The accelerated life testing is the key methodology of assessing product reliability rapidly. This type of life testing is more efficient with low cost than the classical reliability testing. For this, estimating of the underlying model and predicting the future failure times are issues deserve the attention and follow-up. In this paper, a simple step-stress testing experiment is considered when the lifetime data comes from a proportional hazard family under Type-II censoring. We discuss frequentist and Bayes estimators of the underlying model parameters. Prediction of unobserved or censored lifetimes is also tackled here, and frequentist and Bayesian predictors are developed. An algorithm is presented to generate ordered lifetime data from the proportional hazard family under the simple step-stress accelerated lifetime testing. Two numerical examples are also provided to illustrate the estimation and prediction methods presented in this paper. Finally, a Monte Carlo simulation experiment is performed to evaluate the performance of the various estimation and prediction methods developed in this paper. {\color{red} The results show that the Bayesain estimation and prediction under the informative prior perform better than the ones obtained based on frequentist methods. Also, the maximum likelihood method does not work well for predicting future failure times.
