Change point estimation of a normal process variance with monotonic change

Abstract

When a control chart signals an out-of-control condition, a search begins to identify and eliminate the cause of disturbance. Identification of the time when a change manifests itself into the process, referred to as the change point, can help process engineers to perform root cause analyses effectively. In this paper, a Maximum Likelihood Estimator (MLE) is proposed to estimate the time of a monotonic change in the variance of a normal quality characteristic. Using Monte Carlo simulation, performance of the proposed estimator is studied and comprehensively compared to the existing maximum likelihood estimators for simple step and linear trend changes. This simulation is repeated for a number of monotonic change types, following a signal from a Shewhart S-control chart. Numerical results reveal that the proposed estimator provides appropriate and robust estimation, with regard to the magnitude and type of change.

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