Life testing or test-to-failure method and binomial testing method are the two most commonly used methods in product validation and reliability demonstration. The two-parameter Weibull distribution function is often used in the life testing and almost exclusively used in the extended time testing, which can be considered as an accelerated testing method by appropriately extending the testing time but with significantly reduced testing samples. However, the fatigue data from a wide variety of sources indicate that the three-parameter Weibull distribution function with a threshold parameter at the left tail is more appropriate for fatigue life data with large sample sizes. The uncertainties introduced from the assumptions about the underlying probabilistic distribution would significantly affect the interpretation of the test data and the assessment of the performance of the accelerated binomial testing methods, therefore, the selection of a probabilistic model is critically important. In this paper, several new accelerated testing procedures including the extended time testing and increased load/stress testing based on the three-parameter Weibull distribution are investigated. The corresponding formulae of the accelerated testing are also provided and comparisons are made between the two- and three- Weibull functions through several worked examples. Finally, the potential impact of this research on product validation and reliability demonstration are indicated and some recommendations are provided.