The Monte Carlo simulation (named after the administrative area of the Principality of Monaco where the famous Monte Carlo casino is located) is a simulation method for modeling random variables and their distribution functions with the aim of solving definite integrals, ordinary and partial differential equations by stochastic modeling in a sufficiently precise way. Accordingly, complex equation systems of stochastic or deterministic nature, which cannot be solved analytically or only under great effort, can be solved in a mathematical context numerically (“playfully”) by using a MCS. Hereby, the “law of large numbers” constitutes the mathematical justification.
Nowadays, the Monte Carlo simulation is deemed to be the only viable method for calculating complex, multidimensional equation systems, which cannot be solved analytically or which require a very high calculation effort. Accordingly, the MCS has been used successfully not only for physical tasks, but in game theory and mathematical economy, in the theory of information transmission and not least in theory of operation and reliability theory, where it is used for the analysis and examination of
– complex fault trees
– dependencies of states and change of states
– any distribution functions and time dependencies
– flexible maintenance and repair strategies and
– dynamic parameters (“dynamic reliability theory”).
The so called “dynamic reliability theory” is a current object of research. Generally, these complex equations of systems transport theory for the description of dynamic changes of systems can be solved successfully only by using a Monte Carlo simulation. The MCS allows for the modeling of sufficiently precise realistic conditions like stochastic dependencies, time dependencies, ageing processes and physical parameters without limitation.
In general terms, one can say that the MCS is gaining in importance in the industrial field as extensive and costly field tests can be replaced in whole or in parts by computer simulations. The benefits include that material and testing costs for field and laboratory tests can be saved, test conditions are identical and the results are reproducible. Furthermore, the results can easily be compared and interpreted with those of other simulations.
The implementation of the Monte Carlo simulation is constantly being enhanced by more powerful computer systems – even for very many simulation runs. In this respect, also the results which are gained by using a Monte Carlo simulation are becoming more precise.