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Controlling jumps in correlated processes of Poisson counts

✍ Scribed by Christian H. Weiß

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
219 KB
Volume
25
Category
Article
ISSN
1524-1904

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✦ Synopsis

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.

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