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


Yontay P. , WEISS C. H. , TESTİK M. C. , BAYINDIR Z. P.

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, vol.29, no.1, pp.33-42, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 1
  • Publication Date: 2013
  • Doi Number: 10.1002/qre.1289
  • Title of Journal : QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL
  • Page Numbers: pp.33-42

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 (C) 2012 John Wiley & Sons, Ltd.