• 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.4
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• pp.45-51
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• 1993

For studies in reliability, biometry and survival analysis, the length biased distribution is frequently appropriate for certain natural sampling plans. So, we shall convey the preservation of some partial orderings under life length biasd distributions and closures of ILR and NBU classes under life length biasd distributions.

• Kyungpook Mathematical Journal
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• v.3 no.1
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• pp.13-21
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• 1960

• 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.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.41-50
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• 1998

There are various notions of partial ordering between life-times of systems; stochastic ordering failure rate ordering and likeli-hood ration ordering. In this paper we show that for series systems with non i.i.d. exponential lifetimes of components standby redundancy at component level is better than that at system level in failure rate or-dering and likelihood ratio ordering. We also demonstrate that for 2-component parallel systems with i.i.d. exponential lifetimes of com-ponents standby system redundancy is better than standby component redundancy in failure rate ordering and likelihood ratio ordering.

• Bulletin of the Korean Chemical Society
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• v.32 no.1
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• pp.100-104
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• 2011

The structures of the conformers for 1,3-di-t-butyl-2,4-dinitro-tetramethoxysulfonylcalix[4]arene (1) and 1,2-di-t-butyl-3,4-dinitro-tetramethoxysulfonylcalix[4]arene (2) were optimized using DFT BLYP and mPW1PW91/6-31G(d,p) (hybrid HF-DF) calculation methods. We have analyzed the total electronic and Gibbs free energies and the differences between the various conformations (cone, partial-cone (PC), 1,2-alternate, and 1,3-alternate) of 1 and 2. For both compounds, the 1,3-alternate (1,3-A) conformers were calculated to be the most stable, which correlate very well with the experimental results. The orderings of the relative stability of 1 and 2 that resulted from the mPW1PW91/6-31G(d,p) calculations are the following: 1: 1,3-A (syn) > PC (syn) > PC (anti) > 1,2-A (anti) > CONE (syn); 2: 1,3-A (anti) > PC (anti) > PC (syn) > 1,2-A (anti) > 1,2-A (syn) > CONE (syn). The BLYP/6-31G(d) calculated IR spectra of the most stable 1,3-A conformers of 1 and 2 are compared.