Monte Carlo Simulation

Monte Carlo simulation is an alternative approach when analytical calculations are not tractable. Based on the generation of random numbers and on statistics, it requires the simulation of many histories to assess low probabilities with sufficient accuracy. Until recently, it was not really effective but with the huge increase of the computer powerfulness it can, nowadays, be effectively implemented on simple personal computers. After the description of the principles, this chapter describes how to generate random numbers, simulate various distributions and estimate the accuracy of the results. Monte Carlo simulation is the only way to assess the impact of data uncertainty on calculations performed with analytical approaches and also to measure the impact of lineage common cause failures (e.g. failures of items of the same quality, excellent, average or poor at the same time, see Chap. 5 ). Then, the classical approaches (probabilistic and temporal continuity) dealing with the impact of condition changes is analysed. This leads to introduce the failure rate continuity approach and to propose a unified approach gathering all of them. The chapter is completed with a comparison between analytical and Monte Carlo simulation approaches which appear to be complementary.