Is Average Run Length to False Alarm Always an Informative Criterion?

Abstract

Apart from Bayesian approaches, the average run length (ARL) to false alarm has always been seen as the natural performance criterion for quantifying the propensity of a detection scheme to make false alarms, and no researchers seem to have questioned this on grounds that it does not always apply. In this article, we show that in the change-point problem with mixture prechange models, detection schemes with finite detection delays can have infinite ARLs to false alarm. We also discuss the implication of our results on the change-point problem with either exchangeable prechange models or hidden Markov models. Alternative minimax formulations with different false alarm criteria are proposed.

Keywords:

• Average run length
• CUSUM
• Expected false alarm rate
• Quantile run length
• Statistical process control
• Surveillance

Subject Classifications:

• 62L10
• 62L15
• 60G40

ACKNOWLEDGMENTS

The author would like to thank his advisor, Dr. Gary Lorden, for his support, guidance, and encouragement, and Drs. Moshe Pollak and Yi-Ching Yao for stimulating discussions. The author would also like to thank the reviewers for their thoughtful comments. This work was supported in part by Dr. Sarah Hotle's National Institutes of Health under grant R01 AI055343.

Notes

Recommended by Alex Tartakovsky