Statistical Analysis for Log-Normal Distribution in the Presence of Hybrid Censoring and Step-Stress

Accelerated life test experiments aim to generate lifetime data in a short time for the further statistical analysis, and are very useful when the units under experiment are highly reliable. Statistical analysis for lifetime data observed from accelerating life testing in presence of some censoring becomes a challenging task. In this paper, we consider lognormal distribution under a simple step-stress model in the presence of hybrid censoring. We assume that the lifetimes follow the cumulative exposure model, and first obtain maximum likelihood estimates and their associated interval estimates using various methods. We then compute Bayes estimates and associated highest posterior interval estimates under squared error loss function. To observe the effectiveness of the proposed methods under the different situations, we conduct a simulation study.