The simple step-stress model with lifetimes being Weibull distributed under Type-I hybrid censoring, which provides a more flexible model than the exponential model, is considered in this thesis. For this model, the maximum likelihood estimates of its parameters, as well as the corresponding observed Fisher information matrix, are derived. We then evaluate the bias and mean square error of these estimates, and provide the confidence intervals for the parameters using asymptotic distributions, a likelihood ratio test, and two parametric bootstrap resampling methods. Finally, under the constraint that the total experimental cost does not exceed a pre-specified budget, the optimal test plan for the estimated 100pth percentile at the use condition is determined.