Statistical Prediction Based on Ordered Ranked Set Sampling Using Type-II Censored Data from the Rayleigh Distribution under Progressive-Stress Accelerated Life Tests

Abstract

The objective of ranked set sampling is to gather observations from a population that is more likely to cover the population’s full range of values. In this paper, the ordered ranked set sample is obtained using the idea of order statistics from independent and nonidentically distributed random variables under progressive-stress accelerated life tests. The lifetime of the item tested under normal conditions is suggested to be subject to the Rayleigh distribution with a scale parameter satisfying the inverse power law such that the applied stress is a nonlinear increasing function of time. Considering the type-II censoring scheme, one-sample prediction for censored lifetimes is discussed. Numerous point predictors including the Bayes point predictor, conditional median predictor, and best unbiased predictor for future order statistics are discussed. Additionally, conditional prediction intervals for future order statistics are also studied. The theoretical findings reported in this work are shown by illustrative examples based on simulated data as well as real data sets. The effectiveness of the prediction methods is then evaluated by a Monte Carlo simulation study.