Identifying the time of step change in the mean of autocorrelated processes |
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Authors: | Marcus B Perry Joseph J Pignatiello Jr |
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Institution: | 1. Department of Information Systems, Statistics, and Management Science , The University of Alabama , Tuscaloosa , AL , USA;2. Department of Industrial and Manufacturing Engineering , Florida State University , Tallahassee , FL , USA |
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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. Consequently, 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 article, 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 suffer dramatically. |
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Keywords: | ARMA(p q) models autocorrelated processes change-point estimation stationary processes statistical process control (SPC) |
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