The NBUC and NWUC classes of life distributions

Abstract

A new class of life distributions, namely new better than used in convex ordering (NBUC), and its dual, new worse than used in convex ordering (NWUC), are introduced. Their relations to other classes of life distributions, closure properties under three reliability operations, and heritage properties under shock model and Laplace-Stieltjes transform are discussed.

Testing Hypothesis for New Class of Life Distribution Nbufr- t0

“…, for all x, t ≥ 0 [9] introduced the class of new better than used in convex ordering (NBUC) distributions. [10] suggested the class of new better than used of second order(2) as follows.…”

Aging properties of the residual life length of k‐out‐of‐n systems with independent but non‐identical components

“…In the following, we present definitions of some aging properties that are closely related to the main results to be presented in this paper. For details on the results to be summarized here, see References [18][19][20].…”

New partial orderings and applications

“…It is easy to observe that the class 0-IFR corresponds to the class ILR (or PF, density class) (see Ross [13] for the definition), and the classes 1-IFR, 1-IFRA, 1-NBU, 1-NBUCV, 1-NBUFR, 2-IFR, 2-IFRA, 2-NBUFR, and 2-NBAFR are identical to the classes IFR, IFRA, NBU, NBU(2), NBUFR, DMRL, DMRLHA, NBUE, and HNBUE, respectively (see Deshpande et al [4]). Moreover, the classes 1-NBAFR, 3-IFR, and 1-CX are the NBAFR, DVRL, and NBUC classes, introduced by Loh [lo], by Launer [9], and by Cao and Wang [3], respectively. Details on the above-mentioned correspondences may be found in Fagiuoli and Pellerey [5] and references therein.…”