Bayesian Methods for Modeling Recovery Times with an Application to the Loss of Off‐Site Power at Nuclear Power Plants

Bayesian methods can be very useful in modeling applications used in risk assessments. For example, a Bayesian analysis can be used to provide a probabilistic comparison of different probability models relative to a set of data, as well as to provide uncertainty bounds on the predictions from the various models. For more complex models or composite models, the Bayesian methods easily adapt to include the uncertainty on the weights associated with each of the models that comprise the composite model. Industry data representing the time to recovery of loss of off‐site power at nuclear power plants are used within this paper to demonstrate these aspects of Bayesian analysis. SUMMARY AND CONCLUSIONS The Bayesian based method presented in Section 3 for the calculation of posterior odds provides the analyst with a way of quantifying the adequacy of different probability models for a set of data, and thus replaces the subjectivity with an objective criterion. The methods presented in Sections 4 and 5 provide a basis for constructing uncertainty bounds for recovery/probability curves. These uncertainty bounds are useful in risk assessments. The bounds capture parametric uncertainties and uncertainties about relative frequencies of various initiators of events. The methods presented in Section 6 demonstrate how to modify a model to incorporate specific information about the site under study.