Let us assume we have a batch of historical data in a spreadsheet. Our mission-of-the-moment is to use this data and fit probability distributions that describe its past variability (or uncertainty). Consider using either Crystal Ball or ModelRisk to do this task. We offer free trials of both to registered users. If you register here, you can get yours too. Try fitting the same data using these two different packages. Let us know how and why one is better than the other. In demonstrating these capabilities, we gain first-hand experience on the usability and capabilities of the alternatives and which features compared have more priority. The best way to judge is to try them out for yourself.
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?