Multiobjective techniques for optimum parallel redundancy with several cost functions: a trade-off function approach

Abstract

The present work deals with the problem of allocating to the stages of system spare components in parallel in order to improve the reliability of this system under cost-functions. This problem can be regarded directly, that is to maximize the overall reliability under several cost-function constraints (say system cost, system weight, system volume etc.). Several papers have been written on this problem using various mathematical programming methods. But also, of interest could be the inverse problem which is to maintain the overall system reliability over some safety level and it must be done with the cheapest several cost-functions. This topic has been treated by Kettelle (1962) and Barlow and Proschan (1965) in the case of a single cost-function but multiobjective programming techniques are involved in order to describe and solve the same problem in the case of multiple cost-functions to be simultaneously minimized. What the work on hand does is that it considers a systematical multiobjective formulation of this inverse redundancy allocation problem based on various relations introduced in the Cartesian space of the cost-functions, and then solves this problem using the “trade-off” technique.