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

Abstract

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 @e., the probability of loss of assured safety, PLOAS) are presented for several WWSL 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. Example uncertainty and sensitivity analyses for PLOAS involving the representation of uncertainty (i.e., epistemic uncertainty) with probability theory and also with evidence theory are presented.

Effect of delayed link failure on probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links

“…8,9 A fundamental assumption in the representations for PLOAS studied in Refs. [7][8][9][10] is that a link fails instantly when it reaches its failure temperature. The purpose of this presentation is to study representations for PLOAS obtained with the assumption that there is a delay between the time when a link reaches its failure temperature and the time at which the link actually fails.…”

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

“…The complementary concept is aleatory uncertainty, which is an uncertainty that derives from an inherent randomness in the values that a quantity can take on. * [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] The integrals defining S(t) in Eq. (2.1) are obtained from the approximations…”

“…[27] and explicitly stated in Table 2. As examination of Table 2 shows, the representations for PLOAS are fairly complex and certainly too complex for closed form evaluation.…”

“…Two quadrature-based procedures (Le., trapezoidal method and Simpson's method) and two sampling-based procedures (i.e., simple random sampling and importance sampling) are developed in Ref. [27] for the evaluation of the integrals in Table 2 To have a specific example, the time-temperature curve for the WL in Fig. 4 of Ref.…”

“…4 of Ref. [27] and the associated density function for failure temperature are used for illustration. Specifically, this results in temperature curves defined by The CPLOAS program was then used to determine PLOAS with the indicated temperature curves and density functions for all combinations of WLs and SLs indicated in Table 1.…”