Abstract
In this paper, we focus on a fundamental reliability measure, the discrete-time intensity of the hitting time (DTIHT), which is the discrete analogue of the rate of occurrence of failures. The problem of evaluating and estimating the DTIHT is addressed for the first time for semi-Markov chains. First, a simple formula for the evaluation of the DTIHT is derived. Following the previous result, a statistical estimator of this plug-in type function is proposed. The main results given here are the asymptotic properties of this estimator, including the strong consistency and the asymptotic normality. Second, the DTIHT is investigated for hidden Markov renewal chains. Following its evaluation, a statistical estimator is suggested whose asymptotic properties are studied. Finally, we give some numerical examples for illustration purposes. The derived models and results can be used to typical reliability problems encountered in different scientific disciplines.
Conflict of interest disclosure statement
No potential conflict of interest was reported by the authors.