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Expressed differently, the order in which the θi are considered is of no importance to probability statements about the θi , or, the θi play a symmetrical role in relation to all problems of probability (de Finetti, 1937). This assumption is in fact critical to many models used in engineering inference. The definition of exchangeability implies two straightforward facts: (1) Any subset θ1 , θ2 , . . , θm of θ1 , θ2 , . . , θn (2 < m < n) is also exchangeable. Note that the opposite is not necessarily valid; for example, two by two exchangeability of (θ1 , θ2 ), (θ2 , θ3 ) and (θ1 , θ3 ) does not imply exchangeability of the triplet (θ1 , θ2 , θ3 ).
H. D. 2002. Indicators for inspection and maintenance planning of concrete structures, Structural Safety, 24: pp. , Straub, D. A. 2006. A computational Framework for Risk Assessment of RC Structures Using Indicators, Computer-Aided and Infrastructure Engineering, 21(3): pp. 216–230 Hofer, E. 1999. On two-stage Bayesian modeling of initiating event frequencies and failure rates, Reliability Engineering and System Safety, 67: pp. V. 2001. J. 2005. Decision under Uncertainty, Cambridge University Press Kaplan, S.
Related to the entire pipeline system). g. a limit state at a specific pipeline cross-section). Defining the component failure probability PF|θ conditional on a component having a CS θ, then the failure probability for the specific component 0 (or, cross-section) of interest given a set of component data x = (x0 , x1 , . . , xn ) is equal to: where the required pdf is given by the component-specific expression (23). This result is different from the following result (29) which applies to a decision involving an arbitrary component θ (or, any cross-section) following the acquisition of data x = (x0 , x1 , .