A redundancy strategy for minimizing cost in systems with non-disjoint subsystems under reliability constraint

Abstract

The present paper solves a redundancy allocation problem under reliability constraint. To improve the system reliability, use of redundancy, i.e., use of additional components above the minimum number of components required for the system to operate, is a common practice. But it increases the total cost of the system as well. Thus the problem of allocating redundancy to coherent systems with competing choices of system-components needs to be optimally resolved so that the cost of adding redundancy is minimized. In this paper the problem of redundancy allocation is solved by minimizing the total cost subject to meeting a pre-assigned reliability target. The decision variables here are the number of redundancies. The methodology developed here can be applied to any coherent system, simple or complex. The computational complexity increases with the increase in complexity of the system design. The methodology of solving the redundancy allocation problem developed here yields a deterministic optimal solution, which is a polynomial time solution of an established NP-hard problem. Numerical examples have been included to illustrate the method developed here. The sensitivity of the optimal solution, augmented system reliability and related cost of using redundancy has been studied with respect to the specified reliability targets. No assumption about the form of the component life distribution has been made in the study.