Optimal system-profit design of series-parallel systems with multiple failure modes

The problem of achieving optimal subsystems size (m) is considered assuming that failure may take either of two forms. Components are independent and identically distributed and the two kinds of system failures can have different costs. The optimal m that maximizes the average system-profit is determined, and it is shown how m depends on system parameters. The optimal m subject to a system failure in open mode is also determined. Numerical examples illustrate the results