Reconstruction regions for unobserved middle order statistics in the exponential distribution

Abstract

There are some situations in reliability studies in which a middle part of the sample is missing. For example, in life-testing experiments, the experimenter may not enable to observe the middle lifetimes. This may be due to negligence, removal of test units (censoring) and or equipment failure and technical problems in the middle of the experiment. In this paper, the problem of reconstructing unobserved middle lifetimes from the exponential distribution is discussed and reconstruction regions (or sets) are obtained. First, it is shown how to find balanced reconstruction regions for the unobserved middle lifetimes. Then, a constrained minimization problem is used to find the reconstruction region with the smallest area. For illustrative and comparative purposes, a simulation study and two numerical examples are presented.