Analysis of system reliability by Logical Differential Calculus and Decision Diagrams

As a rule, the mathematical description of the system in reliability analysis is defined as system with two states (failure and functioning), that is interpreted as Boolean function. The mathematical tools of Boolean algebra can be used for reliability estimation of the system. The Logical Differential Calculus is one of mathematical tools in Boolean algebra. This tool is used for analysis of influence of Boolean function variables changes on the function value. In case of reliability analysis, this tool is useful in measurement of influence of system component state changes on the system reliability/availability. In reliability engineering, such investigation is named as importance analysis. The new method for calculation of importance measures is proposed in this paper. The mathematical background of this method is Logical Differential Calculus of Boolean function.