Use of Geometric Programming to Maximize Reliability Achieved by Redundancy

This paper considers the problem of optimum allocation of redundant elements in a simple series sytem (maximizing system reliability subject to several linear cost constraints). Under the approximation that the components of the redundancy vector can be treated as continuous variables, the paper formulates this optimization problem as a geometric programming problem, describes techniques for obtaining numerical solutions in general, and obtains asymptotic closed-form solutions. A standard numerical example is used to illustrate that the asymptotic solution, when suitably rounded, compares favorably with the discrete optimal solution.