A linear approximation for redundant reliability problems with multiple component choices

This paper investigates the series-parallel redundant reliability problems subject to multiple separable linear constraints, where each subsystem has multiple component choices. The problems generalize the typical series-parallel reliability problems when the number of component choices for each subsystem is set to one. Instead of conventional approaches, e.g. dynamic programming, geometric programming and piecewise linear approximation, a simple linear programming approach is proposed to approximate the integer nonlinear programming problem. Numerical results for test problems with single (multiple) component choice(s) are reported and compared. Limited numerical results demonstrate the efficiency and the effectiveness of the proposed approach. Additionally, results obtained from the approach proposed herein might provide an effective lower bound for branch-and-bound methods to obtain the global optimum for the problem.