NBU(2)性的偏序刻画

为刻画同一寿命分布类中两个不同分布的NBU(2)性的强弱,本文定义了一个新的偏序,即NBU(2)序,并证明NBU(2)序具有反身性,反对称性和传递性.另外,该偏序与超可加序、NBUE序,增凹序的关系也作了探讨.基于被比较分布是指数的情况,还建立了判定NBU(2)序的一个充要条件.     

特殊关联系统下寿命的封闭性

§1.引言由同一寿命分布类■中的元件组成的关联系统(coherent system),其寿命是否仍属于(?),是可靠性数学中的一个重要问题.见 Barlow 和 Proschan(1975),Klefsj(o|¨)(1982)等.虽然在许多寿命分布类中对构成关联系统是不封闭的,如对 IFR 类,但是,一些特殊的系统,在适当的条件下,其封闭性仍然是成立的.例如,由独立同分布部件组成的 k-n(F)系统,若部件有 IFR 分布,则系统寿命亦属于 IFR 类.Klefsj(o|¨)(1984)对 NBU 类证明了并联系统的封闭性.同时,他提到在部件独立同分布时,并联系统的寿命对 NBUE,DMRL 及 HNBUE 类是否封闭的问题至今仍未解决.这篇短文对 NBUE 及 DMRL 的封闭性给出了证明,而对 HNBUE 的情形有反例说明不封闭.     

年龄点t0之后的NBU性的非参数检验方法

NBU＊t0寿命分布中新元件的寿命随机地大于旧的年龄不小于t0的元件的剩余寿命,这为更广泛地模拟元件的老化和劣化现象提供了丰富的内容。本文首先对那些t0年龄点之后剩余寿命随机等于新元件寿命的元件的结构加以刻画,然后建立了一个非参数检验方法以区分这种随机等价性和t0年龄点后的严格的NBU性,并给出了针对一个NBU＊t0但非NBU的寿命分布的例子的数值模拟结果。     

HDMRL寿命分布类

引言寿命分布类的研究在系统可靠性的估计.可靠性统计理论,策略选择以及经济模型中都有重要的作用.已知的分布类有IFR,甘RA,NBU,NBUE,DMRL,丑双BUE,砚l)VRL,以及NDVRL类等等.对偶类有DPR系列.     

NBUE分布类应力-强度模型的概率上界

研究应力-强度模型的结构的可靠性分析,当元件应力变量分布属于NBUE类,强度变量服从指数分布,给出了应力-强度模型中概率的上界,由此讨论了n个元件组成系统的应力-强度模型概率上界.     

可信性空间上基于生命表的生命函数模型

在可信性空间上讨论寿险精算中人的寿命分布问题.用具有次可加性的可信性测度替代传统寿险精算中的度量算子概率测度,以生命表的基本统计量为参数,推导出一系列生命函数的数学模型.从而,使对人的寿命分布规律的刻画更客观、更准确.     

基于NBUE类寿命分布的更换间隔比较

在介绍期望序和NBUE类分布的定义后,首先证明了年龄更换策略和成批更换策略的更换间隔依期望序分别大于正常更新过程的更换间隔的充要条件是基分布属于NBUE类.随后,还考察了参数不同的年龄更换策略之间和成批更换策略之间的更换间隔.     

基于分散型和扩散型随机序对几种寿命分布类的刻画

本文基于分散型和(或)扩散型随机序，利用随机变量的剩余寿命给出了寿命分布类ILR，IFR，DMRL和IFR(2)及其对偶类的刻画．作为主要结果的一个应用，用k／n-系统的剩余寿命对IFR和DMRLS及其对偶类进行了刻画．这些结果拓宽和加强了文献中已有的结果．     

关于反失效率序,DRHR和IEIT寿命分布类的几个结论

在这篇论文中,首先提出了一个基于期望休止时间序的反失效率序的等价刻画,并且利用膨胀序给出了递增期望休止时间分布类的一个新的刻画.然后,研究了当元件属于某个寿命分布类时所揭示的k-out-t-n系统的休止时间的变化情况,以及同一K-out-t-n系统不同的休止时间变化情况.类似的,考虑了在k-out-t-n系统中最先失效元件的休止时间的情况.     

复扇形指标集上的分布混沌

该文刻画了具有扇形指标集的转移半群在权函数空间中上的稠密分布混沌.由相容权函数的可积性,以及指标集子集的上稠性,对转移半群的分布混沌性给出了一个充分条件.此外,该文还对指标集进行了讨论,给出了转移半群在指标集的某些子集上也是分布混沌的.     

SOME MULTIVARIATE DMRL AND NBUE DEFINITIONS BASED ON CONDITIONAL STOCHASTIC ORDER

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On the right spread order of convolutions of heterogeneous exponential random variables

A sufficient condition for comparing convolutions of heterogeneous exponential random variables in terms of right spread order is established. As a consequence, it is shown that a convolution of heterogeneous independent exponential random variables is more skewed than that of homogeneous exponential random variables in the sense of NBUE order. This gives a new insight into the distribution theory of convolutions of independent random variables. A sufficient condition is also derived for comparing such convolutions in terms of Lorenz order.     

Right Spread序的若干封闭性质

§1Introductionandmotivation Itisalwaysofinteresttocomparethevariabilityoftworandomvariablesinreliability theoryandeconomics.Thecomparisonsbasedonmomentssuchasvarianceandstandard deviationarenotveryinformativealthoughsuchmeasuresaresimpletouse.Meanwhile,sincethesecomparisonsarestaticones,andhencetheirapplicationsinsomefields,e.g.,reliabilityandfinance,arerestricted.Inthesefields,however,somedynamicalcomparisons areneeded.Asaresult,severalstochasticordersthataremorerefinedhavebeen establishedi…     

Sharp bounds for NBUE distributions

Let F be a new better than used in expectation (NBUE) distribution function with mean μ. In a previous paper (Brown in Probab. Eng. Inf. Sci. 20:195–230, 2006), the author derived the following bound. For any t≥μ, $$\overline{F}(t) = \mathit{Pr}(X \ge t) \le e^{-[{t\over\mu}-1]}. $$ The main result of this paper is to show that this bound is sharp. Other sharp bounds for NBUE distributions are also derived.     

具有均值和方差的HNBUE分布类中可靠度的下界

本文导出了具有均值和方差的ＨＮＢＵＥ分布类中可靠度的指数型下界，给出了ＮＢＵ和ＮＢＵＥ分布类中可靠度的新的下界，提供了估计这些分布类中可靠度最低限的方法。     

A generalized Hollander-Proschan type test for NBUE alternatives

In this note we develop a family of test statistics for testing exponentiality against NBUE alternatives. The asymptotic distribution of the test statistics is derived. The test statistics are shown to be asymptotically normal and consistent. This family of test statistics includes the test proposed by Hollander and Proschan (1975) as a special case. Efficiency studies have also been done.     

Reliability bounds for NBUE and NWUE distributions

In [5], many inequalities for NBUE and NWUE life distributions are given. But, since there are some basic observations which do not hold (see Section 1 for details), many results obtained in [5] are not true. In this note we propose some remedies and give some new results.The proect supported by the National Natural Science Foundation of China.     

An upper bound on the expected completion time of PERT networks

In this paper the problem of determining an upper bound on the expected project completion time, described by the PERT network, is considered. It is assumed that activity durations are independent random variables with given means. The exact forms of probability distributions do not have to be known; however, their cumulative distribution functions are expected to belong to the so-called NBUE class. Very simple algorithms for deriving this bound are presented. The computations can even be performed manually for more involved networks. Our approach producing a pessimistic evaluation of the expected value of the project duration, extends considerably the information obtained through the use of the classical PERT that always underestimates this value. The results are illustrated by a simple example, and errors of approximations are discussed.