How Pooling Failure Data May Reverse Increasing Failure Rates
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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Although mixtures of DFR Decreasing Failure Rate distributions are always DFR, some mixtures of IFR Increasing Failure Rate distributions can also be DFR. In this paper, various types of discrete and continuous mixtures of IFR distributions are considered, and conditions developed for such mixtures to be DFR. These conditions show an unexpected result, that certain mixtures of IFR distributions, even those with very rapidly increasing failure rates e.g. Weibull, Truncated Extreme, etc., become DFR distributions. It is common practice to pool data from several different IFR distributions to enlarge sample size, for instance. The results of this paper serve as a warning note that such pooling may actually reverse the IFR property of the individual samples to a DFR property for the mixture.
- Statistics and Probability