Residual lifetime distribution and its applications

Abstract

Let T be a continuous positive random variable representing the lifetime of an entity. This entity could be a human being, an animal or a plant, or a component of a mechanical or electrical system. For nonliving objects the lifetime is defined as the total amount of time for which the entity carries out its function satisfactorily. The concept of aging involves the adverse effects of age such as increased probability of failure due to wear. In this paper, we consider certain characteristics of the residual lifetime distribution at age t, such as the mean, median, and variance, as describing aging. Gamma and Weibull families of distributions are studied from this point of view. Explicit asymptotic expressions for the mean, variance and the percentiles of corresponding residual lifetime distributions are found. Finally these families of distributions are fitted to four sets of actual data, two of which are entirely new. The results can be used in discriminating different shape parameters.