修如新模型下设备的可用度

对可维修的设备考虑一类修如新模型,导出了在该模型下设备在任意时刻的可用度函数.     

结构应力S（t）为X^2—更新过程时最大值概率分布及统计参数的估计

本文讨论结构应力Ｓ（ｔ）在设计基准期（０，Ｔ）内变动规律。当应力变动时间间隔是独立同服从Ｘ＾２－分布的随机变量时，建立Ｘ＾２－更新过程模型，获得Ｘ＾２－更新过程样本函数最大值概率分布的初等函数表达式及最大值ＳＭ的一、二阶矩估计。     

冲击模型可靠度的界

对于冲击模型H(t)=sum from k=0 to ∞ P{N(t)=k}·P_k其中{N(t),t≥0}是更新过程,间隔时间分布函数F(t)存在有限均值,在以下情况下,我们讨论了其界值问题: ①F(t)是IFR类分布;②F(t)是DFR类分布; ③F(t)是NBUE类分布;④F(t)是NWUE类分布.而且对一些特殊情况,其结论更简洁.     

复合更新风险模型下的破产概率

讨论了具有较一般意义的复合更新风险模型下的破产概率,在假定索赔分布属于重尾分布族的前提下,得到了我们所渴望的破产概率的尾等价形式.这一结果恰与经典的Cram啨r-Lundberg模型下的结论相一致.     

保费到达为更新过程的复合更新风险模型

本在经典风险模型基础上，把索赔到达过程Nt加以推广为更新过程。且在保单到达非均匀的前提下，把保单到送过程推广为更新过程Mt，得到有限时间t孕余的瞬时分布ψ（u,θ0,t,α），然后求得时刻t的生存概率ψ（t,u，θ0)。     

更新理论积分方程的解析解

本文利用再生核空间的特性，在Ｗ１２空间中给出了析密度和更新函数的解析表达式，并与已有６文献中的数值结果进行了比较，显示该计算途径是可行的。     

双更新风险模型

本文讨论了具有两个到达过程的更新模型,在只要求点间间距的分布是绝对连续的简单条件下,利用鞅的乘积性质,得到了最终破产概率和有限时间破产概率的一个上界.     

常利率下复合泊松-更新风险模型的破产问题

本文研究了常数利率下, 保费收入为复合Poisson 过程, 理赔到达过程为一般更新过程的风险模型. 利用离散化的方法, 获得了该风险模型的破产概率、破产时余额分布及破产前瞬间余额分布的级数展开式, 推广了文[1] 和文[2] 中的相关结果.     

常利率下复合泊松-更新风险模型的破产问题

本文研究了常数利率下,保费收入为复合Poisson过程,理赔到达过程为一般更新过程的风险模型.利用离散化的方法,获得了该风险模型的破产概率、破产时余额分布及破产前瞬间余额分布的级数展开式,推广了文[1]和文[2]中的相关结果.     

资产价值服从跳-扩散过程的风险债券定价

作为对结构化模型和简化模型的改进,本文将结构化模型和简化模型两者融合后提出了一种特殊的跳-扩散过程.在假设公司价值服从这一类跳-扩散过程的情况下,建立了公司风险债券价值所满足的方程,并利用鞅方法得到了公司债券的定价公式.     

全稳定Q过程构造的一个等价条件

给出了Q过程构造的等价条件,证明了Q过程的构造等价于一个条件方程组的解,以此方法求出了所有的Q过程、F过程、B过程及BF过程的等价条件。     

A Regularly Preemptive Model and its Approximations

A regularly preemptive model D,MAP/D ₁,D ₂/1 is studied. Priority customers have constant inter-arrival times and constant service times. On the other hand, ordinary customers' arrivals follow a Markovian Arrival Process (MAP) with constant service times. Although this model can be formulated by using the piecewise Markov process, there remain some difficult problems on numerical calculations. In order to solve these problems, a novel approximation model MAP/MR/1 with Markov renewal services is proposed. These two queueing processes become different due to the existence of idle periods. Thus, a MAP/MR/1 queue with a general boundary condition is introduced. It is a model with the exceptional first service in each busy period. In particular, two special models are studied: one is a warm-up queue and the other is a cool-down queue. It can be proved that the waiting time of ordinary customers for the regular preemption model is stochastically smaller than the waiting time of the former model. On the other hand, it is stochastically larger than the waiting time of the latter model.     

The tightness in the ergodic analysis of regenerative queueing processes

The tightness of some queueing stochastic processes is proved and its role in an ergodic analysis is considered. It is proved that the residual service time process in an open Jackson-type network is tight. The same problem is solved for a closed network, where the basic discrete time process is embedded at the service completion epochs. An extention of Kiefer and Wolfowitz's “key” lemma to a nonhomogeneous multiserver queue with an arbitrary initial state is obtained. These results are applied to get the ergodic theorems for the basic regenerative network processes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models

This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.     

Analysis of Data from a Series of Events by a Geometric Process Model

Geometric process was first introduced by Lam.A stochastic process {X_i,i=1,2,...} iscalled a geometric process (GP) if,for some a>0,{a~(i-1)X_i,i=1,2,...} forms a renewal process.In thispaper,the GP is used to analyze the data from a series of events.A nonparametric method is introduced forthe estimation of the three parameters in the GP.The limiting distributions of the three estimators are studied.Through the analysis of some real data sets,the GP model is compared with other three homogeneous andnonhomogeneous Poisson models.It seems that on average the GP model is the best model among these fourmodels in analyzing the data from a series of events.     

单部件可修系统的一个几何过程维修模型

本文研究了单部件、一个修理工组成的可修系统的最优更换问题,假定系统不能修复如新,以系统年龄T为策略,利用几何过程求出了最优的策略T^*,使得系统经长期运行单位时间内期望效益达到最大,并求出了系统经长期运行单位时间内期望效益的显式表达式。在一定条件下证明了T^*的唯一存在性。最后还证明了策略T^*比文献[6]中的策略T^*优。     

Warranty cost analysis: Increasing warranty repair times

In this study, we model the warranty servicing costs under nonrenewing and renewing free repair warranties. We assume nonzero increasing repair times with the warranty cost depending on the length of the repair time. An increasing geometric process is used to model the consecutive repair times. We introduce the generalised alternating renewal process, which is an alternating process with cycles consisting of an item's operational time followed by the corresponding repair time. We derive analytical results for a generalised alternating renewal process with a finite time horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under the nonrenewing free repair warranty and renewing free repair warranty. Properties of the model are demonstrated through a simulation study and through the application to warranty claims data from an automotive manufacturer.     

机会维修策略下的系统可用度分析

机会维修是针对多部件系统提出的一类新的维修策略,主要解决部件间存在经济相关性的问题.利用更新过程理论建立了机会维修策略下的系统模型,并给出了系统瞬态和稳态可用度的求解方法.通过分析比较可知,利用更新过程稳态下的某些特性,可以不必求解更新方程而比较简便地求解系统稳态可用度.     

Random pinning model with finite range correlations: Disorder relevant regime

The purpose of this paper is to show how one can extend some results on disorder relevance obtained for the random pinning model with i.i.d disorder to the model with finite range correlated disorder. In a previous work, the annealed critical curve of the latter model was computed, and equality of quenched and annealed critical points, as well as exponents, was proved under some conditions on the return exponent of the interarrival times. Here we complete this work by looking at the disorder relevant regime, where annealed and quenched critical points differ. All these results show that the Harris criterion, which was proved to be correct in the i.i.d case, remains valid in our setup. We strongly use Markov renewal constructions that were introduced in the solving of the annealed model.