To compute Bayes’ estimates for the reliability function and for the hazard rate we examine the accuracy of an approximate method due to D. V. Lindley [Bayesian statistics, Proc. 1st int. Meet., Valencia 1979, 233-245 (1980; Zbl 0458.62002)]. The development of this expansion requires the determination of maximum likelihood estimates and, in this connection, we consider a widely employed iterative procedure for censored Weibull data given by A. C. Cohen [Maximum likelihood estimation in the Weibull distribution based on complete and censored samples. Technometrics 7, 579-588 (1965)].
However, we have chosen to present a new, but equally effective, procedure which has the added advantage of reducing the number of terms in Lindley’s expansion. This is achieved by first transforming to the log Weibull (extreme value) distribution and then making use of its centre of location.