Random Failure Rate

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.