What is the Monte-Carlo Simulation?
Monte Carlo simulation is named after the city of Monte Carlo in Monaco, which is famous for gambling such as roulette, dice, and slot machines. Since the simulation process involves generating chance variables and exhibits random behaviors, it has been called Monte Carlo simulation.
Monte Carlo simulation is a powerful statistical analysis tool and widely used in both non-engineering fields and engineering fields. It was initially used to solve neutron diffusion problems in atomic bomb work at Alamos Scientific Laboratory in 1944.
Monte Carlo simulation performs random sampling and conducts a large number of experiments on the computer. Then the statistical characteristics of the experiments (model outputs) are observed, and conclusions on the model outputs are drawn based on the statistical experiments. In each experiment, the possible values of the input random variables 1 2 ( , , , ) X = X X X L n are sampled (generated) according to their distributions. Then the values of the output variable Y are calculated through the performance function Y g = ( ) X at the samples of input random variables. With a number of experiments carried out in this manner, a set of samples of output variable Y are available for the statistical analysis, which estimates the characteristics of the output variable Y
Reference:
Missouri University of Science and Technology:
http://web.mst.edu/~dux/repository/me360/ch8.pdf