New Matrix Based Algorithm for Calculation of Importance Measures

Abstract

The system reliability/availability is complex term that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures. Some of the most used are importance measures. These measures allow to evaluate the influence of fixed system components or set of components to the system reliability/availability. Importance measures are used 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 algorithm for the calculation some of importance measures is developed based on the matrix procedures. This paper goal is development of new algorithm to calculate importance measures of the system based on the matrix procedures that can be transformed in the parallel procedures/algorithm. This algorithm is developed based on the application of Logical Differential Calculus of Boolean logic for importance analysis of system. The application of parallel algorithm in importance analysis allows the evaluation of system of large dimension. Importance specific of the proposed matrix procedures for calculation of importance measures is the application of structure function for the mathematical representation of 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 truth vector to be used in the matrix transformation. The truth vector of Boolean function is column of the truth table of function if the values of the variables are lexicographically ordered