Calculating an appropriate multiplier for ßλ when modeling common cause failure in triplex systems

The Beta Model for common cause failure (CCF) is well accepted and has proven appropriate for dual architecture Safety Instrumented Systems (SIS). However, it is not directly applicable to a triplex architecture SIS. It has been suggested that CCF for a triplex architecture is appropriately modeled by αβλ. This paper derives α, the multiplier for βλ, required in the evaluation of CCF in triplex systems. It shows that the multiplier, α, varies between 1 and 1.5 as a function of the proportion of CCF which result in all three units of the triplex architecture failing. It further explains why, in the absence of reliable data on the proportion of CCF involving all three units, the most conservative safety evaluation requires setting the multiplier, α, to the value 1.5.