Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations

Exact two-sided guaranteed-coverage tolerance intervals for the exponential distribution which satisfy the traditional “equal-tailedness” condition are derived in the failure-censoring case. The available empirical information is provided by the first rr ordered observations in a sample of size nn. A Bayesian approach for the construction of equal-tailed tolerance intervals is also proposed. The degree of accuracy of a given tolerance interval is quantified. Moreover, the number of failures needed to achieve the desired accuracy level is predetermined. The Bayesian perspective is shown to be superior to the frequentist viewpoint in terms of accuracy. Extensions to other statistical models are presented, including the Weibull distribution with unknown scale parameter. An alternative tolerance interval which coincides with an outer confidence interval for an equal-tailed quantile interval is also examined. Several important computational issues are discussed. Three censored data sets are considered to illustrate the results developed.