ON TESTING CLASSES OF LIFE DISTRIBUTIONS AGAINST VARIOUS ALTERNATIVES

Abstract

Ageing is a phenomenon that has implications on many research areas such as life testing, reliability studies, actuarial science, economics, manufacturing, engineering, medicine and phannaceutical studies among many. At the macro level, states or economic systems like to categorize "old age" since this is an economic dependent state that puts responsibilities on governments and organizations. While at the micro level, a manufacturer would like to know how long a warranty of a product should run, and when to end before the inception of "old age" of the product when lots of maintenance and or repairs become necessary. In medicine, survival analysis and life testing has always centered on the concept of ageing mostly through identifying classes of ageing phenomena. Defining classes that characterize positive ageing has long • been an area of active research. Early developments are embodied in the book of Barlow and Proschan (198 I) where early ageing concepts and

classes such as "increasing failure rate," (IFR), "increasing failure rate average" (IFRA), "new is better than used" (NBU), "new is better than used in expectation" (NBUE), and the "decreasing mean residual lifetime" (DMRL) are defined and studied. During the past several decades various classes of life distributions have been pro-posed in order to model different aspects of aging . The best known of theses classes are IFR, IFRA, DMRL, NBU, NBUE and HNBUE. The relations between these classes are the following .