The issue of testability, intended as a measure of solvability of the parametric fault diagnosis problem in analog linear time-invariant electrical networks, is addressed in this paper. Independently of the considered fault location method, such important metric provides information as to how many and which components can be diagnosed. For the reader's convenience and to set up an appropriate framework for our main achievements, our first concern is to rederive fundamental results concerning analog linear time-invariant electrical network testability hinging on multifrequency measurements. Then a novel algorithm for testability analysis is proposed, which is straightforward and able to circumvent the main drawbacks of formerly proposed methods, such as computational and conceptual complexities, proneness to roundoff errors, and vulnerability to particular cases. A computer program that implements such algorithm is also described. Moreover, the possibility of employing further simplified versions of the latter and their links with a previously proposed approach are discussed on rigorous bases. Finally, examples are provided, which show the effectiveness and robustness of the new algorithms, also by means of a comparison with the old ones. Copyright (c) 2015 John Wiley & Sons, Ltd.