Mean and variance of an alternating geometric process: An application in warranty cost analysis

An alternating geometric process can be used to model the operational and repair times of an ageing system. In applications such as warranty cost analysis, the mean of an alternating geometric process (i.e. the expected number of events by a given time) and the variance are of interest. In this paper, two new approaches are proposed for computing the mean and variance functions of two counting processes related to the alternating geometric process, namely the number of cycles up to time t and the number of failures up to time t. In warranty cost analysis, these approaches can be used to compute the expected number of claims and the expected cost over the warranty period. The usefulness of the proposed approaches in warranty cost analysis is demonstrated for a non-renewing free-repair warranty policy. The new approaches offer benefits over simulation in terms of computational time and accuracy.

Automated summary

The paper introduces the use of alternating geometric processes to model the operational and repair times of an aging system, and proposes new methods for computing the mean and variance functions related to these processes. The utility of these methods in warranty cost analysis is demonstrated, particularly for a non-renewing free-repair warranty policy, offering advantages over simulation in terms of computational time and accuracy.