A Two‐Sided Cumulative Sum Chart for First‐Order Integer‐Valued Autoregressive Processes of Poisson Counts |
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| Authors: | Petek Yontay Christian H Weiß Murat Caner Testik Z Pelin Bayindir |
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| Affiliation: | 1. Department of Industrial Engineering, Hacettepe University, , Ankara, Turkey;2. Department of Mathematics, Darmstadt University of Technology, , Darmstadt, Germany;3. Department of Industrial Engineering, Middle East Technical University, , Ankara, Turkey |
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| Abstract: | Count data processes are often encountered in manufacturing and service industries. To describe the autocorrelation structure of such processes, a Poisson integer‐valued autoregressive model of order 1, namely, Poisson INAR(1) model, might be used. In this study, we propose a two‐sided cumulative sum control chart for monitoring Poisson INAR(1) processes with the aim of detecting changes in the process mean in both positive and negative directions. A trivariate Markov chain approach is developed for exact evaluation of the ARL performance of the chart in addition to a computationally efficient approximation based on bivariate Markov chains. The design of the chart for an ARL‐unbiased performance and the analyses of the out‐of‐control performances are discussed. Copyright © 2012 John Wiley & Sons, Ltd. |
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| Keywords: | autocorrelated counts CUSUM control chart Markov chains approach Poisson INAR(1) model statistical process control |
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