Optical systems are conventionally evaluated by ray-tracing techniques that extract performance quantities such as aberration and spot size. Current optical analysis software does not provide satisfactory analytical evaluation functions for the sensitivity of an optical system. Furthermore, when functions oscillate strongly, the results are of low accuracy. Thus this work extends our earlier research on an advanced treatment of reflected or refracted rays, referred to as sensitivity analysis, in which differential changes of reflected or refracted rays are expressed in terms of differential changes of incident rays. The proposed sensitivity analysis methodology for skew ray tracing of reflected or refracted rays that cross spherical or flat boundaries is demonstrated and validated by the application of a cat's eye retroreflector to the design and by the image orientation of a system with noncoplanar optical axes. The proposed sensitivity analysis is projected as the nucleus of other geometrical optical computations.