Verification of the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links

Two approaches to the calculation of probability of loss of assured safety (PLOAS) in temperature dependent weak link/strong link systems are described and compared on the basis of three test problems. The approaches differ in that the first approach permits a separation of epistemic and aleatory uncertainty in the calculation of PLOAS and the second approach combines epistemic and aleatory uncertainty before the calculation of PLOAS. A discrepancy in the results obtained with the test problems led to the identification of an implementation error for one of the approaches. The importance and efficacy of well-designed verification test problems are demonstrated.     

Verification test problems for the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links

Four verification test problems are presented for checking the conceptual development and computational implementation of calculations to determine the probability of loss of assured safety (PLOAS) in temperature-dependent systems with multiple weak links (WLs) and strong links (SLs). The problems are designed to test results obtained with the following definitions of loss of assured safety: (i) failure of all SLs before failure of any WL, (ii) failure of any SL before failure of any WL, (iii) failure of all SLs before failure of all WLs, and (iv) failure of any SL before failure of all WLs. The test problems are based on assuming the same failure properties for all links, which results in problems that have the desirable properties of fully exercising the numerical integration procedures required in the evaluation of PLOAS and also possessing simple algebraic representations for PLOAS that can be used for verification of the analysis.     

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links

Relationships to determine the probability that a weak link (WL)/strong link (SL) safety system will fail to function as intended in a fire environment are investigated. In the systems under study, failure of the WL system before failure of the SL system is intended to render the overall system inoperational and thus prevent the possible occurrence of accidents with potentially serious consequences. Formal developments of the probability that the WL system fails to deactivate the overall system before failure of the SL system (i.e. the probability of loss of assured safety, PLOAS) are presented for several WL/SL configurations: (i) one WL, one SL; (ii) multiple WLs, multiple SLs with failure of any SL before any WL constituting failure of the safety system; (iii) multiple WLs, multiple SLs with failure of all SLs before any WL constituting failure of the safety system; and (iv) multiple WLs, multiple SLs and multiple sublinks in each SL with failure of any sublink constituting failure of the associated SL and failure of all SLs before failure of any WL constituting failure of the safety system. The indicated probabilities derive from time-dependent temperatures in the WL/SL system and variability (i.e. aleatory uncertainty) in the temperatures at which the individual components of this system fail and are formally defined as multidimensional integrals. Numerical procedures based on quadrature (i.e. trapezoidal rule, Simpson's rule) and also on Monte Carlo techniques (i.e. simple random sampling, importance sampling) are described and illustrated for the evaluation of these integrals.