This paper introduces a general or “distribution-free” model to analyze the lifetime of components under accelerated life testing. Unlike the accelerated failure time (AFT) models, the proposed model shares the advantage of being “distribution-free” with the proportional hazard (PH) model and overcomes the deficiency of the PH model not allowing survival curves corresponding to different values of a covariate to cross. In this research, we extend and modify the extended hazard regression (EHR) model using the partial likelihood function to analyze failure data with time-dependent covariates. The new model can be easily adopted to create an accelerated life testing model with different types of stress loading. For example, stress loading in accelerated life testing can be a step function, cyclic, or linear function with time. These types of stress loadings reduce the testing time and increase the number of failures of components under test. The proposed EHR model with time-dependent covariates which incorporates multiple stress loadings requires further verification. Therefore, we conduct an accelerated life test in the laboratory by subjecting components to time-dependent stresses, and we compare the reliability estimation based on the developed model with that obtained from experimental results. The combination of the theoretical development of the accelerated life testing model verified by laboratory experiments offers a unique perspective to reliability model building and verification.