Monte Carlo Simulation

Monte Carlo Simulation Example - ToolsHero

This article explains the Monte Carlo Simulation in a practical way. After reading it, you will understand the basics of this powerful Decision Making tool.

What is the Monte Carlo Simulation?

The Monte Carlo Simulation is a computer-operated technique in which a physical process is not simulated once, but many times. This way, possible risks in quantitative analysis and decision making come to light. It offers a wide scale of possible outcomes and chances and shows all the possibilities in order to come to the correct decision. It doesn’t only say what could happen, but also the probability of something happening. This simulation technique can be used within different fields, such as finance, insurance, project management, production and engineering.


The term stems from the famous casino in Monte Carlo, the seaside village of Monaco. The simulation technique was first used by scientists who were working on the atom bomb in the Second World War. The term has nothing to do with gambling. It just so happens that in a casino, one gambles based on probability, in the same way probability plays a large part in arriving at a risk analysis in the Monte Carlo simulation.


The Monte Carlo simulation is often used when it turns out that the result of a simulation is not representative enough. This way, it can be determined what the actual expected variations are. The Monte Carlo simulation can also provide sufficient extra reliability in the case of a variation or uncertainty of the starting conditions. This simulation technique is realised with calculations via computers. To come to a desired reliability level, the calculations are repeated tens or even thousands of times, each time with a new set of input variables.


Generally, the Monte Carlo simulation consists of three phases: pre-processor, simulation, post-processing.

1. Pre-processor

First, a complete set of variables, representing a nominal value, need to be entered. Then, the probability distribution is defined. The pre-processor chooses a value at will for each of these variables, taking the probability distribution into account.

2. Simulation

Next, the simulations are executed, whereby each simulation includes a different set of input variables.

3. Post-processing

The Monte Carlo simulation ends with a large output of organised results of the simulations, which are represented in the form of, among others, probability distributions.

Risk analysis

A Monte Carlo simulation performs a risk analysis. The obtained results are calculated over and over again, each time with a different set of random values. Eventually this leads to thousands of possible calculations and possible outcome values. In order to complete the risk analysis, random numbers from the input probability distributions are randomly delivered during the simulation. Because the Monte Carlo simulation repeats this up to thousands of times, this leads to a probability distribution of the possible outcomes. This creates the most complete possible picture of possible risks.

Probability distribution

Insecurities regarding the eventual results and characteristics can arise in each design phase of a system. The associated probability distribution is often difficult to determine as well. This has to do with the variation in physical characteristics and/or the circumstances. By using probability distributions, variables can lead to different outcomes. Therefore, probability distributions are a realistic tool to describe uncertainty in variables of a risk analysis.

Monte Carlo Simulation example

Perhaps a production company of fire-resistant materials wants to test and calculate flammability. These materials are use in shipping and aviation, among other things. The flammability depends on multiple variables, all of which need to be taken into the calculations, according to the Monte Carlo simulation. Think about the different kinds of basic material, coatings, the fiber thickness, the density, melting temperature, evaporation temperature, adhesion and so on.

One simulation with nominal values for all these variables will only show the flammability in one way as a result. According to the Monte Carlo simulation, each input variable needs to be replaced by a spreading around a nominal value, with a corresponding probability distribution. This simulation will be performed a few times as well, producing multiple outcomes with a probability distributions within that field. The result is that the production company receives a realistic picture of the flammability of the fire-resistant materials they produce.

It’s Your Turn

What do you think? Is the Monte Carlo Simulation applicable in your personal or professional environment? Do you recognize the practical explanation or do you have more suggestions? What are your success factors for good decision making?

Share your experience and knowledge in the comments box below.

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More information

  1. Bortz, A. B., Kalos, M. H., & Lebowitz, J. L. (1975). A new algorithm for Monte Carlo simulation of Ising spin systems. Journal of Computational Physics, 17(1), 10-18.
  2. Mooney, C. Z. (1997). Monte carlo simulation (Vol. 116). Sage Publications.
  3. Vose, D. (1996). Quantitative risk analysis: a guide to Monte Carlo simulation modelling. John Wiley & Sons.

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