Redundancy Optimization for Critical Components in High-Availability Technical Systems

We consider a user who buys a number of identical technical systems e.g., medical, manufacturing, or communication systems for which she must have very high availability. In such a situation, there are typically several options that the user can choose to facilitate this availability: cold standby redundancy for critical components, buying spare parts with the systems so failed parts can be replaced quickly, and/or application of an emergency procedure to expedite repairs when there is a stock out. To these options we introduce another: the possibility of initiating an emergency shipment when stock is one. Thus, the user may choose different combinations of the redundancy decision and the timing of applications of the emergency procedure, as well as how much spare parts inventory to purchase. We formulate the problem as the minimization of the total costs---acquisition, spare parts, and repair---incurred for the systems over their lifetimes, under a constraint for the total uptime of all systems. We optimally solve the problem by decomposing the multicomponent problem into single-component problems and then conducting exact analysis on these single-component problems. Using these, we construct an efficient frontier that reflects the trade-off between the uptime and the total costs of the systems. In addition, we provide a method to rank the components by the relative value of investing in redundancy. We illustrate these results through numerical examples.