In this paper, we focus on the parametric inference based on the Tampered Random Variable (TRV) model for simple step-stress life testing (SSLT) using Type-II censored data. The baseline lifetime of the experimental units, under normal stress conditions, follows the Gumbel Type-II distribution with $\alpha$ and $\lambda$ being the shape and scale parameters, respectively. Maximum likelihood estimator (MLE) and Bayes estimator of the model parameters are derived based on Type-II censored samples. We obtain asymptotic intervals of the unknown parameters using the observed Fisher information matrix. Bayes estimators are obtained using Markov Chain Monte Carlo (MCMC) method under squared error loss and LINEX loss functions. We also construct highest posterior density (HPD) intervals of the unknown model parameters. Extensive simulation studies are performed to investigate the finite sample properties of the proposed estimators. Three different optimality criteria have been considered to determine the optimal censoring plans. Finally, the methods are illustrated with the analysis of two real data sets.

翻译：本文聚焦于基于扰动随机变量(TRV)模型的简单步进应力寿命试验(SSLT)的参数推断，采用Ⅱ型删失数据。在正常应力条件下，实验单元的基准寿命服从GumbelⅡ型分布，其中α和λ分别为形状参数和尺度参数。基于Ⅱ型删失样本，推导出模型参数的最大似然估计(MLE)和贝叶斯估计。利用观测Fisher信息矩阵获得未知参数的渐近区间。在平方误差损失和LINEX损失函数下，采用马尔可夫链蒙特卡洛(MCMC)方法得到贝叶斯估计，并构建未知模型参数的最高后验密度(HPD)区间。通过大量模拟研究考察所提估计量的有限样本性质，并考虑三种不同最优性准则确定最优删失方案。最后，通过两个实际数据集的分析说明所提方法。