Optimal prediction regions of future lifetimes under Type-II censored samples

Based on a Type-II censored data from exponential distribution, Bagheri et al. (IEEE Trans Reliab 71(1):100–110, 2022) introduced the joint prediction of future failure times based on Type-II censored data from the exponential distribution. In fact, they developed pivotal quantities for obtaining prediction regions of two future failure times using the stochastic independence of the spacings of increments of order statistics along with a scaling transformation. In this work, we consider the same problem of joint prediction where the prediction likelihood function is used to produce pivotal quantities for obtaining prediction region of two failure times. Based on these pivotal quantities, the optimal prediction regions of the joint failure times are derived. A Monte Carlo simulation study is performed to assess the so developed prediction regions and compare them with ones obtained by Bagheri et al. (IEEE Trans Reliab 71(1):100–110, 2022). Through simulation, it is evident that our joint prediction regions are highly competitive efficiencies compared to their existing counterparts. Further, two real life data sets are analyzed to explain our procedures presented.