Software certification is a notoriously difficult problem. From software reliability engineering perspective, certification process must provide evidence that the program meets or exceeds the required level of reliability. When certifying the reliability of a high assurance system very few, if any, failures are observed by testing. In statistical estimation theory the probability of an event is estimated by determining the proportion of the times it occurs in a fixed number of trials. In absence of failures, the number of required certification tests becomes impractically large. We suggest that subjective reliability estimation from the development lifecycle, based on observed behavior or the reflection of one's belief in the system quality, be included in certification. In statistical terms, we hypothesize that a system failure occurs with the hypothesized probability. Presumed reliability needs to be corroborated by statistical testing during the reliability certification phase. As evidence relevant to the hypothesis increases, we change the degree of belief in the hypothesis. Depending on the corroboration evidence, the system is either certified or rejected. The advantage of the proposed theory is an economically acceptable number of required system certification tests, even for high assurance systems so far considered impossible to certify.