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Reliability and optimal age replacement policy of a system subject to shocks following a Markovian arrival process

Part of: Stochastic processes Special processes Operations research and management science

Published online by Cambridge University Press:  14 February 2025

Dheeraj Goyal Open the ORCID record for Dheeraj Goyal [Opens in a new window] ,
Min Xie  and
Min Gong
Dheeraj Goyal*
Affiliation:
Centre for Intelligent Multidimensional Data Analysis Limited and Indian Institute of Technology Kanpur
Min Xie*
Affiliation:
Centre for Intelligent Multidimensional Data Analysis Limited and City University of Hong Kong
Min Gong*
Affiliation:
Jinan University
*
*Postal address: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Uttar Pradesh-208016, India. Email: dheerajgoyal6897@gmail.com
**Postal address: Centre for Intelligent Multidimensional Data Analysis Limited, Hong Kong Science Park, Hong Kong.
***Postal address: College of Information Science and Technology, Jinan University, Guangzhou, China
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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.

Keywords

Reliabilitymean residual lifetimeage replacementMarkovian arrival processshock models

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60G55: Point processes 60K10: Applications (reliability, demand theory, etc.)
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 18
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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