When to do Monte Carlo Simulation (… and what is it)?

Abstract

Chris and Fred discuss when you should do this thing called Monte Carlo simulation? … in fact … what is it?

Key Points

Join Chris and Fred as they discuss when and how Monte Carlo simulation can help you with reliability modeling and analysis. What is it anyway?

Topics include:

What is ‘Monte Carlo Simulation’? It is really simple. It essentially relies on a computer to randomly simulate things like how long it will take for a component to fail (once you have been able to model it with something like a Weibull distribution). If you have something like a switching system where a switch device will detect when a primary component fails, and then switches to a standby component, then Monte Carlo simulation can really help. The analytical approach means you need to come up with an equation that takes into consideration the reliability of the primary component, the reliability of the standby component before it is used, the reliability of the component of the standby component after it starts being used, and the reliability of the switch itself. All of which changes over time. Good luck with that! But Monte Carlo simulation can really help … especially if you make things even more complicated by trying to take into consideration repair.
Where does the term ‘Monte Carlo’ come from? The Manhattan Project. Physicist Stanislaw Ulam wondered to himself how to work out the likelihood of being able to win the game of solitaire (based on a standard 52 deck of cards). Winning solitaire starts with being dealt a winning hand. Not all deals allow you to win solitaire. And there are 8.06 x 10⁶⁷different ways you can deal with a pack of cards. This is not possible to solve analytically. But Ulam realized that with emerging computing power, he could ask computers to randomly deal 52 cards and assess if the hand was winnable (or not). So computers could simulate (for example) 10 000 deals and find the fraction of winnable hands. This would be a good guess of the overall fraction of winnable hands. And if you wanted to improve the accuracy of this answer, you run more simulations.
… and why was it called ‘Monte Carlo simulation?’ The Manhattan Project that this idea was so powerful, that it needed to be protected. So it needed a code name. So Ulam referred to it as ‘Monte Carlo’ simulation because his uncle enjoyed playing solitaire at the Monte Carlo Casino in Monaco.

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