非单调关联系统FTA定量分析的新方法

本文在利用不交化最小割集矩阵求解非单调关联系统ＦＴＡ的ＰＩＳ基础上，进一步提出了利用所救是的不交化最小割集矩阵进行非单调关联系统定量分析的新方法，这种方法简单，直观，尤其适用于带有重复事件的非单调关联系统。     

通用系统模糊可靠度计算模型

对系统组成单元的含义作了新的定义,建立了单元模糊可靠度及其置信区间的估计模型;建立了常见通用系统的模糊可靠度估计模型;通过对单元模糊可靠度的直接估计,利用所建立的估计模型可以快速方便地预测出系统的模糊可靠度.实例分析给出了估计模型的使用方法,并显示了模型的有效性.     

一类不同可靠度部件非单调关联系统的最优设计

本文对航天系统中应用广泛的一类典型的非单调关联系统（ｎ中取ｒ至ｓ系统）进行了可靠性分析,比较了目前对系统进行可靠度计算的几种方法的优劣,详细研究了给定ｒ,ｓ及不同部件可靠度ｐ_ｉ的情况下,使系统效益达到最高的条件ｎ值的最优配置问题,并结合国外某类航天系统工程中的计算机集成系统给出了一个数值例子,并用面向 Ｗｉｎｄｏｗｓ的 ＶＢ６． ０实现了一个图形交互的求解系统最优配置和系统可靠度的软件．     

基于结构元的复模糊数四则运算

运用模糊数的模糊结构元表述理论,引入了区间[-1,1]上单调函数的某些同序单调变换,将复模糊数的加、减、乘、除运算转换为同序单调函数之间的相应运算.解决了以往基于扩张原理运算中的遍历过程带来的极大不便.同时,讨论了模糊结构元线性生成的复模糊数及其运算.     

模糊线性方程的结构元求解方法

基于模糊结构元方法,通过单调函数的自反单调变换全面系统的给出了在实数域和复数域上模糊线性方程求解的具体方法,并讨论了方程解存在的条件.同时,将这种求解方法应用到求解双重模糊线性方程.     

可修不同部位n中取r至s系统的可靠性分析

本文对可修不同部件ｎ中取ｒ至ｓ系统进行了可靠性分析，这是一类典型的非单调关联系统，研究了该系统的工作条件和故障模式，并针对简单情形得到了此类可修系统的工作状态空间，给出了系统可靠度和系统首次故障前的平均时间ＭＴＴＦＦ的Ｌａｐｌａｃｅ变换表达式。     

可修不同部件n中取r至s系统的可靠性分析

本文对可修不同部件ｎ中取ｒ至ｓ系统进行了可靠性分析，这是一类典型的非单调关联系统。研究了该系统的工作条件和故障模式，并针对简单情形得到了此类可修系统的工作状态空间，给出了系统可靠度和系统首次故障前的平均时间ＭＴＴＦＦ的Ｌａｐｌａｃｅ变换表达式。     

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.     

基于模糊随机变量的结构可靠性分析

研究了广义应力和广义强度同时具有模糊性和随机性时的结构可靠度计算问题,基于模糊随机变量和模糊随机事件的理论,建立了结构模糊可靠度的计算模型.最后通过一算例,验证了该方法的有效性和合理性.     

结构模糊可靠性分析方法的泛灰求解

针对现有的基于区间求解结构模糊可靠度方法的缺陷,提出了一种新的求解结构模糊可靠度方法.该方法利用泛灰数描述与结构基本变量概率分布相关的不确定参数,并将这些泛灰数引入到结构模糊可靠度计算中,得出了较为精确的结构可靠度计算结果.数值算例表明,该方法得到的结构可靠度区间更窄,实现了利用较少的信息量得到较精确的可靠度计算结果,相比传统的结构模糊可靠度计算方法能提供更多、更精确的关于结构安全程度的有用信息.     

带模糊参数的系统模糊可靠度分析

含模糊参数系统的可靠性理论研究具有广泛的实际应用背景,但由于模糊数运算的隶属函数表达困难,影响和制约着模糊参数系统的模糊可靠性理论与应用的研究。本文利用模糊数的结构元表示,给出了模糊表达式隶属函数确定的两种方法,进而得到了具有模糊参数的不可修复串联和并联系统模糊可靠度的隶属函数表达式。     

Applying fuzzy GERT with approximate fuzzy arithmetic based on the weakest t-norm operations to evaluate repairable reliability

In general, the fuzzy Graphical Evaluation and Review Technique (GERT) usually evaluates/analyzes variables with interval arithmetic (α-cut arithmetic) operations, especially those with complicated fuzzy systems. Thus the interval arithmetic operations may occur accumulating phenomenon of fuzziness in complicated systems, and the accumulating phenomenon of fuzziness may make decision-maker that cannot effectively evaluate problems/systems under vague environment. In order to overcome the accumulating phenomenon of fuzziness or credibly reduce fuzzy spreads, this study adopts approximate fuzzy arithmetic operations under the weakest t-norm arithmetic operations (T_ω) to evaluate fuzzy reliability models based on fuzzy GERT simulation technology. The approximate fuzzy arithmetic operations employ principle of interval arithmetic under the weakest t-norm arithmetic operations. Therefore, the novel fuzzy arithmetic operations may obtain fitter decision values, which have smaller fuzziness accumulating, under vague environment. In numerical examples the approximate fuzzy arithmetic operations has evidenced that it can successfully calculate results of fuzzy operations as interval arithmetic, and can more effectively reduce fuzzy spreads. In the real fuzzy repairable reliability model the performance also shows that the approximate fuzzy arithmetic operations successfully analyze the reliability problem and obtain more confident fuzzy results.     

模糊重要度分析方法的研究

阐述故障树分析中从精确到模糊的重要分析法,提出了模糊重要度分析的新方法－中值法,它是用模糊故障树分析技术对结构复杂的新型系统进行可靠性、贮存可靠性研究的重要组成部分。同时,本文用两种模糊重度分析方法对一故障树作了重要度分析。     

Modelling redundancy allocation for a fuzzy random parallel-series system

Due to subjective judgment, imprecise human knowledge and perception in capturing statistical data, the real data of lifetimes in many systems are both random and fuzzy in nature. Based on the fuzzy random variables that are used to characterize the lifetimes, this paper studies the redundancy allocation problems to a fuzzy random parallel-series system.Two fuzzy random redundancy allocation models (FR-RAM) are developed through reliability maximization and cost minimization, respectively. Some properties of the FR-RAM are obtained, in which an analytical formula of reliability with convex lifetimes is derived and the sensitivity of the reliability is discussed. To solve the FR-RAMs, we first address the computation of reliability. A random simulation method based on the derived analytical formula is proposed to compute the reliability with convex lifetimes. As for the reliability with nonconvex lifetimes, the technique of fuzzy random simulation together with the discretization method of fuzzy random variable is employed to compute the reliability, and a convergence theorem of the fuzzy random simulation is proved. Subsequently, we integrate the computation approaches of the reliability and genetic algorithm (GA) to search for the approximately optimal redundancy allocation of the models. Finally, some numerical examples are provided to illustrate the feasibility of the solution algorithm and quantify its effectiveness.     

Dynamic fuzzy reliability models of degraded hold-down structures for folded solar array

The hold-down structures are of considerable importance to the launch of solar array. Due to the difficulties in obtaining sufficient load specimen, it is imprecise to construct the stress as random variables. Therefore, dynamic fuzzy reliability models are developed in this paper, which resolve the problems in dealing with the interaction between the fuzzy stress process and the stochastic strength process. Even for a deterministic fuzzy stress process, the influences of material statistical properties on reliability can be affected by the level α of fuzzy stress. Meanwhile, the level α relates to investment in the collection of information about the fuzzy stress on hold-down bar. Hence, the models can be used for the economic analysis and optimal design of hold-down bar. Finally, key fuzzy parameters of stress, which have significant influences on both the reliability behavior and the effects of material statistical properties on reliability, are identified and some suggestions for the reliability enhancement of hold-down bar are provided in this paper.     

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T_ω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show T_ω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply T_ω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.     

具有Fuzzy概率的Fuzzy可靠性问题的求解途径

本文提出了工程实践中常见的清晰事件－Ｆｕｚｚｙ概率的Ｆｕｚｚｙ可靠性分析问题的求解途径，首先讨论了Ｆｕｚｚｙ数的代数运算法则，然后在此基础上将Ｆｕｚｚｙ可靠性求解问题转换为Ｆｕｚｚｙ数的运算问题，从而使这类Ｆｕｚｚｙ可靠性分析问题在理论上得到解决，本文还给出了一个算例。     

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T_ω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show T_ω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply T_ω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.     

A class of linear differential dynamical systems with fuzzy matrices

This paper investigates the first order linear fuzzy differential dynamical systems with fuzzy matrices. We use a complex number representation of the α-level sets of the fuzzy system, and obtain the solution by employing such representation. It is applicable to practical computations and has also some implications for the theory of fuzzy differential equations. We then present some properties of the 2-dimensional dynamical systems and their phase portraits. Some examples are considered to show the richness of the theory and we can clearly see that new behaviors appear. We finally present some conclusions and new directions for further research in the area of fuzzy dynamical systems.     

求解一类模糊线性微分系统的结构元方法

基于模糊结构元方法,研究了由对称模糊结构元线性生成的一般模糊线性微分系统和双重的一般模糊线性微分系统,给出了模糊线性微分系统解存在的充要条件,得到了结构元线性生成的齐次、非齐次以及双重一般模糊线性微分系统求解方法。最后,给出了这类系统的实际应用。