The reliability of an object with semi-Markov failure rate

In this paper the properties of the reliability function of an object with the failure rate modelled by a semi-Markov process defined on an at most countable state space are presented. Applying the introduced system of renewal equations, the object reliability functions for the alternating and the Poisson failure rate process are obtained. The Laplace–Stieltjes transform of the object reliability function and its mean time to failure are obtained.