As uncertainty and reliability related issues are becoming more critical in engineering design and analysis, proper assessment of the probabilistic behavior of an engineering system is essential. The true distribution for the system response subject to parameter uncertainty should be derived, if possible. However, owing to the complexity of physical systems and mathematical functions, derivation of the exact solution for the probabilistic characteristics of the system response is difficult, if not impossible. In such cases, Monte Carlo simulation is a viable tool to provide numerical estimations of the stochastic features of the system response.
Simulation is a process of replicating the real world based on a set of assumptions and conceived models of reality (Ang and Tang, 1984, pp. 274-332). Since the purpose of a simulation model is to duplicate reality, it is an effective tool for evaluating the effects of different designs on a system’s performance. Monte Carlo simulation is a numerical procedure to reproduce random variables that preserve the specified distributional properties. In Monte Carlo simulation, the system response of interest is repeatedly measured under various system parameter sets generated from known or assumed probabilistic laws. It offers a practical approach to uncertainty analysis because the random behavior of the system response can be duplicated probabilistically.
Two major concerns in practical applications of Monte Carlo simulation in uncertainty and reliability analyses are (1) the requirement of a large number of computations for generating random variates and (2) the presence ofcorrelation among stochastic basic parameters. However, as computing power increases, the concern with the computation cost diminishes, and Monte Carlo simulations are becoming more practical and viable for uncertainty analyses. In fact, Beck (1985) notes that “when the computing power is available, there can, in general, be no strong argument against the use of Monte Carlo simulation.”
