Estimating the probability of failure when testing reveals no failures

Formulas for estimating the probability of failure when testing reveals no errors are introduced. These formulas incorporate random testing results, information about the input distribution, and prior assumptions about the probability of failure of the software. The formulas are not restricted to equally likely input distributions, and the probability of failure estimate can be adjusted when assumptions about the input distribution change. The formulas are based on a discrete sample space statistical model of software and include Bayesian prior assumptions. Reusable software and software in life-critical applications are particularly appropriate candidates for this type of analysis.