• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.105-110
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• 1995

In this paper, we shall convey preservation of some partial orderings and closures of some positive ageing classes under k-out-of-n systems of like components. That is, if the life time of a component A is larger than that of a component B in any of the NBU, DMRL, NBUE, HNBUE, NBUFR and NBUFRA orderings, then a k-out-of-n system formed by i.i.d.. components of type A has larger life time, in that ordering, than that of a similar system consisting of n i.i.d. components type of B. And using these partial orderings, closures of positive aging classes(NBU, DMRL, NBUE, HNBUE, NBUFR and NBUFRA) under the coherent system like components.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.119-127
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• 1996

The concepy of positive aging describles the adverse effects of age on the lifetime of units. Various aspects of this concepts are described in terms of conditional probability distribution of residual life times, failure rates, equilibrium distributions, etc. In this paper we will consider some partial ordering relations of life distribution under residual life functions and equilibrium distributions.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.20-32
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• 1995

The concept of positive ageing describes the adverse effects of age on the lifetime of units. Various aspects of this concept are described in terms of conditional probability distribution of residual life times, failure rates, equilibrium distributions, etc. In this paper, we will consider some partial ordering relations of life distributions under residual life functions and equilibrium distributions. Under residual life distributions, we study the relationships of IFR, NBU and NBUFR classes and that of DMRL and NBUE classes, By using WLR ordering comparison between F and its equilibrium $H_F$, we can decide if F belongs to NBUFR class.