RELIABILITY AND OPTIMAL AGE REPLACEMENT POLICY OF A SYSTEM SUBJECT TO SHOCKS FOLLOWING A MARKOVIAN ARRIVAL PROCESS

Dheeraj Goyal; Min Xie; Min Gong

doi:10.1017/jpr.2024.111

RELIABILITY AND OPTIMAL AGE REPLACEMENT POLICY OF A SYSTEM SUBJECT TO SHOCKS FOLLOWING A MARKOVIAN ARRIVAL PROCESS

Dheeraj Goyal
, Min Xie
, Min Gong

City University of Hong Kong

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

This paper defines and studies a broad class of shock models by assuming that a Markovian arrival process models the arrival pattern of shocks. Under the defined class, we show that the system's lifetime follows the well-known phase-type distribution. Further, we examine the age replacement policy for systems with a continuous phase-type distribution, identifying sufficient conditions for determining the optimal replacement time. Since phase-type distributions are dense in the class of lifetime distributions, our findings for the age replacement policy are widely applicable. We include numerical examples and graphical illustrations to support our results. © The Author(s), 2025.

Original language	English
Pages (from-to)	1010-1027
Number of pages	18
Journal	Journal of Applied Probability
Volume	62
Issue number	3
Online published	14 Feb 2025
DOIs	https://doi.org/10.1017/jpr.2024.111
Publication status	Published - Sept 2025

Funding

We wish to thank the Editor-in-Chief, the Associate Editor, and the anonymous reviewers for their valuable constructive comments and suggestions which led to an improved version of the manuscript. This work is supported by the Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA). The first author received partial support for this work from the Indian Institute of Technology Kanpur through IPDF grant (PDF423).

Research Keywords

age replacement
Markovian arrival process
mean residual lifetime
Reliability
shock models

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED POSTPRINT FILE: This article has been published in a revised form in Journal of Applied Probability https://doi.org/10.1017/jpr.2024.111. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © The Author(s), 2025.

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title = "RELIABILITY AND OPTIMAL AGE REPLACEMENT POLICY OF A SYSTEM SUBJECT TO SHOCKS FOLLOWING A MARKOVIAN ARRIVAL PROCESS",

abstract = "This paper defines and studies a broad class of shock models by assuming that a Markovian arrival process models the arrival pattern of shocks. Under the defined class, we show that the system's lifetime follows the well-known phase-type distribution. Further, we examine the age replacement policy for systems with a continuous phase-type distribution, identifying sufficient conditions for determining the optimal replacement time. Since phase-type distributions are dense in the class of lifetime distributions, our findings for the age replacement policy are widely applicable. We include numerical examples and graphical illustrations to support our results. {\textcopyright} The Author(s), 2025.",

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AU - Xie, Min

AU - Gong, Min

PY - 2025/9

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N2 - This paper defines and studies a broad class of shock models by assuming that a Markovian arrival process models the arrival pattern of shocks. Under the defined class, we show that the system's lifetime follows the well-known phase-type distribution. Further, we examine the age replacement policy for systems with a continuous phase-type distribution, identifying sufficient conditions for determining the optimal replacement time. Since phase-type distributions are dense in the class of lifetime distributions, our findings for the age replacement policy are widely applicable. We include numerical examples and graphical illustrations to support our results. © The Author(s), 2025.

AB - This paper defines and studies a broad class of shock models by assuming that a Markovian arrival process models the arrival pattern of shocks. Under the defined class, we show that the system's lifetime follows the well-known phase-type distribution. Further, we examine the age replacement policy for systems with a continuous phase-type distribution, identifying sufficient conditions for determining the optimal replacement time. Since phase-type distributions are dense in the class of lifetime distributions, our findings for the age replacement policy are widely applicable. We include numerical examples and graphical illustrations to support our results. © The Author(s), 2025.

KW - age replacement

KW - Markovian arrival process

KW - mean residual lifetime

KW - Reliability

KW - shock models

UR - https://www.scopus.com/pages/publications/85219679147

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DO - 10.1017/jpr.2024.111

M3 - RGC 21 - Publication in refereed journal

SN - 0021-9002

VL - 62

SP - 1010

EP - 1027

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 3

ER -

RELIABILITY AND OPTIMAL AGE REPLACEMENT POLICY OF A SYSTEM SUBJECT TO SHOCKS FOLLOWING A MARKOVIAN ARRIVAL PROCESS

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