Ternary decision diagrams for the real-time analysis of non-coherent fault trees

Fault Tree Analysis (FTA) to forecast the probability of system failure. The type of logic for the top event is usually limited to AND and OR gates which leads to a coherent fault tree structure. In noncoherent fault trees components’ working states as well as components’ failures contribute to the failure of the system. The qualitative and quantitative analyses of non-coherent fault trees can introduce further difficulties over and above those seen in the coherent case. It is shown that the Binary Decision Diagram (BDD) method can be used for this type of assessment. The BDD approach can improve the accuracy and efficiency of the quantitative analysis of non-coherent fault trees. This article demonstrates the value of the Ternary Decision Diagram method (TDD) for the qualitative analysis of non-coherent fault trees. A fault tree is converted to a BDD which is a representation of the system structure function (SFBDD). A SFBDD can then be used for the quantification of system failure parameters but is not sufficient for the qualitative analysis that gives prime implicant sets. Established methods for the analysis of noncoherent fault trees require an additional BDD form that encodes all prime implicant sets. The process of applying some of the conversion methods can be time consuming. The aim of the method reported in this paper is to perform both qualitative and quantitative analyses on a fault tree converted to a BDD/TDD logic form. The analysis can be used to provide information to a decision making process for future actions of an autonomous system and therefore must be performed in real time. In these circumstances fast processing and small storage requirements are very important. The method provides a fast processing capability. Small storage could be achieved if a single structure was used for both qualitative and quantitative analyses. Hence a new approach, the Ternary Decision Diagram method, is proposed in this paper. A fault tree is converted to a single TDD structure that enables the complete analysis. The efficiency of the TDD method is discussed and compared to the performance of the established methods for analysis of non-coherent fault trees.