Nonparametric estimation of reliability and survival function for continuous-time finite Markov processes

In this paper, problems of nonparametric statistical inference for reliability/survival, availability and failure rate functions of continuous-time Markov processes are discussed. We assume the state space to be finite. We shall discuss some results on the maximum likelihood estimator of generators for continuous-time Markov processes. The asymptotic properties of this estimator have been discussed and we present the extension of these results by obtaining the asymptotic properties for the estimators of transition matrix and of reliability/survival, availability and failure rate functions for a continuous-time Markov process. The confidence intervals for the proposed estimators are given. Finally we give a numerical example to illustrate the results.