The use of not logic in fault tree analysis

Risk and safety assessments carried out on potentially hazardous industrial systems commonly employ fault tree analysis to predict the probability or frequency of system failure. Causes of the system failure mode are developed in an inverted tree structure where the events are linked using logic gates. The type of logic is usually restricted to AND and OR gates which makes the fault tree structure coherent. The use, directly or indirectly, of the NOT logic gate is generally discouraged as this can result in a non-coherent structure. Non-coherent structures mean that components’ working states contribute to the failure of the system. The qualitative and quantitative analysis of such fault trees can present additional difficulties when compared to the coherent versions. This paper examines some of the difficulties that can occur, and what potential benefits can be derived from the incorporation of NOT logic. It is shown that the binary decision diagram (BDD) method can overcome some of the difficulties in the analysis of non-coherent fault trees.