The international standard IEC/61508 provides the developer with guidelines for the design and implementation of safety related systems according to this standard. This standard states qualitative and quantitative criteria in order to judge a safety related system in such a way that safety critical applications can be implemented. This paper details a quantitative criterion which is the probability of failure on low demand, known as PFD. After an introduction into this topic, the principle steps to calculate the probability of failure with the help of reliability block diagrams for different hardware architecture will be detailed and presented. The PFD-equations will be derived for a 1oo1 architecture with the help of MacLaurin series.