Predicting the reliability of software systems based on a component-based approach is inherently difficult, in particular due to failure dependencies between software components. One possible way to assess and include dependency aspects in software reliability models is to find upper bounds for probabilities that software components fail simultaneously and then include these into the reliability models. In earlier research, it has been shown that including partial dependency information may give substantial improvements in predicting the reliability of compound software compared to assuming independence between all software components. Furthermore, it has been shown that including dependencies between pairs of data-parallel components may give predictions close to the system's true reliability. In this paper, a Bayesian hypothesis testing approach for finding upper bounds for probabilities that pairs of software components fail simultaneously is described. This approach consists of two main steps: 1) establishing prior probability distributions for probabilities that pairs of software components fail simultaneously and 2) updating these prior probability distributions by performing statistical testing. In this paper, the focus is on the first step in the Bayesian hypothesis testing approach, and two possible procedures for establishing a prior probability distribution for the probability that a pair of software components fails simultaneously are proposed.