Identifying the Time of Step Change in the Mean of Autocorrelated Processes

Abstract

Control charts are used to detect changes in a process. Once a change is detected, knowledge of the change point would simplify the search for and identification of the special cause. Conse- quently, having an estimate of the process change point following a control chart signal would be useful to process analysts. Change point methods for the uncorrelated process have been studied extensively in the literature; however, less attention has been given to change point methods for autocorrelated processes. Autocorrelation is common in practice and is often modeled via the class of autoregressive-moving average (ARMA) models. In this paper, a maximum likelihood estimator for the time of step change in the mean of covariance-stationary processes that fall within the general ARMA framework is developed. The estimator is intended to be used as an “add-on” following a signal from a phase II control chart. Considering first-order pure and mixed ARMA processes, Monte Carlo simulation is used to evaluate the performance of the proposed change point estimator across a range of step change magnitudes following a genuine signal from a control chart. Results indicate that the estimator provides process analysts with an accurate and useful estimate of the last sample obtained from the unchanged process. Additionally, results indicate that if a change point estimator designed for the uncorrelated process is applied to an autocorrelated process, the performance of the estimator can su↵er dramatically.