Joint reconstruction and prediction regions for unobserved exponential lifetimes under doubly Type II censoring

The doubly Type II censoring scheme, in which some of the smallest and largest lifetimes are censored, is an important and widely used censoring scheme in life-testing experiments and reliability. In this paper, the problem of simultaneous reconstruction and prediction for unobserved lifetimes in a doubly Type II censored sample from the one-parameter exponential distribution is discussed. For this purpose, the joint reconstruction and prediction (JRP) regions are obtained based on two independent pivotal quantities. First, the balanced JRP regions for the unobserved lifetimes are derived, and then a constrained optimization problem is formulated and solved to find the JRP regions with the smallest area. For illustrative and comparative purposes, a simulation study and two illustrative examples are presented.