Bayesian prediction of the total time on test using doubly censored Rayleigh data

In a Bayesian setting, and on the basis of a doubly censored random sample of failure times drawn from a Rayleigh distribution Fernandez (2000 Statist. Probab. Lett. 48 393-399) considered the problem of predicting an independent future sample from the same distribution. In this article, we extend his work to include the estimation of the predictive distribution of the total time on test up to a certain failure in a future sample, as well as that of the remaining testing time time until all the items in the original sample have failed. Two examples are used to illustrate the prediction procedure.