Quantifying Software Validity by Sampling

The point of all validation techniques is to raise assurance about the program under study, but no current methods can be realistically thought to give 100% assurance that a validated program will perform correctly. There are currently no useful ways for quantifying how ´well-validated´ a program is. One measure of program correctness is the proportion of elements in the program´s input domain for which it fails to execute correctly, since the proportion is zero i.f.f. the program is correct. This proportion can be estimated statistically from the results of program tests and from prior subjective assessments of the program´s correctness. Three examples are presented of methods for determining s-confidence bounds on the failure proportion. It is shown that there are reasonable conditions (for programs with a finite number of paths) for which ensuring the testing of all paths does not give better assurance of program correctness.