Controlling correlated processes of Poisson counts

TLDR

The class of INARMA models is well suited to model the autocorrelation structure of processes with Poisson marginals arising in the context of statistical quality control. After reviewing briefly the basic principles and important members of this broad family of models, we concentrate on the INAR(1) model, which is of particular relevance for quality control. We suggest four approaches to control such count processes, and compare their run‑length performance in a simulation study. Results show that only some of the out‑of‑control situations considered can be controlled effectively with the discussed control schemes. © 2007 John Wiley & Sons, Ltd.

Abstract

Abstract The class of INARMA models is well suited to model the autocorrelation structure of processes with Poisson marginals arising in context of statistical quality control. After reviewing briefly the basic principles and important members of this broad family of models, we concentrate on the INAR(1) model, which is of particular relevance for quality control. We suggest four approaches to control such count processes, and compare their run length performance in a simulation study. Results show that only some of the out‐of‐control situations considered can be controlled effectively with the discussed control schemes. Copyright © 2007 John Wiley & Sons, Ltd.