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Controlling jumps in correlated processes of Poisson counts
Author(s) -
Weiß Christian H.
Publication year - 2008
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.744
Subject(s) - poisson distribution , autocorrelation , bivariate analysis , markov chain , count data , statistics , compound poisson process , computer science , control chart , poisson regression , econometrics , mathematics , poisson process , process (computing) , population , operating system , demography , sociology
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.