Properties of increasing odds rate distributions with a statistical application

We study the family of distributions characterised by an increasing odds rate (IOR), showing that this provides an alternative interpretation of the ‘‘adverse ageing’’ notion, comparable to the well known increasing hazard rate (IHR) model. We prove some preservation properties of this class under several transformations that are often considered in reliability and life testing problems, including formation of order statistics. Moreover, the IOR assumption enables the derivation of survival bounds and tolerance limits, extending the scope of applicability of some known results, which are based, for instance, on the IHR assumption. Finally, we propose a test for the IOR null hypothesis, establishing its consistency and providing a table of simulated p-values.