A Note on Some Reliability Bounds for Multistate Systems

Maymin (1987) proved that for binary systems the path-cut lower bound is sharper than the minimax lower bound when the components are all highly reliable, which was originally conjectured by Barlow and Proschan (1981). This motivates us to consider the problem that whether this property for binary systems remains valid for the more general and complicated multistate systems. An example is constructed to illustrate that this is not the case for general multistate systems. However, an a rmative result is obtained under a mild condition we imposed. We show that this condition is satis ed by the Barlow-Wu (1978) and the N2 classes (Natvig (1982)) of multistate systems. Examples, including a power generation system due to Natvig (1986), are given to illustrate the applications of our results.