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.

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

1988 ◽  
Vol 20 (01) ◽  
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.

Shock models with underlying birth process

1975 ◽  
Vol 12 (01) ◽  
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.

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.

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

A class of correlated cumulative shock models

1985 ◽  
Vol 17 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Ushio Sumita ◽  
J. George Shanthikumar
Keyword(s):  
Failure Time ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Random Variables ◽  
System Failure ◽  
Shock Models ◽  
The Times ◽  
New Better Than Used ◽  
Better Than

In this paper we define and analyze a class of cumulative shock models associated with a bivariate sequence {Xn, Yn}∞n=0 of correlated random variables. The {Xn} denote the sizes of the shocks and the {Yn} denote the times between successive shocks. The system fails when the cumulative magnitude of the shocks exceeds a prespecified level z. Two models, depending on whether the size of the nth shock is correlated with the length of the interval since the last shock or with the length of the succeeding interval until the next shock, are considered. Various transform results and asymptotic properties of the system failure time are obtained. Further, sufficient conditions are established under which system failure time is new better than used, new better than used in expectation, and harmonic new better than used in expectation.

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.

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