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This paper deals with the estimation of reliability R = P[Y < X] when X and Y are two independent random variables with atwo-parameter bathtub shaped failure rate distribution with the samesecond shape parameter. Likelihood and Bayesian methods are proposedto make inferences about R. We obtain the likelihood interval andasymptotic confidence interval for R, and we consider Bayesianpoint estimates of R under both absolute and squared error loss,using either gamma or uniform priors for the three unknown modelparameters. An equal tail Bayesian credible interval for R isinvestigated. Analysis of a real data set is presented forillustrative purposes, and Monte Carlo simulations are performed tocompare: (1) the performance of Bayes estimates under two differentloss functions; and (2) the maximum likelihood and Bayesian methods.

Estimation of P(Y<X) for a Two-parameter Bathtub Shaped Failure Rate Distribution