Numerical calculation of probabilistic fracture mechanic in the piping system

Piping system is one of the critical components in the primary system because failure of those systems will cause loss of coolant accident (LOCA). One of the piping failure cause is fracture mechanic which could be analyzed by deterministic and probabilistic analysis. Probabilistic analysis be done by random variable that could be approached by Monte-Carlo Equation. This equation could be solved by several methods of numerical calculation e.g. : numerical integration, crude Monte-Carlo, stratified sampling and importance sampling, etc. Simple calculation has been done by those methods for 10,000 samplings. The results is that the probability of piping failure is 1.242 x 10-4 for numerical integration; 1.170 x 10-4 for crude Monte-Carlo (standard error = 0.170 x 10-4); 1.239 x 10-4 for stratified sampling ( standard error = 0.007 x 10-4 ); 1.249 x 10-4 for importance sampling ( standard error = 0.015 x 10-4 )