An aging notion derived from the increasing convex ordering: the NBUCA class

    Authors

    I. A. Ahmad; A. Ahmed; I. Elbatal;M. Kayid

    Comments

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    Abbreviated Journal Title

    J. Stat. Plan. Infer.

    Keywords

    classes of life distributions; NBU, NBUC and NBUCA; increasing convex; order; convolution; mixing; shock models; life testing; SPECIALIZED RENEWAL PROCESSES; LIFE DISTRIBUTIONS; MONOTONICITY; PROPERTIES; STOCHASTIC COMPARISONS; PARALLEL SYSTEMS; CLOSURE PROPERTY; SHOCK-MODELS; INEQUALITIES; RELIABILITY; NBU(2); Statistics & Probability

    Abstract

    In this paper, comparison between the life distribution of a new unit with that of the remaining life or a used unit in the increasing convex order leads us to introduce a new class of life distributions which we call new better than used in increasing convex average order and denote by NBUCA. This class includes as subclasses the new better than used, NBU and the new better than used in increasing convex ordering, NBUC. Several properties of this class are presented, including the preservation under convolution, random maxima, mixing and formation of coherent structures. Stochastic comparisons of the excess lifetime at different times of a renewal process when the interarrival times belong to the NBUCA class are established. We provide also some applications of Poisson shock models. Finally testing exponentially against NBUCA is presented. (c) 2004 Elsevier B.V. All rights reserved.

    Journal Title

    Journal of Statistical Planning and Inference

    Volume

    136

    Issue/Number

    3

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    555

    Last Page

    569

    WOS Identifier

    WOS:000233697500003

    ISSN

    0378-3758

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