The foundations of models of dependence in probabilistic safety assessment

Abstract

Two kinds of dependence are distinguished: stochastic and state-of-knowledge dependence. Models of stochastic dependence include common cause failures and deal with component failures. They are conditioned on a set of parameters whose ranges of values and their correlations are assessed in the state-of-knowledge models. It is argued that the parametric stochastic models represent the class of failure causes that are not explicitly modeled. Three such stochastic models are examined: the Basic Parameter (BP) model, the Multiple Greek Letter (MGL) model, and the Multinomial Failure Rate (MFR) model. Two problems of the MGL model are discussed. The first has to do with the definition of the parameters. It is shown that β, γ, etc., of the MGL model are defined with reference to a specific component and are used improperly in the statistical calculations. The second problem stems from the fact that the MGL parameters are defined in terms of component failures rather than the events that cause their failures. This results in an artificial increase of the strength of the statistical evidence. The multivariate Dirichlet distribution is used as the state-of-knowledge distribution in the MFR model, since it can model the correlations between the parameters and is a conjuga distribution with respect to the multinomial distribution, thus facilitating Bayesian updating. The Dirichlet distribution can also be used with the BP model to represent the analyst's state of knowledge concerning the numerical values of the parameters of this model.