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.
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© 2011 Springer-Verlag London Limited
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Nakagawa, T. (2011). Semi-Markov and Markov Renewal Processes. In: Stochastic Processes. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-274-2_5
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DOI: https://doi.org/10.1007/978-0-85729-274-2_5
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Online ISBN: 978-0-85729-274-2
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