RELATIONSHIPS BETWEEN PURE TAIL ORDERINGS OF LIFETIME DISTRIBUTIONS AND SOME CONCEPTS OF

RESIDUAL LIFE

JAVIER ROJO

The Biostatistical Laboratory, Border Biomedical Research Center, University of Texas, El Paso, TX 79968-0519, U.S.A.

(Received March 14, 1994; revised August 21, 1995)

Abstract. The concepts of pure-tail orderings as defined by sq- and Dorderings are shown to order the family of reliability life distributions which age smoothly in a natural way. This ordering extends to comparisons regarding the limiting behavior of the residual life, mean residual life, sojourn time between perfect repairs in repairable systems, failure rate and, through the preservation of sq- and D-orderings by various reliability operations, to certain coherent systems of components that age smoothly. Possible applications of the results to the industrial practice of cannibalization are also noted.

Key words and phrases: Residual life, mean residual life, increasing failure rate, regular variation, D-ordering, coherent systems, decreasing failure rate (DFR), age-smooth life distributions.