Imprecise Probabilities in Fatigue Reliability Assessment of Hydraulic Turbines

Risk analyses are often performed for economic reasons and safety purposes. In some cases, these studies are biased by epistemic uncertainties due to the lack of information and knowledge, which justifies the need for expert opinion. In such cases, experts can follow different approaches for the elicitation of epistemic data, using probabilistic or imprecise theories. But how do these theories affect the reliability calculation? What are the influences of using a mixture of theories in a multivariable system with a nonexplicit limit model? To answer these questions, we propose an approach for the comparison of these theories, which was performed based on a reliability model using the first-order reliability method (FORM) approach and having the Kitagawa–Takahashi diagram as limit state. We also propose an approach, appropriate to this model, to extend the reliability calculation to variables derived from imprecise probabilities. For the chosen reliability model, obtained results show that there is a certain homogeneity among the considered theories. The study also concludes that priority should be given to expert opinions formulated according to unbounded distributions, in order to achieve better reliability calculation accuracy.