Monte Carlo Simulation (MCS)
The Monte Carlo simulation (MCS), named after the Monegasque district Monte Carlo with its famous casino, is a simulation method for the modelling of random variables and their distribution functions with the aim to solve certain integrals, ordinary and partial differential equations etc. sufficiently exactly by stochastic modelling. Using the MCS, complex systems of equations of a stochastic or deterministic nature, which cannot be solved analytically or can only be solved with great effort, can be solved numerically (“playfully”) in a mathematical context. The “law of large numbers” forms the mathematical basis.
Today, Monte Carlo simulation is the only practicable method for calculating complex multidimensional systems of equations which cannot be solved analytically or which require a great deal of computational effort. Accordingly, the MCS is used not only in the physical field but also in game theory and mathematical economics, in the theory of message transmission and, last but not least, in operation and reliability theory for the analysis and consideration of
- Complex fault trees,
- Dependencies of states and state changes,
- Arbitrary distribution functions and time dependencies,
- Flexible maintenance and repair strategies and
- Dynamic influencing variables (“dynamic reliability theory”)
A current object of research is the so-called “dynamic reliability theory”. The complex equations of system transport theory used here to describe dynamic system changes can usually only be successfully evaluated using MCS. The Monte Carlo simulation enables you to model real conditions, such as stochastic dependencies, time dependencies, ageing processes and physical influencing variables, without restrictions.
In general, it can be said that MCS is gaining more and more importance in industry, since complex and expensive field tests can be replaced completely or partially by computer simulations. Among other things, this has the advantage that material and test costs for field and laboratory tests can be saved, the test conditions are identical and the results reproducible. In addition, the results can be easily compared and analyzed with those of other simulations.
The implementation of the Monte Carlo simulation is continuously improved by more powerful computer systems – even with very high simulation runs. In this respect, the results that can be achieved with Monte Carlo simulation are becoming more and more accurate.