Model uncertainty and Bayesian updating in reliability-based inspection

In this paper, a Bayesian procedure is proposed to quantify the modeling uncertainty, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. The procedure is developed first using a simple example and then is applied to a fatigue reliability problem, with the combination of two competing crack growth models and considering the uncertainty in the statistical distribution parameters for each model. This Bayesian failure probability analysis can be incorporated with information from nondestructive inspections performed on the structure to derive more realistic reliability estimates. The procedure for updating the mechanical model, probabilistic model, distribution parameter statistics and reliability is illustrated for the fatigue reliability problem.

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