Change is constant. Or so the saying goes. However, even change is ever-varying. So perhaps we should say: Change is constantly changing. As occupants of planet earth, we intuitively know this and yet strive to keep everything the same, at least those things that do well by us. Uncertainty derails the best of our plans, even uncertainties that we recognize up front.

Tolerance Analysis focuses on dimensional aspects of manufactured physical products and the process of determining appropriate tolerances (read: allowable variations) so that things fit together and work the way they are supposed to. When done properly in conjunction with known manufacturing capabilities, products don't feel sloppy nor inappropriately "tight" (i.e., higher operating efforts) to the customer. The manufacturer also minimizes the no-build scenario and spends less time (and money) in assembly, where workers are trying to force sloppy parts together. Defects are less frequent. There are a wealth of benefits too numerous to list but obvious nonetheless. Let us measure twice and cut once.

In the case of the one-way clutch example, the current MC quality prediction for system outputs provide us with approximately 3- and 6-sigma capabilities (Z-scores). What if a sigma score of three is not good enough? What does the design engineer do to the input standard deviations to comply with a 6 sigma directive?

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.