In this article the maximum likelihood estimates of the model parameters under step-stress partially accelerated life tests (SSPALT) are obtained assuming the Weibull distribution with Type-II censored data. Also, the confidence bounds of the parameters are obtained. In addition, optimum step stress test plans are developed. The optimum test plan determines the optimal stress change point that minimizes the generalized asymptotic variance of the maximum likelihood estimators for the model parameters. That is, improving the quality of the statistical inference.