System Reliability Improvement (Redundancy Allocation)

By Muhammad Al-Salamah

A system consists of N subsystems. Let R_j denote the reliability for the subsystem j, j = 1, 2, … N. Then the system reliability R_s is given by

The reliability of each subsystem is improved by adding redundant components. Let x_j be the number of redundant components for subsystem j. Thus, the subsystem unreliability is related to individual unreliability for subsystem j and is given by

Let c_j be the cost of a component for subsystem j and w_j be the weight of a component for subsystem j. Let C be the total resource available for cost and W be the maximum additional weight allowed for the system. The problem can be written as