Published In

Journal of Applied Probability

Document Type


Publication Date



Mathematical statistics, Stochastic models, Coherent states


We consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature vector for these results to hold. These results are combined with other well-known results in the literature to get more general results for comparing two systems of the same size with different signature vectors and possibly with different independent and identically distributed component lifetimes. Some numerical examples are also provided to illustrate the theoretical results.


This article has been published in a revised form in Journal of Applied Probability This version is free to view and download for private research and study only. Not for re-distribution or re-use. © Copyright (2020) Cambridge University Press

Locate the Document



Persistent Identifier

Included in

Probability Commons