How many backups are needed to keep the system running reliably

A new solution technique called multi stage Monte Carlo optimization is used to solve a multivariate reliability problem for its minimum cost solution. Multi stage Monte Carlo optimization (MSMCO) makes repeated random searches in the feasible solution space of the optimization problem at hand. Stage one of the simulation searches the entire feasible solution space. Then stage two focuses the search in a narrower region centered about the "best answers so far." Then stage three focuses the search in a further reduced region initially centered about the best answer produced from the stage two search. This process is repeated as many times as necessary until convergence to the true optimal or a useful approximation is obtained.