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Controlling jumps in correlated processes of Poisson counts

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  • Christian H. Weiß

Abstract

Processes of autocorrelated Poisson counts can often be modelled by a Poisson INAR(1) model, which proved to apply well to typical tasks of SPC. Statistical properties of this model are briefly reviewed. Based on these properties, we propose a new control chart: the combined jumps chart. It monitors the counts and jumps of a Poisson INAR(1) process simultaneously. As the bivariate process of counts and jumps is a homogeneous Markov chain, average run lengths (ARLs) can be computed exactly with the well‐known Markov chain approach. Based on an investigation of such ARLs, we derive design recommendations and show that a properly designed chart can be applied nearly universally. This is also demonstrated by a real‐data example from the insurance field. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Christian H. Weiß, 2009. "Controlling jumps in correlated processes of Poisson counts," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 551-564, September.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:5:p:551-564
    DOI: 10.1002/asmb.744
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    References listed on IDEAS

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    1. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
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