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We consider probability distributions with constant rate on partiallyordered sets, generalizing distributions in the usual reliability setting([0,∞),≤) that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including momentresults and results concerning ladder variables and point processes. Weconcentrate mostly on discrete posets, particularly posets whose graphsare rooted trees. We pose some questions on the existence of constantrate distributions for general discrete posets

Constant Rate Distributions on Partially Ordered Sets