We generalize an approach to deriving diagnosability results of various interconnection networks in terms of the popular $g$-good-neighbor and $g$-extra fault-tolerant models, as well as mainstream diagnostic models such as the PMC and the MM* models. As demonstrative examples, we show how to follow this constructive, and effective, process to derive the $g$-extra diagnosabilities of the hypercube, the $(n, k)$-star, and the arrangement graph. These results agree with those achieved individually, without duplicating structure independent technical details. Some of them come with a larger applicable range than those already known, and the result for the arrangement graph in terms of the MM* model is new.