Monte Carlo simulation: Predict how certain is uncertainty..

Uncertainty is a fact of life. Uncertainty arises because of many reasons – incomplete knowledge about the reality, complexity, our limitation to predict future events, unforeseen major events etc. We still need to plan, execute and compete in the face of uncertainty. How can we say, then, the probability of success, the best case, worst case, average case estimates of our projects based on the current uncertainties? One of the things we can do is calculate the estimates separately for each of these cases. This is not only tedious, this does not allow asking questions like – what is the probability that the project will be completed within 2 years, 2.5 years, 3 years etc. You can think that a project can take many different paths due to the inherent uncertainties present. Due to this, it can take different time, cost( effort) etc for completion. We may be interested in knowing the spectrum of these time, cost etc variations to make better decisions. This is where the Monte Carlo simulation comes handy. It can walk through the different paths and generate nice graphs that show the time, cost etc distributions with probabilities.

Monte Carlo simulation models can simulate ‘reality’, help make predictions about the future outcome and help in making better decisions. It helps teams cope with uncertainties better. Monte Carlo models can walk through thousands of scenarios and generate predictions by taking randomness into account. Compare this with the difficult mathematical equations which are difficult to solve; some are even intractable. It does not require the users to be very proficient in mathematics. There are many commercial Monte Carlo simulation tools available.

The Monte Carlo simulation models require the inputs to posses a distribution rather than a single number. Generally, normal distribution, triangular distribution etc(also called parametric distributions) are quite popular. If you have historical data( also called non-parametric distributions), the tools will accept them instead of the parametric distributions. By providing the distributions instead if single point estimates we are incorporating randomness into our models. This approach is close to reality than the single-point estimates. How do you interpret the some of the properties of distributions? The mean ( also called the first moment) represents the most expected value. The variance ( also called the second moment) represents the risk associated, the third moment represents the distribution’s skewness and fourth moment measures the peakedness. The accuracy of the model depends on the level to which you have modeled and also the correctness of the data.

If you have data that are correlated you can also include them in the model and make the model know about it. Make sure you include the assumptions as part of the model. You can do sensitiveness analysis of the results on the assumptions. If the results are highly sensitive to one or more assumptions, you need to track the assumptions more closely. You can move them to risks if need be or spend some time to get more clarity on those assumptions.

Monte Carlo simulations can are also used in the robust design techniques. It uses the simulations to carry out the sensitivity analysis, robustness of the design etc. It helps in making the designs robust that can tolerate variations in the process, materials etc and ensures very high quality products.

Monte Carlo simulation tools are also used heavily in finance. It is used for risk analysis, forecasting, sensitivity analysis etc. It is also used by marketing, sales and other disciplines.

Monte Carlo simulation has a wide variety of application than the ones listed above. It is easy to use at the same highly useful.

As always, comments, different views etc are welcome!