It can depend on the degree of similarity being discussed. Fasteners are a common item for "substitution", and it is often informally done in the field. For instance, an approved configuration using MS27039 screws on a panel can have a "minor" modification justified through similarity, by replacing them with a couple of handy AN3 bolts of the same diameter and length and so on. Mechanics let this through all the time, and typically it doesn't raise the flag, though sometimes it should. Minor modifications are defined by the FAR's and it's worth knowing about it, if you need to do things like drawing change notices on a design that may or may not impact the structural substantiation.
A change can easily be classed as "major" because the threshold is pretty low and there's a lot of A** covering going on. An example of a major repair is a puncture to a pressurized fuselage (which was substantiated by test) with an analysis of the patch and doubler you put on. Analysis works here because the skin structure is simple and repetitive and your repair exists within a structural shape that can be analyzed reliably. Usually your goal is to show that you have not reduced the margin of safety, either. An "equivalent strength" analysis uses the base strength of the material as "MS=0" and then proves that the changes leave you with "MS>0".
Changing your parts may lead to a slightly reduced margin of safety somewhere in the structure. Attempting a substantiation by analysis will begin with "MS=0" and there is no room to go down. Even when your original tests showed that there is a positive margin of safety, you probably don't have enough information to know how much the positive margin would be reduced by a change.
When a part or a structure was substantiated by test, changes to it cannot accurately be judged in terms of their effect on the structure, or its margin of safety, or its stiffness, unless a detailed structural analysis is done. Well, the level of structural analysis required to demonstrate such a thing can be as elaborate as a complete substantiation by analysis. Before starting down that road, you have to recognize the reasons that the thing was load-tested in the first place. The same logic or regulations will probably rule out the analysis you want to do for the change, too.
Steven Fahey, CET