1. bookVolume 43 (2017): Issue 1 (October 2017)
Journal Details
License
Format
Journal
eISSN
2083-4608
First Published
26 Feb 2008
Publication timeframe
4 times per year
Languages
English
access type Open Access

The Renewal Process Generated By Return Times of Semi-Markov Process in Reliability Models

Published Online: 30 Apr 2018
Volume & Issue: Volume 43 (2017) - Issue 1 (October 2017)
Page range: 365 - 380
Journal Details
License
Format
Journal
eISSN
2083-4608
First Published
26 Feb 2008
Publication timeframe
4 times per year
Languages
English
Abstract

The renewal process generated by the return times of semi-Markov process to a given state is considered in the paper. The return time to a state j and also a first passage time from a given state i to the state j of semi-Markov process are basic concepts that are used to determine this process. The systems of equations for distributions, expectations and secondond moments of these random variables are presented. Theorem concerning the asymptotic distribution of the considered renewal process is presented in this article. Moreover an illustrative example from the reliability theory is presented in the paper.

Keywords

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[2] Grabski, F.: Semi-markowskie modele niezawodności i eksploatacji. Badania Systemowe, tom30; IBS PAN, Warszawa, 2002.Search in Google Scholar

[3] Grabski, F. : Semi-Markov Processes: Application in System Reliability and Maintenance. Elsevier, Amsterdam, Boston, Heidelberg, London, New York Oxford, Paris, San Diego, San Francisco, Sydney, Tokyo, 2015.Search in Google Scholar

[4] Korolyuk VS, Turbin AF. Semi-Markov processes and their applications. Naukova Dumka, Kiev 1976, (in Russian).Search in Google Scholar

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