  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.
