在常规故障和临界人为错误条件下具有易损坏储备部件复杂系统的可靠性分析

讨论了一个由两个部件和一个储备部件并且具有临界人为错误和常规故障的随机模型,研究了易损坏部件对系统的影响,故障系统的修复时间是任意分布的.运用泛函分析的方法,通过分析系统主算子的谱特征,给出了系统的可靠性分析的证明.     

具有常规原因和人为错误的两个不同部件平行系统解的性质

讨论了一个由于常规原因和人为错误引起故障的两不同部件并行系统的模型,修复后的故障系统恢复正常.在假设修复率非常数的前提下,运用纯分析的方法给出了两不同部件并行系统解的性质,绕过了该系统解是否存在的问题.     

考虑负载共享的线性连续k-out-of-n:F系统检测策略优化

针对线性连续k-out-of-n:F系统提出定期检测策略,每隔固定周期对系统中各部件状态进行检查并以新部件更换故障部件,若系统发生故障则立即停机并更换故障部件.由于受到负载共享的影响,各工作部件故障率不仅与系统中发生故障的部件数量相关,还与其相邻部件状态有关;为此,引入损伤故障率模型描述部件故障率.基于故障序列图和更新报酬理论建立定期检测策略优化模型以最小化单位时间内的期望成本,确定最优检测周期.最后,通过算例分析验证模型的有效性.     

有延迟修理的两部件串联系统的预防维修策略

研究由两个部件串联组成的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态. 当部件发生故障后进行故障维修, 因为各种原因可能会延迟修理. 部件在每次故障维修后的工作时间形成随机递减的几何过程, 且每次故障后的维修时间形成随机递增的几何过程. 以部件进行预防维修的间隔T和更换前的故障次数N组成的二维策略(T,N)为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析.     

基于可靠性指标的冷贮备可修系统与单部件可修系统关系分析

讨论冷贮备可修系统与单部件可修系统在可靠性指标方面的关系,具有理论价值和实际意义.首先讨论由两部件组成的冷贮备可修系统与单部件可修系统的关系,假设冷贮备可修系统的每个部件的工作寿命都服从一般分布,部件故障后的修理时间服从指数分布,得到在稳态可用度、稳态故障频度、瞬时可用度和瞬时故障频度等指标方面冷贮备可修系统等价于相应的单部件可修系统,推导了若干个定理和推论,给出了相应结论;然后探讨带有冷贮备的多部件串联系统在求解可靠性指标时转化为相应单部件系统的思路:将带有一个冷贮备的多部件串联可修系统等价为一般的串联系统,进一步等价单部件可修系统.为工程上广泛存在的带有冷贮备的多部件系统的可靠性指标计算提供基础及相应公式.     

基于部件等级更新和组重要度的维修策略

针对多部件系统,提出一种基于部件等级更新和组重要度并考虑备件订购的维修策略.首先定义部件等级来确定系统结构,引入生存signature来更新随部件等级更新的系统结构,基于系统可靠度和维修成本建立一个组重要度,并基于当前的系统结构、部件平均故障时间和订购成本设计一个备件订购规则.基于以上,提出适应性故障维修规则和两层面预防维修规则并建立相应的维修模型,使用遗传算法对其优化.最后,以变电站自动化系统为例验证了该策略既可改善系统可靠度,又可降低维修费用,对维修的理论和实践有较大价值.     

由常规故障和临界人为错误引起系统故障的可修复系统动态解的最优控制

研究了由两个运行部件和一个储备部件并且具有常规故障和临界人为错误的随机模型,故障系统的修复时间是任意分布的.先把系统方程的解转化为Volterra 积分方程的形式,证明了系统方程中正解的存在唯一性,再以泛数指标泛函作为衡量系统可控性的标准,研究该系统的最优控制问题.     

修理设备可更换和修理延迟的两类故障状态并联可修系统

考虑两同型部件组成的并联可修系统,每个部件有两类故障状态,部件故障后修理有延迟,且修理设备在修理故障部件的过程中也可能发生故障.假定部件的寿命和修理设备的寿命服从指数分布,部件发生故障后的修理延迟时间、修理时间和修理设备故障后的更换时间均服从一般分布,利用马尔可夫更新过程理论和拉普拉斯变换工具,求得了系统有关的可靠性指标.     

在常规故障和临界人为错误条件下具有易损坏存储部件并联可修系统稳态解中p_0的最优控制

讨论了两个部件并联和一个储备部件,并且具有临界认为错误和故障的可修系统稳态解中p_0的最优控制问题.     

具有使用及维修优先权的三部件冷贮备系统的几何模型

研究了两个不同型部件串联带有一个冷贮备部件的可修型冷贮备系统.假定三个部件的工作时间和维修时间均服从指数分布,对部件2的修理是几何维修而对部件1和3的修理则是修复如新,且部件2比部件3有优先使用权和优先维修权.在这些假设下,运用补充变量法与几何过程理论,得出了系统可靠度,首次故障前平均时间,可用度,瞬时故障频度和修理工空闲的概率等可靠性指标.     

Optimal burn-in for maximizing reliability of repairable non-series systems

Burn-in is a manufacturing process applied to products to eliminate early failures in the factory before the products reach the customers. Various methods have been proposed for determining an optimal burn-in time of a non-repairable system or a repairable series system, assuming that system burn-in improves all components in the system. In this paper, we establish the trade-off between the component reliabilities during system burn-in and develop an optimal burn-in time for repairable non-series systems to maximize reliability. One impediment to expressing the reliability of a non-series system is in that successive failures during system burn-in cannot be described precisely because a failed component is not detected until the whole system fails. For approximating the successive failures of a non-series system during system burn-in, we considered two types of repair: minimal repair at the time of system failure, and repair at the time of component or connection failure. The two types of repair provide bounds on the optimal system burn-in time of non-series systems.     

Extended optimal inspection policies for a system in storage

A system such as missiles and spare parts of aircraft has to perform a normal operation in a severe environment at any time when it is used. However, the system is in storage for a long time from the delivery to the usage and its reliability goes down with time. Thus, a system in storage should be inspected and maintained at periodic times to hold a higher reliability than is prespecified.The following inspection model is considered: A system has three types of units, where unit 1 is maintained, unit 21 is not maintained but is replaced and unit 22 is neither maintained nor replaced. The system is overhauled if its reliability becomes lower than a prespecified probability. The number of replacements and time until overhaul are derived. Using these results, the average cost is obtained and both an optimal inspection time and an optimal replacement time to minimize it are numerically discussed.     

Dynamical behavior in a stage-structured differential-algebraic prey-predator model with discrete time delay and harvesting

A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; Furthermore, local stability of the model system with discrete time delay is studied. It reveals that the discrete time delay has a destabilizing effect in the population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Finally, numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper.     

A Stochastic Analysis of Power Doubling Time for a Subcritical System

The power doubling time for a subcritical system is identified as a stochastic first-passage time problem. Using stochastic point kinetics equations, relations for the mean doubling time and the standard deviation in doubling time are derived. It is shown that the power doubling time for a subcritical system is independent of whether the system is fast or thermal, weakly depends on source strength, and is approximately proportional to the inverse of the reactivity for small negative values of the reactivity.     

可修复系统解的渐近稳定性及最优检测时间

应用C0半群理论,证明了服从一般分布的可修复系统的唯一非负时间依赖解的存在性,并指出该解恰是系统算子的0本征值对应的规范化后的本征向量.然后基于系统静态可用度,给出了系统检测时间和系统静态可用度之间的关系表达式,并分析了系统最优检测时间的存在性.     

Resonance and chaos of micro and nano electro mechanical resonators with time delay feedback

The resonance and chaos of micro (nano) electro mechanical resonators with time delay feedback is concerned in the paper. Based on the experimental results, a lumped single degree-of-freedom (1DOF) model is studied and the effects of time delay displacement and velocity feedback on the system are investigated. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The Melnikov function method is then extended to the two time delay systems, and the analytically required condition for chaos was obtained. Finally, the fourth-order Runge–Kutta method, point-mapping method and spectrum diagram are used to simulate the evolution of the dynamic behavior of the time delay control system. Also, the stability of this time delay control system is studied thoroughly. The results show that time delay feedback is a good method for the control system and that reasonable selection of control system parameters can effectively suppress the vibration level for micro/nano-electro-mechanical resonator systems.     

Optimal inspection policies for a storage system with degradation at periodic tests

A system such as missiles and spare parts of aircrafts is in storage for a long time from transportation to usage. The reliability of a system in storage will go down with time, and so, it should be inspected and maintained at suitable times to hold a high reliability. However, we do not wish to inspect a system too often because each inspection involves a cost and sometimes might degrade some parts of a system during the test interval.This paper considers a periodic inspection policy for a storage system which has to hold a higher reliability. A system has two types of units, where Unit 1 is maintained at each test, however, Unit 2 is degraded with time and at each test. A system is also overhauled, if the reliability becomes lower than a prespecified value q. The reliability of a system is derived, and using this result, the time and the average cost until overhaul is obtained. The optimal policies which maximize the time to overhaul and minimize the average cost are discussed. Finally, numerical examples are given.     

Robustness and exponentiality in redundant repairable systems

A redundant system of independent repairable components with general failure time and repair time distributions is considered. It is shown that the system failure time has an expectation dependent only on the mean failure times and mean repair times of the components and not on their distributions. An intuitive argument is provided, based on the time of onset of the quasi-stationary distribution on the set of working states, to show that for highly reliable systems, the system failure time is exponentially distributed to good approximation. The argument also justifies a simple figure of merit for the quality of the exponential approximation. A key ingredient in the analysis is the system relaxation time, an informal review of which is provided.     

Problems of two-sided boundary control for the wave equation on subcritical intervals in classes of strong generalized solutions

We consider quantum mechanics for which the system time is one of generalized coordinates. The generalized Hamiltonian has an unbounded spectrum, which allows us to introduce a Hermitian time operator. In the proposed formulation of quantum mechanics, a system time and observer’s time are introduced. The Schrödinger equation in the system time either does not hold or holds only approximately. The wave function is assumed to be square integrable with respect to all coordinates, including the system time. In some limit, this formalism reproduces standard quantum mechanics and the corresponding measurement theory.     

有两种故障状态的两部件串联系统的预防维修策略

本文研究的是由两个部件串联组成且有两种故障状态的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态。每个部件发生故障都有两种状态, 可维修和不可维修。当部件的故障为可维修故障时, 修理工对其进行故障维修, 且每次故障维修后的工作时间形成随机递减的几何过程, 每次故障后的维修时间形成随机递增的几何过程。当部件发生N次可维修故障或一次不可维修故障时进行更换。以部件进行预防维修的间隔和更换前的可维修故障次数N组成的二维策略(T, N) 为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析。