One- and two-sample prediction based on doubly censored exponential data and prior information

Abstract

On the basis of a doubly censored sample from an exponential lifetime distribution, the problem of predicting the lifetimes of the unfailed items (one-sample prediction), as well as a second independent future sample from the same distribution (two-sample prediction), is addressed in a Bayesian setting. A class of conjugate prior distributions, which includes Jeffreys' prior as a special case, is considered. Explicit expressions for predictive densities and survivals are derived. Assuming squared-error loss, Bayes predictive estimators are obtained in closed forms (in particular, the estimator of the number of failures in a specified future time interval is given analytically). Bayes prediction limits and predictive estimators under absolute-error loss can readily be computed using iterative methods. As applications, the total duration time in a life test and the failure time of a {\it k-out-of-n} system may be predicted. As an illustration, a numerical example is also included.