Optimal design of parallel-series systems with competing failure modes

The problem of achieving optimal subsystem size for parallel-series systems, assuming that components and systems are subject to two types of failure modes, open and short, is addressed. Components are statistically independent and identically distributed; the costs of the two modes of system failures need not be the same. The number of subsystems (m), for a given number of components in each subsystem (n), is optimized so that: the mean system profit is maximized showing how m depends on system parameters and showing that there does not exist a pair (m,n) maximizing the mean system-profit, and the mean system cost is minimized. The results are illustrated by several numerical examples