Simplifying the solution of redundancy allocation problems

Redundancy allocation is a useful technique in designing systems that have high levels of reliability while satisfying limitations on cost, weight, volume, etc. Performing redundancy allocation typically involves formulating and solving an appropriate mathematical programming problem. In the literature, a wide variety of these problems have been formulated and a large number of solution techniques have been proposed. As a result, redundancy allocation problems are typically perceived to be quite difficult to solve. However, very little analysis has been performed for the purpose of quantifying the true difficulty of these problems. In this paper, four basic redundancy allocation problems are addressed. Strategies are defined for solving these four problems to optimality by either partial or total enumeration. In all four cases, the results indicate that these redundancy allocation problems are very simple to solve. These enumeration strategies should provide insight into developing simpler strategies for solving more complex redundancy allocation problems.