On the expected number of failures detected by subdomain testing and random testing

We investigate the efficacy of subdomain testing and random testing using the expected number of failures detected (the E-measure) as a measure of effectiveness. Simple as it is, the E-measure does provide a great deal of useful information about the fault detecting capability of testing strategies. With the E-measure, we obtain new characterizations of subdomain testing, including several new conditions that determine whether subdomain testing is more or less effective than random testing. Previously, the efficacy of subdomain testing strategies has been analyzed using the probability of detecting at least one failure (the P-measure) for the special case of disjoint subdomains only. On the contrary, our analysis makes use of the E-measure and considers also the general case in which subdomains may or may not overlap. Furthermore, we discover important relations between the two different measures. From these relations, we also derive corresponding characterizations of subdomain testing in terms of the P-measure.