Accelerated tests decrease the strength or time to failure and the cost of testing by exposing the test specimens to higher levels of stress conditions increased sizes or levels of environmental variables which cause earlier breakdowns and shorter lifetimes than the normal-use condition .These environmental variables and levels of stress conditions are referred to as the “accelerating variables” in the statistics and reliability literature. One of the appropriate model selection procedures is to compare the overall MSEs of the models. However, since the power-law Weibull model is based on a Weibull distribution and the proposed and GLM-based models are based on an inverse Gaussian distribution, it is not appropriate to compare the AIC of the power-law Weibull model with other models. In this paper, extend a general cumulative damage model and the power-law Weibull model for materials failure to the several accelerating variables case. A real-data example is presented, and the Generalized Pareto distribution as a lifetime model under simple-step-stress ALT is considered. Maximum likelihood estimates of parameters and their asymptotic variance are obtained. The performance of the estimates is evaluated by a simulation study with different pre-fixed values of parameters.