A method for estimating the parameters of reliability models

The maximum likelihood estimates (MLE) of transition rates in a finite-state continuous-time Markov process with an absorbing state are obtained, when there are a number of independent realizations of the process. This process is explained as a model for deteriorating systems of reliability theory through example. The asymptotic properties of MLES as the observed number of realizations tend to infinity are studied. Extension of these results to semi-Markov processes is discussed.