Safety systems are used for automatic shutdown of a plant when the system state tends to become unsafe. The primary attribute of importance for such systems is the measure of their safety, i.e. Probability of Failure on Demand (PFD). Two-out-of-four systems are gaining importance because they are less vulnerable to spurious trips and thus offer higher availability in addition to higher safety as compared to other coincidence logic systems. IEC 61508 is the internationally accepted standard which outlines the requirements, principles, and methods for safety assessment of safety systems. However, IEC 61508 does not specify PFD of a 2oo4 coincidence logic safety system. Thus, a method using reliability block diagram is investigated in this study to determine simplified algebraic expression for PFD2oo4.