Transfer Functions (or Response Equations) are useful to understand the "wherefores" of your system outputs. The danger with a good many is that they are not accurate. ("All models are wrong, some are useful.") Thankfully, the very nature of Tolerance Analysis variables (dimensions) makes the models considered here concrete and accurate enough. We can tinker with their input values (both nominals and variance) and determine what quality levels may be achieved with our system when judged against spec limits. That is some powerful stuff!
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?
In my last couple of posts, I provided an introduction into the topic of Tolerance Analysis, relaying its importance in doing upfront homework before making physical products. I demonstrated the WCA method for calculating extreme gap value possibilities. Implicit in the underlying calculations was a transfer function (or mathematical relationship) between the system inputs and the output, between the independent variables and the dependent variable. In order to describe the other two methods of allocating tolerances, it is necessary to define and understand the underlying transfer functions.