Semi-Markov and Markov Renewal Processes

Toshio Nakagawa ()
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Toshio Nakagawa: Aichi Institute of Technology

Chapter Chapter 5 in Stochastic Processes, 2011, pp 123-148 from Springer

Abstract: Abstract State space is usually defined by the number of units that are working satisfactorily. As far as the applications to reliability theory is concerned, we consider only a finite number of states, contrast with a queueing theory. We mention only the theory of stationary Markov processes with a finite-state space. It is shown that transition probabilities, first-passage distributions, and renewal functions are given by forming renewal equations. Furthermore, some limiting properties are summarized when all states communicate.

Keywords: Mass Function; System Failure; Regeneration Point; Renewal Equation; Embed Markov Chain (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-85729-274-2_5

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