A new aging concept derived from the increasing convex ordering

T. H. M. Abouelmagd, A. A. E. Ahmed, Enayat M. Abd Elrazik, Mahmoud M. Mansour, A-Hadi N. Ahmed and Ahmed Z. Afify

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 12, 2904-2916

Abstract: In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call “new better than used in convex ordering of second order”. This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented.

Date: 2019
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DOI: 10.1080/03610926.2018.1473593

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