WNBUE Class and its Applications to Signature-Based Bounds for Reliability of Coherent Systems

The inequalities are established here rational functions of the weighted moments and conditional weighted tail moments of the underlying failure distribution. In this paper, we first introduce a new notion of aging called “weighted new better (worse) than used in expectation” and then we present a procedure for developing reliability inequalities based on this new aging notion. Next, we apply it to obtain the reliability of a coherent system by using the Samaniego signature when the component lifetimes are independent and identically distributed. Specially, we use the new bounds for consecutive-type systems. These new bounds are easy to compute as they depend on the system signature and the parent distribution.