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.
The other RSS equation, that of predicted output mean, has a term dependent on 2nd derivatives that is initially non-intuitive:
Why is that second term there?
A few posts ago, I explained the nature of transfer functions and response surfaces and how they impact variational studies when non-linearities are concerned. Now that we have the context of the RSS equations in hand, let us examine the behavior of transfer functions more thoroughly.
As stated before, the first derivative of the transfer function with respect to a particular input quantifies how sensitive the output is to that input. However, it is important to recognize that Sensitivity does not equal Sensitivity Contribution. To assign a percentage variation contribution from any one input, one must look towards the RSS output variance (σY2) equation: