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Semi-Markov Processes: Applications in System Reliability and Maintenance by Franciszek Grabski

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Semi-Markov process

Abstract

This chapter provides the definitions and basic properties related to a discrete state space semi-Markov process (SMP). The SMP is constructed by the so-called Markov renewal process (MRP) that is a special case of the two-dimensional Markov sequence. The MRP is defined by the transition probabilities matrix, called the renewal kernel and an initial distribution, or by other characteristics that are equivalent to the renewal kernel. The counting process corresponding to the SMP allows us to determine the concept of process regularity. The process is said to be regular if the corresponding counting process has a finite number of jumps in a finite period. The chapter also shows the other methods of determining ...

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