One of my colleagues asked whether uncertainty margin should be added to the input or the response, particularly for a nonlinear system. I recommend adding to the response. He asked that I write a paper using an acceleration base input which he supplied. The results are given in the following paper for a spring-mass system with nonlinear stiffness.
Note that waiting until the end of the analysis to add margin is the method used by Sam DiMaggio at SpaceX.
On the other hand, NASA’s Isam Yunis recommends applying the uncertainly factor to the input.
Isam and I both agree that deriving environments is ultimately a matter of engineering judgment.
See also: Normal Tolerance Factors
– Tom Irvine