Coherent Systems with Multi-State Components

The theory of binary coherent systems is generalized for multi-state components. The system state is defined to be the state of the “worst” component in the “best” min path, or equivalently, the state of the “best” component in the “worst” min cut. Many of the results for the binary case can be computed for multi-state systems using the binary structure and reliability function concepts. Monotonicity results are now valid with respect to stochastic ordering of component probability vectors.