面向维修的机械系统可靠度预测与仿真研究

机电产品在服役期间因零件失效而产生故障,重组维修破坏了原有的系统可靠性模型,因而需要对设备可靠性问题重新进行研究和评价。基于机电系统中零件的失效时间分布密度函数,研究了在重组维护过程中机电系统服役期间零件年龄结构的分布规律,发展了机电系统可靠性数学模型。通过仿真研究,探讨了系统服役期间年龄结构、可靠度和失效率的发展规律,定量地研究了失效时间分布密度函数的参数对系统可靠度的影响。这对于评估机械系统的可靠性和全生命周期的失效率,制定合理的维修策略具有重要意义。     

双参数Rayleigh分布环境因子的经验Bayes估计及应用

本文针对Rayleigh分布位置参数已知的情形,给出了Rayleigh分布环境因子的极大似然估计和经验Bayes估计,并将环境因子的估计结果应用于Rayleigh部件的可靠性评估,给出了该部件可靠度函数与失效率的估计。最后的随机模拟例子表明,经验Bayes估计优于极大似然估计,并且在考虑环境因子的情形下,Rayleigh部件可靠性指标的估计优于未考虑环境因子时的估计。     

联合分布函数蒙特卡罗模拟及结构可靠度分析

针对复杂极限状态方程可靠度计算问题,提出了基于理论联合分布函数以及2 种近似联合分布函数的结构失效概率蒙特卡罗模拟方法,并给出了计算流程图.采用2 个算例证明了所提方法的有效性.结果表明:所提的失效概率模拟方法的计算精度很高,尤其适用于复杂极限状态方程的可靠度计算问题.2 种联合分布函数近似构造方法得到的失效概率精度相当,近似方法与精确方法结果的差异随失效概率的减小而增大,而且随着变量间相关性的增加而增加.当失效概率小于10-3时,近似方法的失效概率误差较大.     

修理工可单重休假的带有一个冷贮备部件的Gaver并联系统

本文研究了修理工可单重休假的带有一个冷贮备部件的Gaver并联可修系统。假定部件的工作时间服从指数分布,修理时间和修理工的休假时间均服从一般连续分布。利用向量Markov过程理论和Laplace变换的方法,求出了系统可靠度的Laplace变换,系统首次故障前平均时间的表达式,系统的稳态可用度和稳态故障频度等可靠性指标。此外,还建立了系统效益模型并通过数值比较分析了各参数对系统效益的影响。     

基于Copula函数的并联结构系统可靠度分析

不完备概率信息条件下变量联合分布函数的确定及其对结构系统可靠度的影响还缺少系统地研究,该文目的在于研究表征变量间相关性的Copula函数对结构系统可靠度的影响规律。首先,简要介绍了变量联合分布函数构造的Copula函数方法。其次,提出了并联系统失效概率计算方法,并推导了相应的计算公式。最后以几种典型Copula函数为例研究了Copula函数类型对结构并联系统可靠度的影响规律。结果表明:表征变量间相关性的Copula函数类型对结构系统可靠度具有明显的影响,不同Copula函数计算的系统失效概率存在明显的差别,这种差别随构件失效概率的减小而增大。当并联系统的失效区域位于Copula函数尾部时,Copula函数的尾部相关性对系统可靠度有明显的影响,计算的失效概率比没有尾部相关性的Copula函数的失效概率大。当组成并联系统的两构件功能函数间正相关时,系统失效概率随相关系数的增大而增加;当构件功能函数间负相关时,系统失效概率随相关系数的增大而减小。此外,无论构件失效概率和变量间相关系数如何变化,Copula函数计算的失效概率都位于系统失效概率的上下限内。     

考虑使用与维修优先权的冷贮备系统可靠性模型分析

针对装备系统中部件关键重要程度不同的情况,以具有使用与维修优先权的多部件冷贮备系统为研究对象,利用适用性较强的phase-type（PH）分布代替以往在可靠性建模中采取的指数分布、Weibull分布等典型分布,统一描述了系统各部件的寿命和维修时间,并建立了通用性更好的系统可靠性模型。在模型解析过程中,采用矩阵解析方法,获得了系统的可靠度函数、稳态可用度以及系统平均开工时间、平均停工时间等工程实践中常用的系统可靠性指标解析表达式,并利用算例验证了模型的适用性,讨论了贮备部件数量对系统可靠性指标的影响。研究结果表明,利用PH分布对具有使用和维修优先权的冷贮备系统进行可靠性解析建模,不仅具有良好的解析特性,而且能够有效地保证模型的适用性,在工程实践中具有良好的应用价值。     

非平稳地震作用下强非线性结构动力可靠度分析

针对结构-地震动双重不确定影响下强非线性结构地震可靠度难以精确求解的问题,基于极值分布理论,提出了一种非平稳地震作用下非线性结构地震可靠度分析的高效数值方法。首先采用随机函数的降维思想对非平稳地震动进行降维模拟,将谱表达方法模拟非平稳地震动时需要的上千个高维随机变量减少到2个基本随机变量,大大减少了概率空间的维数;然后提出了一种改进的伪相关性折减拉丁超立方抽样方法确定积分点,从而对结构非线性地震响应极值分布分数矩进行有效估计,最后采用分数阶矩最大熵原理获得结构非线性地震响应极值分布,实现了小失效概率水平下非线性结构地震可靠度的精确估计。数值算例表明,该方法通过300次的动力分析就能够对结构-地震动双重不确定影响下强非线性结构地震响应的极值分布进行估计,其能够在兼顾效率和计算精度时对小失效概率水平下结构的动力可靠度进行精确计算,与既有方法相比,其计算量仅为现在方法的1/5,该方法能够为结构的地震风险评估提供一种有效途径。     

具有人类失效和关闭准则的三部件系统的可靠性分析

本文讨论了一类具有人类失效和关闭准则的三部件系统的两种可靠性模型。通过利用Markov更新和交替更新理论,我们获得模型Ⅰ和Ⅱ中系统可用度和在(0,t]内系统失效次数的期望值,还得到了模型Ⅱ中系统首次失次数的期望值,和模型Ⅱ中系统首次失效前的时间分布。     

2D C/SiC复合材料的可靠性评价

采用概率论和数理统计方法, 以研究分析2D C/SiC复合材料的弯曲强度分布规律为切入点, 比较了失效概率预测值与实验值, 用可靠度、 风险函数和可靠强度评价了该材料可靠性。通过线性回归分析和拟合优度检验得到正态、 对数正态和三参数Weibull分布模型均可表征其弯曲强度分布规律; 确定了该材料弯曲强度失效概率、 可靠度函数、 风险函数和可靠强度的数学模型中的参数, 可以预测给定强度条件和许用可靠度条件下的多种可靠性指标; 材料弯曲强度均值的三种模型预测值与实测值最大相对误差仅0.07%, 计算得到的失效概率曲线与实验弯曲强度的失效分布均符合很好。      

两不同部件并联可修系统稳态可靠度的最优控制

本文针对修复时间服从任意分布的两不同部件并联可修系统的模型,将系统稳态可靠度的最优控制问题转化为求指标泛函在Banach空间上的极值问题,并通过证明指标泛函在Banach空间中的序列弱紧集上下半弱连续给出了最优控制元的存在性.     

Estimation of exponential component reliability from uncertain life data in series and parallel systems

Estimating reliability of components in series and parallel systems from masking system testing data has been studied. In this paper we take into account a second type of uncertainty: censored lifetime, when system components have constant failure rates. To efficiently estimate failure rates of system components in presence of combined uncertainty, we propose a useful concept for components: equivalent failure and equivalent lifetime. For a component in a system with known status and lifetime, its equivalent failure is defined as its conditional failure probability and its equivalent lifetime is its expectation of lifetime. For various uncertainty scenarios, we derive equivalent failures and test times for individual components in both series and parallel systems. An efficient EM algorithm is formulated to estimate component failure rates. Two numerical examples are presented to illustrate the application of the algorithm.     

Sharp inequalities for quantiles of system lifetime distributions from failure-dependent proportional hazard model

We consider coherent systems with components whose exchangeable lifetime distributions come from the failure-dependent proportional hazard model, i.e., the consecutive failures satisfy the assumptions of the generalized order statistics model. For a fixed system and given failure rate proportion jumps, we provide sharp bounds on the deviations of system lifetime distribution quantiles from the respective quantiles of single component nominal and actual lifetime distributions. The bounds are expressed in the scale units generated by the absolute moments of various orders of the component lifetime centered about the median of its distribution.     

不可"修复如新"的线形相邻n中取连续n-1好系统的可靠性分析

本文对n中取连续n-1好系统存部件的寿命和维修时间均服从指数分布且故障部件不可以“修复如新”的假设下进行可靠性研究。采用补充变量法以及广义马尔可夫过程理论,得到了系统的瞬时可用度、可靠度等可靠性指标的Laplace变换表达式以及系统首次故障前的平均时间,并且以5中取连续4好系统为例说明了已得结论的实用价值。     

Estimation in coherent reliability systems through copulas

The problem of estimating the parameter of a common distribution of components' lifetimes from system's lifetime data is of interest and importance in reliability engineering. The present paper deals with this problem when the common component distribution is exponential with mean μ and the lifetimes of components have an exchangeable joint distribution which is constructed by the help of Archimedean copula. In particular we obtain moment estimator of μ for Clayton and Ali-Mikhail-Haq copulas. We illustrate the findings of the paper for a special class of coherent systems called consecutive k-within-m-out-of-n:F system. A simulation study is performed to investigate the properties of the moment estimator. The method presented in this paper can be applied to all coherent systems.     

Reliability Analysis of Zero‐Failure Data with Poor Information

For costly and dangerous experiments, growing attention has been paid to the problem of the reliability analysis of zero‐failure data, with many new findings in world countries, especially in China. The existing reliability theory relies on the known lifetime distribution, such as the Weibull distribution and the gamma distribution. Thus, it is ineffective if the lifetime probability distribution is unknown. For this end, this article proposes the grey bootstrap method in the information poor theory for the reliability analysis of zero‐failure data under the condition of a known or unknown probability distribution of lifetime. The grey bootstrap method is able to generate many simulated zero‐failure data with the help of few zero‐failure data and to estimate the lifetime probability distribution by means of an empirical failure probability function defined in this article. The experimental investigation presents that the grey bootstrap method is effective in the reliability analysis only with the few zero‐failure data and without any prior information of the lifetime probability distribution. Copyright © 2011 John Wiley & Sons, Ltd.     

Economic design of a circular consecutive--out-of-:F system with -step Markov dependence

A circular consecutive-k-out-of-n:F system consists of n components arranged along a circular path. The system fails if and only if at least k consecutive components in the system fail. The system reliability, the expected system life, and the expected number of failures are obtained under the assumption that the failure rate of a component depends on the number of consecutive failed components that follow it. A procedure to find the optimal k and a simulation procedure to search the near-optimal k are proposed with illustrative numerical examples. An expected cost per unit time is considered as the objective function to be minimized.     

Reliability analysis for a circular consecutive-2-out-of-n:F repairable system with priority in repair

A circular consecutive-2-out-of-n:F repairable system with one repairman is studied in this paper. When there are more than one failed component, priorities are assigned to the failed components. Both the working time and the repair time of each component is assumed to be exponentially distributed. Every component after repair is as good as new. By using the definition of generalized transition probability and the concept of critical component, we derive the state transition probability matrix of the system. Methodologies are then presented for the derivation of system reliability indexes such as availability, rate of occurrence of failure, mean time between failures, reliability, and mean time to first failure.     

A new efficient algorithm for computing the imprecise reliability of monotone systems

Reliability analysis of complex systems by partial information about reliability of components and by different conditions of independence of components may be carried out by means of the imprecise probability theory which provides a unified framework (natural extension, lower and upper previsions) for computing the system reliability. However, the application of imprecise probabilities to reliability analysis meets with a complexity of optimization problems which have to be solved for obtaining the system reliability measures. Therefore, an efficient simplified algorithm to solve and decompose the optimization problems is proposed in the paper. This algorithm allows us to practically implement reliability analysis of monotone systems under partial and heterogeneous information about reliability of components and under conditions of the component independence or the lack of information about independence. A numerical example illustrates the algorithm.     

Estimating system reliability with fully masked data under Brown-Proschan imperfect repair model

This article presents a statistical procedure for estimating the lifetime distribution of a repairable system based on consecutive inter-failure times of the system. The system under consideration is subject to the Brown-Proschan imperfect repair model. The model postulates that at failure the system is repaired to a condition as good as new with probability p, and is otherwise repaired to its condition just prior to failure. The estimation procedure is developed in a parametric framework for incomplete set of data where the repair modes are not recorded. The expectation-maximization principle is employed to handle the incomplete data problem. Under the assumption that the lifetime distribution belongs to the two-parameter Weibull family, we develop a specific algorithm for finding the maximum likelihood estimates of the reliability parameters, the probability of perfect repair (p), as well as the Weibull shape and scale parameters (α, β) The proposed algorithm is applicable to other parametric lifetime distributions with aging property and explicit form of the survival function, by just modifying the maximization step. We derive some lemmas which are essential to the estimation procedure. The lemmas characterize the dependency among consecutive lifetimes. A Monte Carlo study is also performed to show the consistency and good properties of the estimates. Since useful research is available regarding optimal maintenance policies based on the Brown-Proschan model, the estimation results will provide realistic solutions for maintaining real systems.