A new explanation of decreasing failure rate of a mixture of exponentials

It is well known that the mixture of exponential distributions has a decreasing failure rate, even though each component in the mixture has a constant failure rate. This result is elegant but sometimes seen as a paradox. This paper shows that the proportion of strong (weak) subpopulation with small (large) failure rates in the mixture increases (decreases) as time passes. Based on this fact, a non-Bayes explanation is given for the mixture of exponentials to have a decreasing failure rate.