An ARL-unbiased modified chart for monitoring autoregressive counts with geometric marginal distributions

Abstract

Geometrically distributed counts arise in the industry. Ideally, they should be monitored using a control chart whose average run length (ARL) function achieves a maximum when the process is in control; that is, the chart is ARL-unbiased. Moreover, its in-control ARL should coincide with a reasonably large and prespecified value. Because dependence among successive geometric counts is occasionally a more sensible assumption than independence, we assess the impact of using an ARL-unbiased chart specifically designed for monitoring independent geometric counts when, in fact, these counts are autocorrelated. We derive an ARL-unbiased modified chart for monitoring geometric first-order integer-valued autoregressive or GINAR(1) counts. We provide compelling illustrations of this chart and discuss its use to monitor other autoregressive counts with a geometric marginal distribution.

Keywords:

• Average run length
• binomial thinning
• randomized signals
• statistical process control

SUBJECT CLASSIFICATIONS:

• 60J10
• 62P30

ACKNOWLEDGEMENTS

We are grateful to the two reviewers, the Associate Editor, and the Editor-in-Chief, who reviewed our work and provided pertinent comments and suggestions, resulting in an improved version of our original article.

DISCLOSURE STATEMENT

The authors have no conflicts of interest to report.

Additional information

Funding

The first author acknowledges the financial support of the Portuguese FCT–Fundação para a Ciência e a Tecnologia, through the projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT/IST-ID (Center for Computational and Stochastic Mathematics), Instituto Superior Técnico, Universidade de Lisboa.