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Reliability assessment of system under a generalized run shock model

Part of: Systems theory and control: General Markov processes

Published online by Cambridge University Press:  16 January 2019

Min Gong ,
Min Xie  and
Yaning Yang
Min Gong*
Affiliation:
University of Science and Technology of China City University of Hong Kong
Min Xie*
Affiliation:
City University of Hong Kong
Yaning Yang*
Affiliation:
University of Science and Technology of China
*
* Postal address: Shenzhen Research Institute, City University of Hong Kong, 8 Yuexing First Road, Shenzhen, Guangdong, China. Email address: mingong3-c@my.cityu.edu.hk
** Postal address: Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China. Email address: minxie@cityu.edu.hk
*** Postal address: Department of Statistics and Finance, University of Science and Technology of China, 96 Jinzhai Road, 9 Hefei, Anhui, China. Email address: ynyang@ustc.edu.cn
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Abstract

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In this paper we are concerned with modelling the reliability of a system subject to external shocks. In a run shock model, the system fails when a sequence of shocks above a threshold arrive in succession. Nevertheless, using a single threshold to measure the severity of a shock is too critical in real practice. To this end, we develop a generalized run shock model with two thresholds. We employ a phase-type distribution to model the damage size and the inter-arrival time of shocks, which is highly versatile and may be used to model many quantitative features of random phenomenon. Furthermore, we use the Markovian property to construct a multi-state system which degrades with the arrival of shocks. We also provide a numerical example to illustrate our results.

Keywords

Run shock modelphase-type distributionMarkov chainreliability functioninter-arrival timemean residual life

MSC classification

Primary: 93A30: Mathematical modeling (models of systems, model-matching, etc.)
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1249 - 1260
Copyright
Copyright © Applied Probability Trust 2018 

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