Residual life function and some characterization results
by
Ramesh C. Gupta
Department of Mathematics and Statistics, University of Maine

In life testing situations, the additional life time given that a component has survived up to time t is called the residual life function (RLF) of the component. More specifically, if X is the life of a component, then the random variable X_t = X-t / X>t is called the residual life function. In this talk, some reliability functions connected with the residual life distribution will be presented and some of their properties will be examined. In particular, the moments of X will be studied and it is investigated if the first, second or general moment of X characterizes the distribution. It will be shown that in addition to the mean residual life function, the second residual moment also characterizes the distribution. Also the variance residual life and the residual coefficient of variation determine the distribution. The general moments are studied and situations are investigated when the general moments determine the distribution.

Date received: August 30, 2003