On the moments of residual life in reliability and some characterization results

Abstract

In reliability studies, it is well known that the mean residual life function determines the distribution uniquely. In this paper we study the problem "do higher moments of residual life determine the distribution"? We show, by means of a counterexample, that one higher moment is not enough to determine the distribution uniquely. However, a method is given to determine the distribution if the ratio of two consecutive moments is known. Also it is shown that the constancy of the rth moment, for any positive real number r guarantees that the distribution is exponential. Similar problems are investigated for partial moments and it is shown that unlike truncated moments, one partial moment is enough for the determination of the distribution. Some illustrations are given to exhibit the methods.