Failure rates estimation of Markov chains

In this paper, we consider two definitions of failure rate. The usual failure rate, BMP-failure rate, has been defined by Barlow, Marshall and Porschan [1] & [2] and the new definition of failure rate, RG-failure rate, has been proposed by Roy and Gupta [3]. We define the estimator of two failure rates for finite state space Markov chains, and we show that they are uniformly strongly consistent and that each of them converges to a normal random variable. The construction of confidence intervals is also given. From the standard empirical estimators of the two failure rates, which have been discussed by Bracquemond [4], we compare numerically our results with the empirical results