Log-concave and concave distributions in reliability

Nonparametric classes of life distributions are usually based on the patter n of aging in some sense. The common parametric families of life distributi ons also feature monotone aging. In this paper we consider the class of log -concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log-normal, Pareto, and Gompertz d istributions) are log-concave, while the remaining life of maintained and o ld units tend to have a concave distribution. The classes of concave and lo g-concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operati ons, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. (C) 1999 John Wi ley & Sons, Inc.