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

Richard Arnold, Stefanka Chukova, Yu Hayakawa, Sarah Marshall*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 (Formula presented.) and the number of failures up to time (Formula presented.). 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.

Original languageEnglish
Pages (from-to)2968-2985
Number of pages18
JournalQuality and Reliability Engineering International
Issue number6
Publication statusPublished - 2022 Oct


  • alternating geometric process (AGP)
  • expected warranty cost
  • geometric process (GP)
  • mean function of AGP
  • non-renewing free repair warranty policy
  • variance function of AGP

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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