Control and Cybernetics vol. 42 (2013) No. 3 On new aging lasses based on the reversed mean residual life order∗ by Kambiz Ahmadi and Majid Rezaei Department of Statistis, University of Birjand, Iran K.Ahmadibirjand.a.ir, Mjrezaeibirjand.a.ir Abstrat: In this paper, we introdue new onepts of aging for lifetime distributions. The main idea is the omparison between reversed mean residual life of the random variables X and (X − t | X > t), for all t > 0. Firstly, with some examples, we highlight the role of the proposed aging lasses in reliability and life testing. Then, we try to nd the onnetion between the new aging lasses and other aging lasses well-known from the literature. Reliability properties of the new lasses are studied. Formally, we derive the preservation property under monotoni transformations. Some other haraterization and impliations are studied. Keywords: reversed mean residual life, stohasti order, aging lass, preservation, haraterizations, IRMR. 1. Introdution and denitions Stohasti orderings have long been a topi of interest in the reliability theory, eonomis, atuarial sienes, survival analysis and many other branhes of statistis. Beause the aurate distribution of the life of an element or a system is often unavailable pratially, nonparametri aging properties are quite useful for modeling aging or wear-out proesses, and for onstruting maintenane poliies. Suh aging lasses are derived via several notions of omparison between random variables. In the ontext of lifetime distributions, some stohasti orderings of probability distributions have been used to give haraterizations and new denitions of aging lasses. By aging we mean the phenomenon whereby an older system has a shorter remaining lifetime, in some statistial sense, than a younger one, Bryson and Siddiqui (1969). The main goal of this work is to provide another onept of aging for lifetime distributions along with some reliability properties of this onept. The new aging onept is based on stohasti omparison of new lifetime unit and the used one, aording to the reversed mean residual life order. ∗ Submitted: Marh 2013; Aepted: June 2013
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