This chapter investigates the rate of occurrence of failures (ROCOF) is addressed for the first time for semi-Markov chains. The ROCOF may be interpreted as the expected number of transitions of a semi-Markov chain to a subset of its state space at a specific time. Two different proposed nonparametric estimators of the stationary distribution are presented and the estimator of the availability is expressed in terms of them. The chapter introduces the measure of the probability of the first occurred failure and the necessary preliminaries of a semi-Markov model and the definitions of the reliability measures are given. The chapter depicts their empirical estimation and their strong consistency. It also applies these results to a numerical example. The problem of evaluating and estimating the ROCOF and the probability of the first occurred failure is addressed for the first time for discrete-time semi-Markov systems, along with the steady-state availability.
|Title of host publication||Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference|
|Publication status||Published - 2014|