The NBUC and NWUC classes of life distributions

1991 ◽  
Vol 28 (2) ◽  
pp. 473-479 ◽  
Author(s):  
Jinhua Cao ◽  
Yuedong Wang
Keyword(s):  
Shock Model ◽  
Stieltjes Transform ◽  
Closure Properties ◽  
Convex Ordering ◽  
New Class ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

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.

The NBUC and NWUC classes of life distributions

1991 ◽  
Vol 28 (02) ◽  
pp. 473-479 ◽  
Author(s):  
Jinhua Cao ◽  
Yuedong Wang
Keyword(s):  
Shock Model ◽  
Stieltjes Transform ◽  
Closure Properties ◽  
Convex Ordering ◽  
New Class ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

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.

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

Closure of the NBUC class under formation of parallel systems

1993 ◽  
Vol 30 (04) ◽  
pp. 975-978 ◽  
Author(s):  
M. I. Hendi ◽  
A. F. Mashhour ◽  
M. A. Montasser
Keyword(s):  
Parallel Systems ◽  
Convex Ordering ◽  
Distributed Components ◽  
New Better Than Used ◽  
Better Than ◽  
Independent And Identically Distributed

The class of new better than used in convex ordering (NBUC) is shown to be closed under formation of parallel systems with independent and identically distributed components.

scholarly journals The new better than used failure rate class of life distribution

1988 ◽  
Vol 20 (1) ◽  
pp. 237-240 ◽  
Author(s):  
A. M. Abouammoh ◽  
A. N. Ahmed
Keyword(s):  
Failure Rate ◽  
Life Distribution ◽  
Shock Models ◽  
Rate Class ◽  
Life Distributions ◽  
Dual Class ◽  
New Better Than Used ◽  
Ageing Distribution ◽  
Better Than

A new concept of ageing distribution, namely new better than used in failure rate (NBUFR), is introduced. Different properties of the NBUFR class and its dual class are presented. Its relations to other classes of life distributions are investigated. Finally, NBUFR survival under shock models is discussed.

Shock models with underlying birth process

1975 ◽  
Vol 12 (1) ◽  
pp. 18-28 ◽  
Author(s):  
M. S. A-Hameed ◽  
F. Proschan
Keyword(s):  
Failure Rate ◽  
Life Distribution ◽  
Birth Process ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

This paper extends results of Esary, Marshall and Proschan (1973) and A-Hameed and Proschan (1973). We consider the life distribution of a device subject to a sequence of shocks occurring randomly in time according to a nonstationary pure birth process: given k shocks have occurred in [0, t], the probability of a shock occurring in (t, t + Δ] is λ kλ (t)Δ + o (Δ). We show that various fundamental classes of life distributions (such as those with increasing failure rate, or those with the ‘new better than used' property, etc.) are obtained under appropriate assumptions on λ k, λ (t), and on the probability of surviving a given number of shocks.

Some properties of ageing notions based on the moment-generating-function order

2004 ◽  
Vol 41 (3) ◽  
pp. 927-934 ◽  
Author(s):  
Xiaohu Li
Keyword(s):  
Generating Function ◽  
Renewal Process ◽  
Moment Generating Function ◽  
Stochastic Comparison ◽  
Life Distributions ◽  
Convex Linear Combination ◽  
The Moment ◽  
New Better Than Used ◽  
Ageing Notions ◽  
Better Than

Classes of life distributions based on the moment-generating-function order are investigated in this paper. It is shown firstly that the class ℳ is closed under both convex linear combination and geometric compounding. Secondly, the class NBUmg (new better than used in the moment-generating-function order) is proved to be closed under increasing star-shaped transformations. Finally, the interplay between the stochastic comparison of the excess lifetime of a renewal process and the NBUmg interarrivals is studied.

A Multivariate New Better than Used Class Derived from a Shock Model

1983 ◽  
Vol 31 (1) ◽  
pp. 177-183 ◽  
Author(s):  
Emad El-Neweihi ◽  
Frank Proschan ◽  
Jayaram Sethuraman
Keyword(s):  
Shock Model ◽  
New Better Than Used ◽  
Better Than
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