Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 217, Issue 24, Pages 9956-9965Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.04.055
Keywords
Random failure rate; Markov renewal process; Semi-Markov process; Furry-Yule process
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Usually, a reliability function is defined by a failure rate which is a real function taking the non-negative real values. In this paper the failure rate is assumed to be a stochastic process with non-negative and right continuous trajectories. The reliability function is defined as an expectation of a function of that random process. Particularly, the failure rate defined by the semi-Markov processes is considered here. The theorems dealing with the renewal equations for the conditional reliability functions with a semi-Markov process as a failure rate are presented in this paper. A system of that kind of equations for the discrete state space semi-Markov process is applied for calculating the reliability function for the 3-states semi-Markov random walk. Using the introduced system of renewal equations for the countable state space, the reliability function for the Furry-Yule failure rate process is obtained. (C) 2011 Elsevier Inc. All rights reserved.
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