Minimal Cut Vectors and Logical Differential Calculus

Reliability analysis of Multi-State System is one of fields, where the methods of the multiple-valued logic are used efficiently. Multi-State System is a mathematical model in reliability engineering, which allows considering some performance level in the system reliability behavior. The principal problem in the reliability engineering is identification of the system components that have the most influence on the system reliability. One of possible approaches, which can be used for this task, is to identify minimal cut sets (or minimal cut vectors (MCVs)). MCVs represent situations in which the repair of any damaged component causes the system improvement. In this paper, the new theoretical background for identification of MCVs is considered. The presented method is based on logical differential calculus.