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Random Failure Rate

Grabski F.

Journal of Polish Safety and Reliability Association

2012

Vol. 3, No. 2

209--216

The reliability function defined by a failure rate which is a stochastic process with nonnegative and right continuous trajectories is presented in this paper. The reliability function with an at most countable state space semi-Markov failure rate process is investigated. A theorem concerning of equations for a conditional reliability function with a semi-Markov process as a failure rate is presented in this paper. The solutions of the proper renewal equations allow getting the reliability functions for the finite space semi-Markov random walk, for the Poisson process and for the Furry-Yule process as a failure rate.

The random failure rate

Grabski F.

Journal of Polish Safety and Reliability Association

2007

Vol. 1

143--149

A failure rate of the object is assumed to be a stochastic process with nonnegative, right continuous trajectories. A reliability function is defined as an expectation of a function of a random failure rate process. The properties and examples of the reliability function with the random failure rate are presented in the paper. A semi-Markov process as the random failure rate is considered in this paper.

Applications of semi-Markov processes in reliability

Grabski F.

Journal of Polish Safety and Reliability Association

2007

Vol. 1

127--142

The basic definitions and theorems from the semi-Markov processes theory are discussed in the paper. The semi-Markov processes theory allows us to construct the models of the reliability systems evolution within the time frame. Applications of semi-Markov processes in reliability are considered. Semi-Markov model of the cold standby system with repair, semi-Markov process as the reliability model of the operation with perturbations and semi-Markov process as a failure rate are presented in the paper.