How do Monte Carlo analysis results differ from those derived via WCA or RSS methodologies? Let us return to the one-way clutch example and provide a practical comparison in terms of a non-linear response. From the previous posts, we recall that there are two system outputs of interest: stop angle and spring gap. These outputs are described mathematically with response equations, as transfer functions of the inputs.

In past blogs, I have waxed eloquent about two traditional methods of performing Tolerance Analysis, the Worst Case Analysis and the Root Sum Squares. With the advent of ever-more-powerful processors and the increasing importance engineering organizations place on transfer functions, the next logical step is to use these resources and predict system variation with Monte Carlo Analysis.

With uncertainty and risk lurking around every corner, it is incumbent on us to account for it in our forward business projections, whether those predictions are financially-based or engineering-centric. For the design engineer, he may be expressing dimensional variance in terms of a tolerance around his nominal dimensions. But what does this mean? Does a simple range between upper and lower values accurately describe the variation?

Dr David Berlinski (2000) makes the historical observation that two great ideas have most influenced the technological progress of the Western world:

The first is the calculus, the second the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. (Berlinski, p. xv)

Dr Berlinski concludes that:

The great era of mathematical physics is now over. The three-hundred-year effort to represent the material world in mathematical terms has exhausted itself. The understanding that it was to provide is infinitely closer than it was when Isaac Newton wrote in the late seventeenth century, but it is still infinitely far away…. The algorithm has come to occupy a central place in our imagination. It is the second great scientific idea of the West. There is no third. (Berlinski, pp. xv-xvi)

Source: Berlinski, D (2000). The Advent of the Algorithm: The 300-Year Journey from an Idea to the Computer. San Diego, CA: Harcourt.

Related Posts: Enter the Algorithm

According to Prof Ronald A Howard (1992):

Three of the warranties that I would like to have in any decision situation are that:

1. The decision approach I am using has all the terms and concepts used so clearly defined that I know both what I am talking about and what I am saying about it;
2. I can readily interpret the results of the approach to see clearly the implications of choosing any alternative, including of course, the best one; and
3. The procedure used to arrive at the recommendations does not violate the rules of logic (common sense).

Plain and simple... Source: Howard, R A (1992), Heathens, Heretics, and Cults, Interfaces, 22(6), 15-27.

Prof Frank H Knight (1921) proposed that "risk" is randomness with knowable probabilities, and "uncertainty" is randomness with unknowable probabilities. However, risk and uncertainty both share features with randomness. The illustration below explains the relationship of the concepts better than words...

Source: Knight, F H (2002/1921), Risk, Uncertainty and Profit, Washington, DC: BeardBooks.

When using tools such as Excel, Crystal Ball or ModelRisk, it is very important to be able to translate a mental model to a mathematical one. Let me illustrate, when you think about your business, you often will think of abstract notions such as profit or margins. These are mental constructs because their are no physical representations of profit or margins (except a pile of cash) only mathematical ones.