In the design of a flare header system, it is common practice to design the system for the total load from all the relief valves discharging into the system for a given scenario such as power failure or cooling water failure. The total load can be reduced by the application to the process of one or more safety instrumented functions (SIFs) which are designed to eliminate specific loads. However full credit for all the SIFs cannot be taken because some of them may fail when called on to operate. Thus, to design the flare system, the designer must assume some of the SIFs fail and the question to be decided is how many SIFs should he assumed to have failed. The purpose of this article is to show how to determine the number of SIFs likely to fail on a given demand. It is shown that the probability of failure is governed by the binomial probability distribution. This probability is independent of system geometry and individual loads. The ideas of the binomial probability distribution are then expanded to show how, by explicit consideration of system geometry and individual loads, the size of the system may be further reduced. (C) 2009 American Institute of Chemical Engineers Process Saf Prog 29: 166-173, 2010