Bayesian analysis of an n unit system operating in a  random environment

Leo Alexander; T.; Xavier; S.

Volume : III, Issue : I, January - 2014

Bayesian analysis of an n unit system operating in a random environment

Leo Alexander, T. , Xavier, S.

Abstract :

The system under consideration is an n unit system operating in a random environment, wherein the environment determines the number of units required for the satisfactory performance of the system at every instant of time. Assuming that the environment is described by a Markov Process, the maximum likelihood and consistent estimators of $\"\"$ , the limiting property of the estimator $\"\"$ , Uniformly Minimum Variance Unbiased estimator (UMVUE) of $\"\"$ and UMVUE of the expected number of operable units in the system are obtained. Further, a 100(1-a) % asymptotic confidence interval for the expected number of operable units in the system, Bayes estimator of $\"\"$ under squared error loss, the minimum posterior risk associated with Bayes estimator and the minimum Bayes risk of $\"\"$ are obtained.