Variance quantification of functional reliability estimates using re-sampling techniques

Passive systems, which completely depend on natural phenomena such as gravity, conduction and convection to accomplish the safety functions, are increasingly being used in new generation nuclear reactor designs. However, since the driving forces of passive systems are weak, they are more vulnerable to associated uncertainties and there may be a non-zero probability for the system to deviate from the intended behavior and leads to functional failure. Methods for quantification of the functional failure include Monte-Carlo simulation of the system uncertainties using a validated mechanistic code. Generally, the mechanistic codes used for complex system modeling are computationally expensive and Monte-Carlo simulation for estimating small failure probabilities requires more time and often become prohibitive. In this respect, recently, functional reliability methodologies including advanced simulation techniques such as subset simulation, Markov chain Monte-Carlo, importance sampling, and response conditioning method are reported in open literature. Unlike in the case of direct Monte Carlo simulation, for the probability estimates obtained using these advanced simulations, analytical formulas are not available to estimate standard error and confidence interval. In this paper, the estimation of standard error and confidence interval of functional reliability estimates using computationally efficient re-sampling methods based on bootstrap technique are described. Numerical application of these methods, to quantify the variability of functional reliability estimates, is also explained.