Aging Intensity of Nonnegative Univariate Absolutely Continuous Distributions

Abstract

In this chapter we characterize nonnegative univariate absolutely continuous random variable by the aging intensity function (Sect. 2.1). Using this function we propose the characterizations of Weibull and inverse Weibull related distributions (Sect. 2.2). 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 by their aging intensity function than by their failure rate function. Further on, some other than Weibull family life distributions are presented (Sect. 2.3). However, in this case characterization by the failure rate seems to be easier. Moreover, aging intensity orders are studied for the considered Weibull distributions (Sect. 2.4). 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 (Sect. 2.5).