C.12. From Chapter 18

RSS Linear Transfer Functions St = the critical sigma of the total assembly or process s1, s2, s3, s4, etc. are the sigmas of the variables linearly affecting the critical sigma of an assembly or process. Each variable's influence must be stated in common units consistent with the part, assembly, or process. For example, if we are studying the thickness variation of an injected molded part and one of the contributing variables is the weight of the injected raw material, we need to state that variable's sigma in "thickness variation per sigma," rather than in "weight unit per sigma."

C.12.1. Use on Problem Type

Use the simplified linear transfer function to understand the effect of each component on the total variation of a part, an assembly, or a process. The sum of the squares of the contributing variable's sigma must equal the square of the sigma of the total assembly or process. If the sum is too low, one or more variables are missing. Each sigma contribution must have units consistent with the product effect being measured. In this way, it is valid to compare the sigmas to see which variable is more critical.

This formula is not applicable to non-linear processes, like many chemical processes that have complex interactions among input variables and therefore require non-linear transfer functions. Non-linear transfer functions, which require partial derivatives, are beyond the scope of this book (and most Six Sigma work).