检验在t0处F是否比G具有更强的NBU性

对NBU－t0元件在t0处的NBU性强弱提出了一个比较方法，并据此比较方法建立了一个基于U-统计量的对NBU性强弱的大子样非参数检验方法，同时对该检验的渐近无偏性及其性质作了探讨，并给出了一个更广泛的检验方法．     

独立元件组成的n中取k系统剩余寿命的年龄性质

研究了独立元件组成的n中取k系统的剩余寿命长度的年龄性质,该系统在时刻t＜0有n-k个元件失效.对于几类寿命分布元件,讨论了元件仅仅独立的情形下,n中取k个系统剩余寿命的特征.     

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.     

一类并联系统的剩余寿命和平均剩余寿命

研究了n个独立但不同分布的元件构成的一类并联系统的剩余寿命和平均剩余寿命,即在t_1时刻有l个元件失效,第k个元件的寿命恰好是t_2(0≤lkn,0≤t_1t_2),系统在t_2时刻仍然工作的条件下并联系统的可靠性函数和平均剩余寿命.     

马尔科夫过程的应用——研究设备元件年龄的概率分布

把设备元件的寿命看作独立同分布的随机变量。若某元件在一个很小的单位长△t 内发生的条件概率近似于故障函数λ(t)。利用λ(t)的表达式求出寿命分布函数F(t)。设N(t)为时间t 以前的更新次数。本文研究元件年龄过程X(t)的极限分布和转移概率。推出了以N(t)和F(t)表示的数学表达式。     

NBU分布类的拟合优度检验

一个寿命分布F称为属于新的比旧的好的分布类(NBU),若: R(x y)≤R(x)R(y) x,y≥0这里R(x)=1-F(x)。若R(x y)≥R(x)R(y),称作旧的比新的好(NWU)。本文讨论可靠性中应用非常广泛的NBU分布类的检验问题,即下列检验问题:原假设H_0:F是NBU的。备选假设H_A:F不是NBU。给出了检验函数。并证明了备选假设是H_A:F是NWU时,检验是无偏的。     

失效单调关联系统中可存活元件的剩余寿命的混合表示

本文中研究的是由$n$个独立同分布元件构成的单调关联系统,当该单调关联系统失效时得到了系统中可存活元件的剩余寿命的可靠性函数的混合表示.基于signature的概念,对两个系统的剩余寿命进行了随机比较.     

依赖于年龄的冲击模型

本文讨论更一般化的冲击模型。时间t时,冲击次数为k的条件下,系统仍未失效的概率为P_k(t),它不仅依赖于冲击次数,还依赖于时间t。从而系统的生存概率为: H(t)=sum from k=0 to ∞ (P{N(t)=K})。本文对一般Poisson冲击过程以及具有独立、平稳、非负增量性的连续磨损过程,证明了H对于P_k(t)的分布类的继承性,即在一些正则条件下,当P_k(t)属于二维 IFR(NBU)时,H属于IFR(NBU),及当P_k(t)对任意t, 对k属于IFRA时,H属于IFRA。最后给出了一些应用。     

寿命分布NBUE性质的一个新刻画及应用

本文介绍绝对连续型NBUE寿命分布的一个新的刻画：一个寿命分布具有NBUE性当且仅当它随机地大于具有相应的平衡分布的随机变量。讨论了此刻画在可靠性与寿命检验中的应用，并建立了严格NBUE性的一个非参数检验方法。     

关于只有一个变点模型的非参数推断

这里 μ(t)为非随机函数,μ′(t)为 μ(t)的导函数,α,θ.为未知常数,0相似文献   

A model to predict the residual life of rolling element bearings given monitored condition information to date

In condition monitoring practice, one of the primary concernsof maintenance managers is how long the item monitored can survivegiven condition information obtained to date. This relates tothe concept of the condition residual time where the survivaltime is not only dependent upon the age of the item monitored,but also upon the condition information obtained. Once sucha probability density function of the condition residual timeis available, a consequencial decision model can be readilyestablished to recommend a ‘best’ maintenance policybased upon all information available to date. This paper reportson a study using the monitored vibration signals to predictthe residual life of a set of rolling element bearings on thebasis of a chosen distribution. A set of complete life dataof six identical bearings along with the history of their monitoredvibration signals is available to us. The data were obtainedfrom a laboratory fatigue experiment which was conducted underan identical condition. We use stochastic filtering to predictthe residual life distribution given the monitored conditionmonitoring history to date. As the life data are available,we can compare them with the prediction. The predicted resultsare satisfactory and provide a basis for further studies. Itshould be pointed out that although the model itself is developedfor the bearings concerned, it can be generalized to modellinggeneral condition-based maintenance decison making providedsimilar conditions are met.     

Modelling condition monitoring intervals: A hybrid of simulation and analytical approaches

This paper reports on a study of modelling condition monitoring intervals. The model is formulated based upon two important concepts. One is the failure delay time concept, which is used to divide the failure process of the item into two periods, namely a normal working period followed by a failure delay time period from a defect being first identified to the actual failure. The other is the conditional residual time concept, which assumes that the residual time also depends on the history condition information obtained. Stochastic filtering theory is used to predict the residual time distribution given all monitored information obtained to date over the failure delay time period. The solution procedure is carried out in two stages. We first propose a static model that is used to determine a fixed condition monitoring interval over the item life. Once the monitored information indicates a possible abnormality of the item concerned, that is the start of the failure delay time, a dynamic approach is employed to determine the next monitoring time at the current monitoring point given that the item is not scheduled for a preventive replacement before that time. This implies that the dynamic model overrides the static model over the failure delay time since more frequent monitoring might be needed to keep the item in close attention before an appropriate replacement is made prior to failure. Two key problems are addressed in the paper. The first is which criterion function we should use in determining the monitoring check interval, and the second is the optimization process for both models, which can be solved neither analytically nor numerically since they depend on two unknown quantities, namely, the available condition information and a decision of the time to replace the item over the failure delay time. For the first problem, we propose five appealingly good criterion functions, and test them using simulations to see which one performs best. The second problem was solved using a hybrid of simulation and analytical solution procedures. We finally present a numerical example to demonstrate the modelling methodology.     

Reversibility and dependence in a U-shaped production line

We deal with a U-shaped production line with multiple machines and a multifunction worker. The worker visits machines in a cyclic fashion and operates an item on each machine. The operation consists of detaching the processed item from the machine, sending it to the next machine, putting the new item on the machine and switching it on. Walking times of the worker and processing and operation times are i.i.d. random variables for each machine. We show that the sum of the firstn cycle times is stochastically the same as that in the reversed system where machines are arranged in the reversed order. We give examples where the distributions of waiting and cycle times depend on the machines, called starting ones, where the worker begins operation at time 0. A sufficient condition is derived under which the limiting expected waiting and cycle times do not depend on the starting machines.     

Equilibrium properties of the M/G/1 queue

Summary Various aspects of the equilibrium M/G/1 queue at large values are studied subject to a condition on the service time distribution closely related to the tail to decrease exponentially fast. A simple case considered is the supplementary variables (age and residual life of the current service period), the distribution of which conditioned upon queue length n is shown to have a limit as n. Similar results hold when conditioning upon large virtual waiting times. More generally, a number of results are given which describe the input and output streams prior to large values e.g. in the sense of weak convergence of the associated point processes and incremental processes. Typically, the behaviour is shown to be that of a different transient M/G/1 queueing model with a certain stochastically larger service time distribution and a larger arrival intensity. The basis of the asymptotic results is a geometrical approximation for the tail of the equilibrium queue length distribution, pointed out here for the GI/G/1 queue as well.     

Likelihood ratio inference for mean residual life of length-biased random variable

In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d. observations of the true distribution, empirical likelihood (EL) procedure is proposed for the inference on mean residual life (MRL) of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio (LR) directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results.     

Life expectancy under random censorship

This paper deals with estimation of life expectancy used in survival analysis and competing risk study under the condition that the data are randomly censored by K independent censoring variables. The estimator constructed is based on a theorem due to Berman [2], and it involves an empirical distribution function which is related to the Kaplan-Meier estimate used in biometry. It is shown that the estimator, considered as a function of age, converges weakly to a Gaussian process. It is found that for the estimator to have finite limiting variance requires the assumption that the censoring variables be stochastically larger than the “survival” random variable under investigation.     

Optimum Discarding in a Bufferless System

This paper considers queueing systems without buffer. The problem is finding an optimum discipline that gives the minimal number of request discards in a given interval or the minimum discard probability. In the case of a single server fed by an arbitrary request input flow, it is proved that the discipline that discards the request having the maximum residual life is optimal. This result is extended to the system with more than one server. For G/G/1/0, it is given a condition under which the discipline that discards the request in service minimizes the discard probability. Also for a G/G/1/0, we state the problem of finding optimum discipline in terms of the discrete age Markov chain. The problem of minimization of one-step discard probability is stated. It is solved for a system with C servers and general point process of new arrivals.     

Reliability bounds on HNBUE life distributions with known first two moments

In this paper, we study upper and lower bounds for the reliability function in harmonic new better than used in expectation (HNBUE) life distribution class with known first two moments. Here we say a life distribution has HNBUE property if the integral harmonic mean value of the residual life in any interval [0,t] is no more than its mean. By a constructive proof, we determine the lower and upper reliability bounds analytically and show that these bounds are all sharp.     

A heuristic for the one-dimensional cutting stock problem with usable leftover

A heuristic algorithm for the one-dimensional cutting stock problem with usable leftover (residual length) is presented. The algorithm consists of two procedures. The first is a linear programming procedure that fulfills the major portion of the item demand. The second is a sequential heuristic procedure that fulfills the remaining portion of the item demand. The algorithm can balance the cost of the consumed bars, the profit from leftovers and the profit from shorter stocks reduction. The computational results show that the algorithm performs better than a recently published algorithm.