Monitoring Warranty Claims With Cusums

Abstract

Manufacturers monitor products in field use with respect to the quality and reliability of their performance, and warranty claims data are one valuable source of information. Updated warranty claims data are examined periodically by manufacturers, and formal monitoring procedures are a useful adjunct that can help identify emerging problems. This article presents cusum procedures for monitoring claims, designed to allow changes in claim rates to be detected in as timely a manner as possible. The determination of plans with given signal probabilities under nominal and increased rates is based on Markov chain calculations which are easy to implement. The procedures are motivated by and illustrated on warranty claims for North American automobiles. This article has online supplementary material.

KEY WORDS:

• Automobile warranty claims
• Manufacturing periods
• Markov chain approximations
• Poisson distribution
• Signal probabilities

ACKNOWLEDGMENTS

This research was supported by a grant to the first author from the Natural Sciences and Engineering Research Council of Canada. Parts of this work were done during a visit by the first author to the Department of Mathematics, Imperial College London. The authors thank the reviewers and editors for valuable suggestions.