Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA
Copyright © 2010 Kyle Siegrist. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider probability distributions with constant rate on partially
ordered sets, generalizing distributions in the usual reliability setting
that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment
results and results concerning ladder variables and point processes. We
concentrate mostly on discrete posets, particularly posets whose graphs
are rooted trees. We pose some questions on the existence of constant
rate distributions for general discrete posets.