Research on the system function-structure analysis based on its implicit relation

To understand the system function-structure under different background relations, two analysis methods are proposed based on space fault tree and factor space theory. They are the system function-structure minimal disjunctive formula and the system function-structure simplest formula. The former establishes the axiom system of system function-structure analysis based on factor logic, and proves that the system function-structure obtained by function-structure analysis method is a minimal disjunction formula. The latter gives a more detailed analysis steps based on the former idea, which is mainly used to determine the implicit relation between system function and component function. The background sets consisting of the 16 and 32 background relations are studied with these two methods. The results show that the complete background relations can obtain a certain system function-structure uniquely; the incomplete background relations can obtain a family of certain system function-structures. If the incomplete background relations are a subset of the complete background relations, then the incomplete background relations must has a linear relation between functions to complement the incomplete background relations. At the same time, the system function equivalent and replacement relation are obtained. It is also proved that the system function-structure obtained from several subsets of the background sets is the simplest and the condition required for the simplest structure of the background set is strict. At present, the above methods are mainly used for system reliability analysis in safety system engineering.