A review of SIL theory and a demonstration on the need to truncate the exponential distribution for the generation of SIS failures: Example for a 1oo1 channel architecture
Résumé
This paper deals with the modelling of Safety Instrumented System (SIS) in order to assess the SIL level of this latter one. At first, the underlying mathematical theory is presented focusing mainly on expected value and exponential distribution. Due to SIL theory and related mathematical assumptions, the need to truncate exponential distribution for the generation of failures with Monte Carlo simulation is demonstrated in case of SIS architectures being periodically tested. Two Stochastic P-temporised Petri Nets are proposed to illustrate this small but crucial difficulty of modelling. Through to the implementation of both proposed Petri Nets, the ability of the truncated exponential distribution for the generation of failures with Monte Carlo simulation within the time interval between two tests is demonstrated. Finally, simulations and experimental results are given.
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