiple mean shifts in Gaussian processes, specifically applied to phase I control chart analysis, with demonstrated efficiency through simulations.

Contribution

It proposes a novel likelihood ratio test approach for multiple change point detection in phase I data, improving accuracy in identifying process mean shifts.

Findings

Effective detection of multiple shifts demonstrated in simulations

High accuracy and precision in change point estimation

Applicable to large datasets with outliers and multiple shifts

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.