Characterizations of Distributions Through Aging Intensity

In this paper, we characterize univariate positive absolutely continuous random variable through the aging intensity function. Using this function, we propose the characterizations of Weibull- and inverse-Weibull-related distributions. They are alternatives to the basic two-parameter Weibull distribution to be used in reliability analysis of elements and systems. We find that for presented distributions, it is easier to characterize them through their aging intensity function than through their failure rate function. Further on, some other than Weibull family life distributions are presented. However, in their case, characterization through the failure rate seems to be easier. Moreover, aging intensity orders are studied for the considered Weibull distributions. They allow us to decide that one random variable has the better aging property than another one. To show the practical usefulness of the aging intensity, the analysis of this function through some data is performed.