The Matrix Procedures for Calculation of Importance Measures

Abstract

System reliability/availability is a complex concept that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures in reliability analysis. Some of the most used indices are important measures. These measures allow us to evaluate the influence of fixed system components or set of components to the system reliability/availability. Importance measures are used today to allow for various aspects of the impact of system elements on its failure or operability. Analysis of element importance is used in the system design, diagnosis, and optimization. In this paper new algorithms for the calculation, some of the important measures are developed based on the matrix procedures. This paper's goal is the development of a new algorithm to calculate importance measures of the system based on the matrix procedures that can be transformed in the parallel procedures/algorithms. These algorithms are developed based on the application of Logical Differential Calculus of Boolean logic for the important analysis of the system. The application of parallel algorithms in importance analysis allows the evaluation of the system of large dimensions. Importance specific of the proposed matrix procedures for calculation of importance measures is the application of structure-function for the mathematical representation of the investigated system. This function defined the correlation of the system components states and system reliability/ availability. The structure-function, in this case, is defined as a truth vector to be used in the matrix transformation. The truth vector of a Boolean function is a column of the truth table of function if the values of the variables are lexicographically ordered. Therefore, the structure-function of any system can be represented by the truth vector of 2n elements un-ambiguously.