How Pooling Failure Data May Reverse Increasing Failure Rates

摘要

Although mixtures of decreasing failure rate (DFR) distributions are always DFR,some mixtures of increasing failure rate (IFR) distributions can also be ultimately DFR. In this article, various types of discrete and continuous mixtures of IFR distributions are considered, and conditions are developed for such mixtures to be ultimately DFR. These conditions lead to a result that certain mixtures of IFR distributions, even those with very rapidly increasing failure rates (e.g., Weibull, truncated extreme), ultimately become DFR distributions. The results of this article indicate that such pooling may actually reverse the IFR property of the individual samples to a DFR property.