Failure profiles of coherent systems

In this paper we first introduce and study the notion of failure profiles which is based on the concepts of paths and cuts in system reliability. The relationship of failure profiles to two notions of component importance is highlighted, and an expression for the density function of the lifetime of a coherent system, with independent and not necessarily identical component lifetimes, is derived. We then demonstrate the way that failure profiles can be used to establish likelihood ratio orderings of lifetimes of two systems. Finally we use failure profiles to obtain bounds, in the likelihood ratio sense, on the lifetimes of coherent systems with independent and not necessarily identical component lifetimes. The bounds are relatively easy to compute and use.