Determining optimal redundancy for systems with random lifetimes

The problem of allocating spares to remote machines is examined. No reallocation of the spares between machines is possible, and the life distribution of each spare depends upon the machine on which it is used. The machines are subsystems of a system whose useful life terminates in a finite, but random, amount of time (e.g., from a catastrophe or obsolescence), or when a machine depletes its store of spares. An efficient algorithm determines the allocation of spares that maximizes the minimum probability of a machine depleting its spares before the system´s useful life terminates. These results are extended to the case when the spares are divisible. An example illustrates the results