A.Matrosova, T. Bohan
Tomsk State University, Russia
The random testing quality problem can be spelled out as follows. For a given combinational circuit that has to be tested with N random patterns one should find single stuck faults detected with a probability less than P if they exist. P is the given threshold. A similar problem has been discussed in the paper . Its authors have proposed to replace a detection probability with a signal probability and then obtain signal probability bounds instead of the precise value. In the paper  a precise method of a signal probability calculation is suggested . If a signal probability of a fault is less than P one should obtain its detection probability.
A precise method of a detection probability calculation is suggested in this paper. It is based on using orthogonal disjunctive forms (ODNFs). A disjunctive form is orthogonal if its any two conjunctions are orthogonal w.r.t., a certain variable, i.e. one of them contains this variable without an inversion, and the other has this variable with an inversion. The proved theorems allow cutting the calculation required. A computer tool is developed to estimate possibilities of the method through using bench-marks and other practical circuits.
If the detection probability of the stuck faults is less than P the fault is called a "hard fault". Having increased the number of random patterns one can try to make this fault an "casy" one. If the necessary increase is impossible the fault remains a "hard" one and cannot be detected. In this case one should modify the logic to make the fault easy detected. The developed tool allows to verify a testability of combinational circuit that is find its "bad" nodes if they exist.