Tests of univariate and bivariate stochastic ageing

摘要

Concepts of ageing describe how a population of units or systems improves or deteriorates with age. Many classes of life distributions are categorized and defined in the literature according to their ageing properties. An important aspect of such classifications is that the exponential distribution is nearly always a member of each class. The notion of stochastic ageing is important in any reliability analysis, and many test statistics have been developed for testing exponentiality against various ageing alternatives. This paper is an overview of these developments. The author begins with a table of ageing classes together with key references, followed by a brief discussion on the characterization of exponentiality. Test procedures are summarized, and followed by the main review. Tests of exponentiality against other alternatives are explained for randomly censored data. Finally, tests of multivariate ageing properties are listed. Some of the life classes have been derived more recently and, as far as is known, no test statistics have been proposed. On the other hand, several tests are available for some classes. Relative efficiency of a test is discussed whenever appropriate.