Abstract
ABSTRACT In this paper, we shall study a homogeneous ergodic, finite state, Markov chain with unknown transition probability matrix. Starting from the well known maximum likelihood estimator of transition probability matrix, we define estimators of reliability and its measurements. Our aim is to show that these estimators are uniformly strongly consistent and converge in distribution to normal random variables. The construction of the confidence intervals for availability, reliability, and failure rates are also given. Finally we shall give a numerical example for illustration and comparing our results with the usual empirical estimator results.
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