In this note, we consider a coherent system with the property that, upon failure of the system, some of its components remain unfailed in the system. Under this condition, we study the residual lifetime of the live components of the system. Signature based mixture representation of the joint and...

Many quantities of interest in the study of renewal processes may be expressed as the solution to a special type of integral equation known as a renewal equation. The main purpose of this paper is to provide bounds for the solution of renewal equations based on various reliability...