The second edition of the international standard of IEC 61508, functional safety of electrical/electronic/programmable electronic safety-related system (SRS), was published in 2010. This international standard adopts a risk-based approach by which safety integrity requirements can be determined. It presents a formula to estimate the hazardous event rate taking account of non-perfect proof-tests. But it is not clear how to derive the formula. In the present paper, firstly, taking account of non-perfect proof-tests, the relationship between the dangerous undetected failure of SRS, the demand on the SRS and hazardous event is modeled by a fault tree and state-transition diagrams. Next, the hazardous event rate is formulated by use of the state-transition diagrams for the determination of the safety integrity requirements. Then, a comparison is made between the formulas obtained by this paper and given in the standard, and it is found that the latter does not always present rational formulation.