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

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.

A Multivariate New Better Than Used Class Derived from a Shock Model.

1980 ◽  
Author(s):  
Emad El-Neweihi ◽  
Frank Proschan ◽  
Jayaram Sethuraman
Keyword(s):  
Shock Model ◽  
New Better Than Used ◽  
Better Than

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.

Distribution properties of the system failure time in a general shock model

1984 ◽  
Vol 16 (2) ◽  
pp. 363-377 ◽  
Author(s):  
J. G. Shanthikumar ◽  
Ushio Sumita
Keyword(s):  
Failure Time ◽  
Sufficient Conditions ◽  
System Failure ◽  
Shock Model ◽  
Completely Monotone ◽  
Shock Models ◽  
Subsequent Interval ◽  
New Better Than Used ◽  
Better Than

In this paper we study some distribution properties of the system failure time in general shock models associated with correlated renewal sequences (Xn, Yn) . Two models, depending on whether the magnitude of the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length of the subsequent interval to the next shock, are considered. Sufficient conditions under which the system failure time is completely monotone, new better than used, new better than used in expectation, and harmonic new better than used in expectation are given for these two models.

Distribution properties of the system failure time in a general shock model

1984 ◽  
Vol 16 (02) ◽  
pp. 363-377 ◽  
Author(s):  
J. G. Shanthikumar ◽  
Ushio Sumita
Keyword(s):  
Failure Time ◽  
Sufficient Conditions ◽  
System Failure ◽  
Shock Model ◽  
Completely Monotone ◽  
Shock Models ◽  
Subsequent Interval ◽  
New Better Than Used ◽  
Better Than

In this paper we study some distribution properties of the system failure time in general shock models associated with correlated renewal sequences (X n, Y n) . Two models, depending on whether the magnitude of the nth shock X n is correlated to the length Y n of the interval since the last shock, or to the length of the subsequent interval to the next shock, are considered. Sufficient conditions under which the system failure time is completely monotone, new better than used, new better than used in expectation, and harmonic new better than used in expectation are given for these two models.

Tail of compound distributions and excess time

1996 ◽  
Vol 33 (01) ◽  
pp. 184-195 ◽  
Author(s):  
Xiaodong Lin
Keyword(s):  
Size Distribution ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Claim Size ◽  
Compound Distributions ◽  
Fundamental Identity ◽  
Claim Size Distribution ◽  
Simple Bounds ◽  
New Better Than Used ◽  
Better Than

Bounds on the tail of compound distributions are considered. Using a generalization of Wald's fundamental identity, we derive upper and lower bounds for various compound distributions in terms of new worse than used (NWU) and new better than used (NBU) distributions respectively. Simple bounds are obtained when the claim size distribution is NWUC, NBUC, NWU, NBU, IMRL, DMRL, DFR and IFR. Examples on how to use these bounds are given.

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.

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