On calculating generalized confidence intervals for the two-parameter exponential reliability function

In a recent paper, approximate and simulated-based generalized confidence limits for the reliability function of a two-parameter exponential model under failure censoring have been proposed by Roy and Mathew [Roy, A. and Mathew, T., 2005. A generalized confidence limit for the reliability function of a two-parameter exponential distribution. Journal of Statistical Planning and Inference, 128, 509-517]. Nevertheless, in some cases, those limits may be greater than 1. In order to overcome this difficulty, the generalized pivot used by Roy and Matthew must be conveniently truncated. In this article, the distribution and density functions of the new pivotal quantity are presented in closed forms. Confidence limits and intervals of shortest length with exact nominal coverages are found immediately by merely solving the appropriate nonlinear equations. Reliability testing is easily carried out using the generalized pivot. The results derived can also be applied to related distributions, as the Pareto model. A numerical example is included for illustrative purposes.