基于NBUMg类分布的更换策略比较

证明了年龄更换策略和成批更换策略依矩母函数序减少(增加)任意时间间隔内的失效次数的充要条件是基分布具有NBUMg (NWUMg)性质;更换间隔不同的成批更换策略在相同工作时间内的失效次数也作了比较.     

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.     

带借贷利率和门槛分红策略的Erlang(n)盈余过程（英文）

本文考虑带借贷利率和门槛分红策略的Erlang(n)盈余过程:当保险公司的盈余为负数时,允许保险公司以某借贷利率向银行借贷以继续经营业务;当保险公司的盈余超过某个正的门槛值时,保险公司将向其股东支付红利.我们研究了绝对破产时支付红利现值的矩母函数和m阶矩函数.特别地,在Erlang(2)盈余情形下,当索赔额的分布服从指数分布时,我们得到总分红现值的精确解析式;并且利用数值模拟的方法对参数进行了敏感性分析.     

两部件冷备系统的可靠性分析及其最优更换策略

本文研究了两个不同部件、一个修理工组成的冷贮备可修系统,假定它们的寿命分布和维修分布均匀为指数分布,但故障后均不能修复如新时,我们利用几何过程和补充变量法求得了一些可靠性指标,并以故障次数为策略,以长期运行单位时间内的期望效益为目标函数,确定了最优的故障次数,便得目标函数达到最大值,从而保证了系统的可用度。     

逆Weibull分布随机变量的随机比较(英文)

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

Ⅰ型极值分布随机变量的随机比较(英文)

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

保修策略下的系统最优更换模型

本文研究了单部件组成系统的保修策略 ,提出了一种新的按比例保修和免费保修策略 .在假定故障部件不能“修复如新”的条件下 ,利用几何过程分别考察了顾客和商家关于产品的长期运行平均费用 ,求出了它们的明显表达式 ,并且可以通过数值法或分析法求出其最优保修期 .     

泊松冲击下阈值为几何过程的可修系统的最优更换策略（英文）

本文研究泊松冲击下的单部件可修系统,假设系统并非"修复如新".系统失效有可能由于外部冲击或者内部因素引起,并且冲击到达服从一个泊松过程.当冲击量大于系统的预先定好的一个阈值,则系统就会失效.假设系统在维修以后相邻之间的阈值形成一个几何过程,而系统的修理时间服从α-幂过程.利用更新过程理论,求出系统经长期运行单位时间内的期望损失及相应的最优更换策略.最终通过数值案例验证了模型中的结果.     

修理设备可更换的k/n(G)表决可修系统

研究了修理设备可更换的k/n(G)表决可修系统,其中修理设备在修理故障部件时可能发生失效.假定部件和修理设备的寿命服从负指数分布,故障部件的修理时间和修理设备的更换时间服从一般分布的条件下,利用马尔可夫更新过程理论和拉普拉斯变换(Laplace-Stieltjes变换),分别讨论了系统首次故障前的平均时间,可用度,故障频度及修理设备的不可用度和失效频度,获得了相关指标的递推表达式.在此基础上,给出了1/2(G)表决可修系统和(n-1)/n(G)表决可修系统相关可靠性指标的表达式.     

某些新广义函数类(英文)

给出由非标准离散函数及其差商所定义的新广义函数的某些类,它们密切联系于通常的直至某阶为连续可微的函数．周的一个深刻的定理被用来建立这些类与非标准Ｓｏｂｏｌｅｖ空间之间的关系．     

Samples without Replacement: Discrete Analogs of Some Continuous Distributions

Some characterizations of distributions based on regressional properties of order statistics are obtained for random samplings without replacement. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 40–50.     

Some New Results on Stochastic Comparisons of Spacings from Heterogeneous Exponential Distributions

Some new results are obtained on stochastic orderings between random vectors of spacings from heterogeneous exponential distributions and homogeneous ones. LetD₁, …, D_nbe the normalized spacings associated with independent exponential random variablesX₁, …,X_n, whereX_ihas hazard rateλ_i,i=1, 2, …, n. LetD*₁, …, D*_nbe the normalized spacings of a random sampleY₁, …, Y_nof sizenfrom an exponential distribution with hazard rateλ=∑ⁿ_i=1 λ_i/n. It is shown that for anyn2, the random vector (D₁, …, D_n) is greater than the random vector (D*₁, …, D*_n) in the sense of multivariate likelihood ratio ordering. It also follows from the results proved in this paper that for anyjbetween 2 andn, the survival function ofX_j:n−X_1:nis Schur convex.     

Replacement Policies with Used Items Constraint

Various block replacement policies with used items have appeared in the literature. These policies use new as well as used items (created by the policies) for replacement. In these policies no constraint is placed on the number of used items used in each cycle. This paper considers these policies with a constraint (of practical significance) to ensure that the expected number of used items used per cycle is less than or equal to the expected number of used items created per cycle.     

Optimal Policies for Investment with Time-Varying Return Distributions

We develop a model in which investors must learn the distribution of asset returns over time. The process of learning is made more difficult by the fact that the distributions are not constant through time. We consider risk-neutral investors who have quadratic utility and are selecting between two risky assets. We determine the time at which it is optimal to update the distribution estimate and hence, alter portfolio weights. Our results deliver an optimal policy for asset allocation, that is, the sequence of time intervals at which it is optimal to switch between assets, based on stochastic optimal control theory. In addition, we determine the time intervals in which asset switching leads to a loss with high probability. We provide estimates of the effectiveness of the optimal policy.     

Optimal Repair Limit Replacement Policies with Imperfect Repair

This paper considers the repair limit replacement policies with imperfect repair. The repair is imperfect in the sense that the mean life of a repaired system is less than the mean life of a new system. Furthermore, we examine the repair limit replacement policy for the case in which there are two types of repair-local and central repair. The local repair is imperfect whilst the central repair is perfect (i.e. the system is as good as new after central repair). The optimal policies are derived to minimize the expected cost per unit of time for an infinite time span. Analytical results are presented along with numerical examples.     

Continuity Properties of Distributions with Some Decomposability

Absolute continuity and smoothness of distributions in the nested subclasses ~L _m (B), m = 0, 1, 2,..., of the class of all B-decomposable distributions are studied. All invertible matrices are classified into two types in terms of P.V. numbers. The minimum integer m for which all full distributions in ~L _m (B) are absolutely continuous and the minimum integer m for which all absolutely continuous distributions in ~L _m (B) have the densities of class C ^r for 0 r are discussed according to the type of the matrix B related to P.V. numbers.