Availability Allocation Using a Family of Hyperbolic Cost Functions

This paper develops a technique for allocating the parameters, repair time and failure rate, to each component of a system at the lowest possible cost. The allocations are subject to the constraint of a required availability. To make an analytic solution possible, the assumptions of constant failure rates, s-independent components, series system, and no multiple failures were made. Each component is assumed to have a hyperbolic cost function associated with changing its failure rate and its repair time. A Lagrange Multiplier method was used to solve the problem.