On closure properties of NBU(2) class of life distributions

2005 ◽  
Vol 9 (2) ◽  
pp. 103-106
Author(s):  
Dian-tong Kang
Keyword(s):  
Closure Properties ◽  
Life Distributions

A useful ageing property based on the Laplace transform

1983 ◽  
Vol 20 (3) ◽  
pp. 615-626 ◽  
Author(s):  
Bengt Klefsjö
Keyword(s):  
Laplace Transform ◽  
Damage Model ◽  
Cumulative Damage ◽  
Closure Properties ◽  
Shock Models ◽  
The Laplace Transform ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
Ageing Property

The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.

Some results on the relative ageing of two life distributions

1994 ◽  
Vol 31 (4) ◽  
pp. 991-1003 ◽  
Author(s):  
Debasis Sengupta ◽  
Jayant V. Deshpande
Keyword(s):  
Hazard Ratio ◽  
Partial Ordering ◽  
Closure Properties ◽  
Partial Orderings ◽  
Life Distributions ◽  
Crossing Hazards ◽  
Moment Bounds

Kalashnikov and Rachev (1986) have proposed a partial ordering of life distributions which is equivalent to an increasing hazard ratio, when the ratio exists. This model can represent the phenomenon of crossing hazards, which has received considerable attention in recent years. In this paper we study this and two other models of relative ageing. Their connections with common partial orderings in the reliability literature are discussed. We examine the closure properties of the three orderings under several operations. Finally, we give reliability and moment bounds for a distribution when it is ordered with respect to a known distribution.

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 new family of life distributions

1969 ◽  
Vol 6 (02) ◽  
pp. 319-327 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Crack Extension ◽  
Renewal Theory ◽  
Critical Value ◽  
Parameter Family ◽  
Closure Properties ◽  
New Family ◽  
Life Distributions ◽  
Number Of Cycles ◽  
Two Parameter

Summary A new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

Some properties of two families of classes of life distributions

2002 ◽  
Vol 39 (03) ◽  
pp. 581-589 ◽  
Author(s):  
N. R. Mohan ◽  
S. Ravi
Keyword(s):  
Discrete Analogue ◽  
Closure Properties ◽  
The Family ◽  
Life Distributions

We study the closure properties of the family ℒ(α) of classes of life distributions introduced by Lin (1998) under general compounding. We define a discrete analogue of this family and study some properties.

A useful ageing property based on the Laplace transform

1983 ◽  
Vol 20 (03) ◽  
pp. 615-626 ◽  
Author(s):  
Bengt Klefsjö
Keyword(s):  
Laplace Transform ◽  
Damage Model ◽  
Cumulative Damage ◽  
Closure Properties ◽  
Shock Models ◽  
The Laplace Transform ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
Ageing Property

The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.

Some generalized variability orderings among life distributions with reliability applications

1991 ◽  
Vol 28 (02) ◽  
pp. 374-383 ◽  
Author(s):  
M. C. Bhattacharjee
Keyword(s):  
Random Variables ◽  
Parallel Systems ◽  
Reliability Theory ◽  
Dominance Relation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closure Properties ◽  
Life Distributions ◽  
The Mean ◽  
Necessary And Sufficient

We investigate a generalized variability ordering and its weaker versions among non-negative random variables (lifetimes of components). Our results include a necessary and sufficient condition which justifies the generalized variability interpretation of this dominance relation between life distributions, relationships to some weakly aging classes in reliability theory, closure properties and inequalities for the mean life of series and parallel systems under such ordering.

A new family of life distributions

1969 ◽  
Vol 6 (2) ◽  
pp. 319-327 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Crack Extension ◽  
Renewal Theory ◽  
Critical Value ◽  
Parameter Family ◽  
Closure Properties ◽  
New Family ◽  
Life Distributions ◽  
Number Of Cycles ◽  
Two Parameter

SummaryA new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

Some results on the relative ageing of two life distributions

1994 ◽  
Vol 31 (04) ◽  
pp. 991-1003 ◽  
Author(s):  
Debasis Sengupta ◽  
Jayant V. Deshpande
Keyword(s):  
Hazard Ratio ◽  
Partial Ordering ◽  
Closure Properties ◽  
Partial Orderings ◽  
Life Distributions ◽  
Crossing Hazards ◽  
Moment Bounds

Kalashnikov and Rachev (1986) have proposed a partial ordering of life distributions which is equivalent to an increasing hazard ratio, when the ratio exists. This model can represent the phenomenon of crossing hazards, which has received considerable attention in recent years. In this paper we study this and two other models of relative ageing. Their connections with common partial orderings in the reliability literature are discussed. We examine the closure properties of the three orderings under several operations. Finally, we give reliability and moment bounds for a distribution when it is ordered with respect to a known distribution.

scholarly journals On the Dynamic Cumulative Past Quantile Entropy Ordering

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2001
Author(s):  
Haiyan Wang ◽  
Diantong Kang ◽  
Lei Yan
Keyword(s):  
Stochastic Models ◽  
Natural Science ◽  
Stochastic Order ◽  
Random Variables ◽  
Uncertainty Management ◽  
Stochastic Orders ◽  
New Order ◽  
Closure Properties ◽  
Life Distributions

In many society and natural science fields, some stochastic orders have been established in the literature to compare the variability of two random variables. For a stochastic order, if an individual (or a unit) has some property, sometimes we need to infer that the population (or a system) also has the same property. Then, we say this order has closed property. Reversely, we say this order has reversed closure. This kind of symmetry or anti-symmetry is constructive to uncertainty management. In this paper, we obtain a quantile version of DCPE, termed as the dynamic cumulative past quantile entropy (DCPQE). On the basis of the DCPQE function, we introduce two new nonparametric classes of life distributions and a new stochastic order, the dynamic cumulative past quantile entropy (DCPQE) order. Some characterization results of the new order are investigated, some closure and reversed closure properties of the DCPQE order are obtained. As applications of one of the main results, we also deal with the preservation of the DCPQE order in several stochastic models.

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