Analytical Uncertainty Propagation for Availability Assessment of Stochastic Multi-state Systems
Résumé
The proposed method generalizes uncertainty propagation methods for complex stochastic multi-states system modeling. Until now, analytical methods for uncertainty propagation are only used in simple system modeling as fault tree model. These methods are usually based on moment calculation or variance evaluation. In complex system cases or when complex mathematic factors affect the uncertainties, asymptotic calculation or Monte Carlo simulation are often used to estimate the resulting availability. The proposed method is based on an analytical calculation of the probability of the system states to propagate analytically the uncertainty in the model. It allows a better assessment of the availability of stochastic multi-state systems. The analytical methods used are based on calculus of conjoint probability density function, Universal Generating Function model and associated operators. The method consists in an analytical propagation of uncertainty in the model and an output uncertainty assessment. Particularly, it is able to deduce analytically the output availability of the system with the associated uncertainty. For complex UGF modeling, the analytical calculation to the sub-systems and Monte Carlo simulation on the resulting UGF system model are applied. Consequently, the computing time for the simulation could be drastically reduced.