Structural and System Reliability

Chapter 10 describes Bayesian methods for parameter estimation and updating of structural reliability in the light of observations. The chapter begins with a description of the sources and types of uncertainties. Uncertainties are categorized as aleatory or epistemic; however, it is argued that this distinction is not fundamental and makes sense only within the universe of models used for a given project. The Bayesian updating formula is then developed as the product of a prior distribution and the likelihood function, yielding the posterior (updated) distribution of the unknown parameters. Selection of the prior and formulation of the likelihood are discussed in detail. Formulations are presented for parameters in probability distribution models, as well as in mathematical models of physical phenomena. Three formulations are presented for reliability analysis under parameter uncertainties: point estimate, predictive estimate, and confidence interval of the failure probability. The discussion then focuses on the updating of structural reliability in the light of observed events that are characterized by either inequality or equality expressions of one or more limit-state functions. Also presented is the updating of the distribution of random variables in the limit-state function(s) in the light of observed events, e.g., the failure or non-failure of a system.