The testability distribution of a VLSI circuit is modeled as a series of step functions over the interval [0, 1]. The model generalizes previous related work on testability. Unlike previous work, however, we include estimates of testability by random vectors. Quadratic programming methods are used to estimate the parameters of the testability distribution from fault coverage data (random and deterministic) on a sample of faults. The estimated testability is then used to predict the random and deterministic fault coverage distributions without the need to employ test generation or fault simulations. The prediction of fault coverage distribution can answer important questions about the “goodness” of a design from a testing point of view. Experimental results are given on the large ISCAS-85 and ISCAS-89 circuits.