Traditional software testing methods combined krsith probabilistic models cannot nieasure arid assess dependability for software that requires v e n high reliabilio (failure rate < 10-'/hour) and availabilit?. (>0. 999999). This paper proposes a novel approach, drawing on findings and methods that have been described individriull~ hut have never been combined, applied in the late testing phase or early operational phase, to quantifi depetitlubility for U categon of critical sofhvare with such high requirenietits. The concepts that are integrated ure: operational profle, rare conditions, importance sampling, stress testing, and measurement-based dependabilir). evaluation. In the approach, importance sanipling is applied on the operational profile to guide the testing of critical operations of the software, thereby accelerating the occurrence of rare conditions which have been shown to be a leading cause of failure in critical systems. The failure rates measured in the testing are then transformed to those that would occur in the normal operation by the likelihood ratio function of the importance sanipling theory, and finally depetidabilih for the tested software system is evaluated by using measurement-based dependabilio modeling techniques. When the acceleration factor is large (over loo), which is r)pical for a category of software of interest, it is possible to quantib a very high reliability or availability in a reasonable test duration. Some feasible methods to inipletnent the approach are discussed based on real data.