We propose an approach for assessing the mean failure frequency of a program, based on the statistical test of hypotheses. The approach can be used to establish stopping rules and evaluate the quality of a program based on its mean failure frequency during the late testing phases. Our proposal shows how to set and satisfy conservative bounds for the minimum number of test executions that are needed to achieve a target mean failure frequency with a specified level of statistical significance, based on the quality goal of testing and the specific test execution profile chosen. We relax a few assumptions of the literature, so our approach can be used in a larger set of real-life cases.