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.