Simultaneous allocation of reliability & redundancy using simplex search

Abstract

Here, the existing work in reliability apportionment and redundancy allocation is extended by considering a solution technique to a problem which requires finding the optimal level of subsystem reliability as well as an integer solution for the number of redundant subsystems. The solution technique combines the simplex search method and a heuristic approach developed by Aggarwal (1975) for finding the optimal number of redundant subsystems. The implementation of the simplex search algorithm requires only two types of calculations: (1) generation of a regular simplex given a base point and appropriate scale factor; and (2) calculation of a reflected point. Aggarwal's heuristic approach for finding the optimal number of subsystems is based on the concept that a subsystem is added to the stage where its addition produces the greatest ratio of "increment increases in reliability" to the "product of increments increase in resources" usage. The proposed optimization procedure is demonstrated with two examples. The first example demonstrates the procedure while the second provides evidence of the flexibility of the procedure.