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

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10

Semi-Markov Failure Rate Process

Abstract

In this chapter the reliability function is defined by the stochastic failure rate process with a nonnegative and right-continuous trajectories. Equations for the conditional reliability functions of an object are derived under the assumption that the failure rate is a semi-Markov process with an at most countable state space. A proper theorem is presented. The equations for Laplace transforms of conditional reliability functions for the finite space semi-Markov random walk failure rate process are presented in the chapter. The countable linear systems of equations for the appropriate Laplace transforms allow us to find the reliability functions for the Poisson and the Furry-Yule failure rate processes. ...

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