A note on some new renewal ageing notions

Abstract

Many notions have been proposed to describe the ageing property of a lifetime. Some of the earlier developments can be found in Barlow and Proschan (Statistical Theory of Reliability and Life Testing, Holt, Reinhart and Winston, New York, 1975) and Gnedenko et al. (Mathematical Methods of Reliability Theory, Academic press, New York, London, 1969). Recently, Abouammoh et al. (Statist. Probab. Lett. 48 (2000) 189) introduced new classes arising from stochastic comparisons with the stationary renewal distribution. We show here that their new renewal better than used in expectation class contains only the exponential random variables.