Prediction limits for an exponential distribution: a Bayes predictive distribution approach

A life testing experiment that has a one-parameter exponential distribution with constant failure rate is considered. Using the gamma prior, the authors derive the posterior distribution for that failure rate and hence the predictive distribution of future observations. Available data are from type II censored sampling. Methods are derived for constructing prediction limits for the jth smallest of some set of future observations from the same failure process using the predictive distribution. On the basis of a Monte Carlo study of 1000 future samples, the proportion of times the limits include the first future observation (as a particular case for numerical illustration) has been obtained and found to be very high. The results are compared with the classical limits derived by J.F. Lawless in 1972