Predictive analysis of Type-II censored data in step-stress life testing using tampered random variable model

In this paper, we consider the prediction problem of the future failure times based on observed Type-II right-censored data from Lehmann family of distribution under simple step stress life testing (SSLT) scenario. We explore various point predictors including best unbiased predictor (BUP), maximum likelihood predictor (MLP), and conditional median predictor (CMP) of the censored items. Furthermore, we extend our analysis to include the derivation of prediction intervals (PIs) using pivotal quantity method and highest conditional density (HCD) method. We conduct an extensive simulation study to evaluate the effectiveness of the point and interval predictors. The criteria employed for comparative evaluation include prediction bias and root mean square prediction error for point predictors, alongside average length and coverage probability for prediction intervals. Finally, we have analyzed two real life data sets for illustrative purposes. The first data set contains the failure times of 35 solar lighting devices from an SSLT experiment, while the second data set contains the lifetimes of nanocrystalline embedded high-k device data.