An example of a Monte Carlo simulation risk analysis model for Statistical Modeling

This simple model estimates how long a device will operate before failing, considering the reliability of all of its key components.

Technical difficulty: 1

Techniques used: Monte Carlo simulation in Excel, Exponential distribution

ModelRisk functions used: VoseExpon, VoseInput, VoseOutput

Model description

The risk analysis model is built using Excel with our Monte Carlo simulation add-in called ModelRisk. It uses the following formatting convention:

This example models a simple device with the following components:

This represents a device which will work only if:

• Component A is working; and
• At least one of Components B, C and D are working; and
• At least one of Components E and F are working.

In the model, each component is given a MTTF (mean time to failure). This is used with an Exponential distribution in the Time of failure column to simulate the day on which the component will actually fail.

The time that the device actually fails (the output, in yellow) is then simply MIN(A, MAX(B,C,D),MAX(E,F)) where each letter represents the simulated time of failure of the respective component.

Results

The model takes about 12 seconds to run 50,000 samples. It is set up to directly show three reports within the ModelRisk ResultsViewer at the end of the simulation, which are described below.

The first tab shows a histogram plot of the time to failure of the device:

One can see, for example, that the most likely cost lifetime is around 200 days. The second tab shows the descending cumulative distribution for the lifetime:

One can see, for example, that the lifetime has a 5% chance of being more than 810 days, and that there is a 5% chance it will be less than 33 days.

The third tab looks at how much each component contributes to the total lifetime uncertainty – the longer the bar, the more risk that component adds:

For example, component A is contributing about 470 days of uncertainty (506 - 36, the positions of each end of the bar). Components E and F are the next most important and contribute the same as we would expect, and components B, C and D contribute the least. The tornado sensitivity plot is great at showing where to focus to try to reduce overall uncertainty.