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Different Weibull lifetime models are presented whose scale, shape and minimum lifetime parameters are stress-dependent. This allows describing and predicting the lifetime of products with a Weibull distribution more accurately wherever stress-dependence applies to the failure mechanism. For instance, this is the case for failures due to fatigue, on which this paper focusses. The proposed procedure encompasses a two-step maximum likelihood estimation and a Fisher matrix (FM) confidence bounds calculation, followed by a model evaluation. This model evaluation is conducted by means of a general plausibility check (PC), likelihood ratio test (LRT) and Bayesian information criterion (BIC). Their applicability to accelerated life test data is discussed and validated using test data. Finally, a simulation study confirms a wide range of applicability.

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