A Two-Sided Cumulative Sum Chart for First-Order Integer-Valued Autoregressive Processes of Poisson Counts

作者：Yontay Petek; Weiss Christian H; Testik Murat Caner^*; Bayindir Z Pelin

来源：Quality and Reliability Engineering International, 2013, 29(1): 33-42.

DOI：10.1002/qre.1289

• autocorrelated counts
• CUSUM control chart
• Markov chains approach
• Poisson INAR(1) model
• statistical process control

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.

• 出版日期2013-2