New algorithm for Multi-Valued Decision Diagram construction

Abstract

In reliability analysis, the system mathematical representation development is an important step. All mathematical models can be divided into two groups depending on a number of analyzed system performance levels in point of view of reliability analysis: Binary-State System (BSS) and Multi-State System (MSS). Only two performance levels as failure and functioning are considered in BSS. MSS allows considering and evaluation more than only two states. The representation of the system as MSS permits to implement reliability examination in more details but has higher complexity. There are various types of the mathematical representation of a system for BSS and MSS that depends on the mathematical approach used for system reliability evaluation (i.e. mathematical approach for the calculation of reliability indices and measures). The structure function is one of the possible mathematical representations of MSS. New algorithm for structure function construction is considered in this paper. This algorithm is based on the minimization of the structure function truth table, taking into account the principle of orthogonalization. The formed minimal truth table is transformed into Multi-Valued Decision Diagrams (MDD) directly. MDD is used for analysis of extensive dimension data in Algebra Logic (Multiple-Valued Logic). MDDs have been successfully used in reliability computation due to their compact and easy representation of structure function.