TY - JOUR

T1 - Mean and variance of an alternating geometric process

T2 - An application in warranty cost analysis

AU - Arnold, Richard

AU - Chukova, Stefanka

AU - Hayakawa, Yu

AU - Marshall, Sarah

N1 - Funding Information:
This research was supported by: Japan Society for the Promotion of Science KAKENHI Grant‐in‐Aid for Scientific Research (C), Grant Number: 18K04621 Auckland University of Technology Research and Study Leave Grant in Aid, 2020.
Publisher Copyright:
© 2021 John Wiley & Sons Ltd.

PY - 2022/10

Y1 - 2022/10

N2 - 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.

AB - 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.

KW - alternating geometric process (AGP)

KW - expected warranty cost

KW - geometric process (GP)

KW - mean function of AGP

KW - non-renewing free repair warranty policy

KW - variance function of AGP

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U2 - 10.1002/qre.2964

DO - 10.1002/qre.2964

M3 - Article

AN - SCOPUS:85112071904

VL - 38

SP - 2968

EP - 2985

JO - Quality and Reliability Engineering International

JF - Quality and Reliability Engineering International

SN - 0748-8017

IS - 6

ER -