Reliability and Probability of First Occured Failure for Discrete-Time Semi-Markov Systems

Stylianos Georgiadis, Nikolaos Limnios, Irene Votsi

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearch

Abstract

This chapter investigates the rate of occurrence of failures (ROCOF) is addressed for the first time for semi-Markov chains. The ROCOF may be interpreted as the expected number of transitions of a semi-Markov chain to a subset of its state space at a specific time. Two different proposed nonparametric estimators of the stationary distribution are presented and the estimator of the availability is expressed in terms of them. The chapter introduces the measure of the probability of the first occurred failure and the necessary preliminaries of a semi-Markov model and the definitions of the reliability measures are given. The chapter depicts their empirical estimation and their strong consistency. It also applies these results to a numerical example. The problem of evaluating and estimating the ROCOF and the probability of the first occurred failure is addressed for the first time for discrete-time semi-Markov systems, along with the steady-state availability.
Original languageEnglish
Title of host publicationApplied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference
PublisherWiley
Publication date2014
Pages167-179
Chapter12
ISBN (Print)9781118539422
ISBN (Electronic)9781118701881
DOIs
Publication statusPublished - 2014
Externally publishedYes

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