System failures can lead to severe economic losses, often necessitating mission termination when system failure risk becomes critical. Focusing on k-out-of-n : F balanced systems equipped with a multi-mode protective device (PD), this research explores mission abort strategies (MASs). The system comprises m sectors, with each sector containing n uniform components. The PD has four modes: failure, defective, normal operation and not triggered. The system operates under shock conditions. To maintain balance after component failures, the system either deactivates one component in the remaining m-1 sectors or activates a standby component in the same sector. When any sector accumulates k failed and standby components, the system fails. The study employs the Markov process imbedding methodology (MPIM) to derive two key reliability metrics: mission success probability (MSP) and system survivability (SS). Three optimization models are established to achieve the dual objectives of maximizing MSP while minimizing expected costs. Finally, a numerical example of the UAV with a cooling system demonstrates how to determine the optimal reduction factor and MASs yielding minimal expected costs.

ABSTRACT In practical industrial engineering, systems with dependent and competing failure modes, such as aerospace systems and civil engineering structures, are ubiquitous. These systems usually simultaneously experience two failure modes: gradual internal degradation and external shock. The ultimate failure of the system results from the competition between the soft failure processes and the hard failure processes. With the wide application of intelligent management and artificial intelligence systems, this paper particularly focuses on the damage evolution processes of a system with intelligent characteristics, such as the damage self‐healing processes. By combining the cumulative shock model with the shock model to create a mixed shock model, we analyze the evolution processes of internal performance degradation and external shock damage induced by the self‐healing mechanism. We propose a novel system reliability model with dependent and competing failure processes that has practical significance for improving the accuracy of competing failure systems reliability assessments. Finally, to verify the practicability and validity of the model, empirical studies were conducted using examples of the corrosion process and prestressed strength of concrete degradation of reinforcement concrete (RC) pillar pier of sea bridges with pre‐mixed self‐healing capsules.

As two major types of damage, natural degradation and random shocks usually emerge in a system simultaneously and may exhibit some complex dependencies. An interesting and not negligible phenomenon is that systems at different health levels have differing resistance to these two damage processes. This study presents a multistate model to capture the main characteristics of a system with dependencies of both damage processes on the current damage level. In the case of multistage damage-level dependencies, the proposed model can be seen as an extension of existing multistage models, i.e., a composite model of n-stage shock process and m-stage degradation. The reliability and probability of system states at time t are derived under the framework of the Markov renewal process. We also use a Monte Carlo simulation to mimic the system lifespan and improve the multistate model. Finally, a study case of microelectromechanical systems is provided to demonstrate the application of the proposed methodology.

A common cause failure occurs when two or more elements fail due to a shared cause. The system with such failure often needs different repairmen and a multi-level maintenance strategy. The paper studies the reliability of k-out-of-n: G repairable systems considering common cause failure and multi-level maintenance strategy. The models with a multi-level maintenance strategy are established by considering the failure of all and partial components due to common cause failure. The reliability indices of the systems, such as availability and the mean time to first failure, are derived. An optimization maintenance model is established by minimizing the cost, and a three-level maintenance strategy is determined. Numerical examples are provided to illustrate the application. The results show that the multi-level maintenance strategy improves the system reliability and reduces the maintenance costs of systems with common cause failure.

In this paper, the Markov renewal process is developed to characterize the system subjected to multiple failure mechanisms. The evolution of the system state is defined as a semi-Markov process whose kernels are derived considering two shock scenarios. One is the mixed shock scenario, combining the extreme shock model and the δ-shock model, while the other is the cumulative shock scenario. Throughout the derivation, the mutual interactions between continuous fatigue degradation and shock are taken into account. Shocks lead to degradation increment and nonlinear fatigue damage accumulation, while the fatigue process intensifies damage due to shocks. Notably, the nonlinear fatigue damage accumulation involves retardation effects. In this study, a reliability model focused on the mutual interaction among failure modes is derived from the kernel of the semi-Markov process. The mean time to failure (MTTF) is also calculated. Moreover, the impacts of the shock thresholds on MTTF are discussed. Finally, two case studies based on real fatigue testing data of steel 350WT and aluminum alloy 2024-T351 are provided to illustrate the implementation and effectiveness of the proposed model.

Cascading failure is a phenomenon that minor disturbances trigger a chain reaction failure of the system, causing the disaster to quickly spread in the system and causing part or all of the system to collapse. Traditional cascading models that based on the assumption that the propagation time of cascading failures can be ignored are inadequate for modeling and analyzing all the practical cascading failure systems. It is necessary to develop a general methodology for the cascading failure systems with cascading failure propagation speed and different load effects. This paper derives new models which extend the load effect mode and consider the propagation speed of cascading failure. In the models, the time of the cascading failure propagation is considered. Three load effect modes are proposed that consider the number of remaining working components, the influence range of the failed parts, and the distance between the failed parts and the unfailed components. Additionally, the reliability of the systems with different types of cascading failures is analyzed, and formulas computing reliability indexes are derived. Numerical examples are provided to demonstrate the application of the proposed methodology.

系统所遭受的冲击和退化损害过程广泛存在着多阶段特征和相互依赖关系,为了更精确建模和分析系统冲击和退化间的依赖性,论文建立了多阶段冲击和退化过程的复合模型,提出了一种更加广义的冲击和退化过程依赖关系,即二者同时对系统损害累积过程产生贡献,进而导致系统阶段的改变,而状态转移又反馈性地影响冲击和退化过程.通过构造马尔可夫更新过程,基于半马尔科夫核,得到此类冲击退化模型的可靠度解析表达.

系统signature是分析系统可靠性的一个强有力的工具.本文研究了多状态系统的动态signature.Signature概念被拓展到多维的情形,并将其应用于两状态元件下多态关联系统的分析,得到系统在每一状态下的联合生存函数的表达式,探究了系统在时刻的动态signature,为处于工作状态的多状态系统在时刻t接受检查,发现其处于l(t)状态并且恰好已发生了q(t)次元件失效,分别给出了两状态元件多态关联系统动态signature及其剩余寿命的表达式.

When a unit should provide reliability at mission time, the mission success probability or failure probability becomes an important constraint of planing inspection policies. From this viewpoint, this paper considers the optimization problems of periodic and sequential inspection policies with mission failure probabilities. In this paper, the mission time is also considered as a renewal point for inspection polices, but the failure cost occurred at mission time is higher than the total cost of inspection and failure detection. We give an upper limit of the failure probability at mission time, i.e., mission failure probability, to minimize the total expected cost of inspection policies. In addition, the extended models of inspection policies for an mission interval, a constant renewal time and the random mission times are given directly.

Reliability of a system may differ greatly when operating under different environments. However, the existing works have either neglected the environment factor in system reliability analysis or considered this factor for binary systems or systems subject to a single environment (parameter). In this paper, we make contributions by modeling a multi‐state system operating under hybrid dynamic environments affected by multiple environmental parameters. Different Markov chains with finite states are used to represent the random system behavior and dynamic environments, leading to an aggregated Markov process that models the overall system behavior. An effective approach based on state partitions and aggregations is suggested for assessing the system reliability indexes, including reliability, availability, multi‐point availability, and environment‐based reliability. A high‐pressure homogenizer system is analyzed to demonstrate the proposed model and show the comparison of the reliability of system under fixed and dynamic environment.

Traditional binary-state systems have only two discrete system states: functional and non-functional. However, many practical facilities have more than two states and should be studied as a multi-state system (MSS). This chapter makes new contributions by modelling and analyzing the reliability and safety of MSSs with dependent component lifetimes. It discusses modelling and analyses of the reliability of dependent MSSs. The copula is used to model the dependent relationships of different components of an MSS. The copula connects a multivariate distribution to its marginal in such a way that it captures the entire dependence structure in the multivariate distribution. The copula selection problem can be split into three stages: get the lifetime data of components and the system; use a statistical method to estimate the parameters of the candidate copulas; and choose the appropriate copula from the candidates. The chapter presents a multi-state model, and the copula model is also applied to address the dependent relationship within the system.

With the advancement of computer and network technologies, Internet-based social networks called social networking services have become popular. Trust is a crucial basis for interactions among parties in social networks. Based on trust scores of direct links between parties, a trust sensitivity analysis can help identify which direct link(s) in a social network contributes the most to a trust relationship between parties who are not directly connected in the network. This paper generalizes the research object from two-state social networks to multistate social networks since the trust grade for people in a real social connection may have multiple levels. We model asymmetric multitrust level and multiparty social network systems and propose a probabilistic method based on multivalued decision diagrams (MDDs) to perform trust sensitivity analysis of social networks. Numerical examples are provided to demonstrate the application of the proposed methodology.

基于适应性教育理念,建立能刻画课程标准整体适应性的定量化模型,在8个民族聚居省、自治区(新疆、甘肃、宁夏、内蒙古、西藏、广西、贵州、四川)及北京市抽取158所学校,以学生、教师等的测试卷、调查问卷、访谈记录为信息源,分析当地义务教育阶段数学课程标准适应性,旨在使民族教育教学现状与国家课程标准要求之间的关系得以量化呈现.结果 显示民族地区整体对义务教育阶段数学课程标准的适应性较低,且差距在初中阶段明显增加.依据以上研究提出国家数学课程标准应有利于民族地区教育的发展和推动民族地区教育进步的建议,只有国家标准设定合理,才有可能实现基础教育的“普及性”.本文提出的研究思路与方法模型对国家课程标准适应性评价研究具有良好的普适性.

动态变化是现代复杂工程系统的典型特征,动态相依系统可靠性理论能更好地揭示系统在工作阶段复杂的状态的性能,动态相依系统成为可靠性研究领域的热点和难点.本文基于随机Copula模型研究了可靠性系统在动态相依下的可靠性,介绍了随机Copula模型,基于极大似然理论的参数估计方法,给出了基于随机Copula模型的串联与并联系统在动态相依下的可靠度计算方法,并对独立系统、静态相依系统及动态相依系统的可靠度进行了比较分析,最后给出了数值算例.仿真算例的结果,验证了本文方法的可行性和有效性.

System signature shows powerful features such as system reliability analysis, system design and system life comparison. The difficulty of signature calculation increases exponentially with the system architecture being more complex and the increase of the component number. For systems with sequential failure effect, we propose a novel approach to compute the signature. A concept called vector for number of modular failure orderings is defined and the modular decomposition signature method is proposed based on the vector. It is efficient for the signature computation of the systems with a large number of components. As applications of the method, the signature formulas of modular parallel systems, series systems and standby systems are investigated. The signature results are more concise compared with the previous methods. Numerical examples and applications are provided to demonstrate the proposed methodology.

北京市是全国第一批承办内地高中班(校)的城市,也是目前内地班办学规模最大的城市,研究北京市内地高中班(以下简称内高班)学生的数学学业成就的影响因素对提高内高班数学课程教学质量具有重要意义.本文通过对调查问卷、测试卷结果进行统计分析,展现了北京市内高班学生数学学习的整体情况,其中,学习状态是影响内高班学生学业成绩的核心问题.据此提出建议,运用启发式教学来提高学生独立思考的能力,关注学生的心理建设,以及培养学生养成良好学习习惯,应是今后内高班教学改革和质量提升的重点方向.

A safety‐critical system (SCS) is a system whose failure could result in a certain serious consequence, such as loss of life and significant damage to property or environment. Examples of SCSs abound in real‐world applications, such as medical instruments, emergency shutdown systems, and fire/gas detection systems. An SCS can assume 1 of 3 states: working, safe failure, and dangerous (or unsafe) failure. To analyze reliability and safety of SCSs accurately, we build multi‐state models of an SCS and its constituent units. The dependent relationships (nonlinear correlation) of different parts within a safety‐critical unit as well as across the units are modeled using the Copula method. Formulas computing reliability and safety indexes of a safety‐critical unit and of safety‐critical series or parallel systems are derived. Numerical examples are provided to demonstrate the application of the proposed methodology.

本文对6957名内地初中班和高中班学生进行了调查问卷,从学习习惯、学习动力、学业倾向三方面考察内地班学生的理科学习态度.通过统计分析发现,内地班学生的学习动力积极向上,但随着年级的升高在下降;内地班学生的学业倾向和学习习惯还有待进一步引导.应积极开展教学方式的新变革,加强内地班学生理科阅读能力的培养.

Hardware-software co-design systems abound in diverse modern application areas such as automobile control, telecommunications, big data processing, and cloud computing. Existing works on reliability modeling of the co-design systems have mostly assumed that hardware and software subsystems behave independently of each other. However, these two subsystems may have significant interactions in practice. In this paper, an analytical approach based on paths and integrals is proposed to analyze reliability of nonrepairable hardware-software co-design systems considering interactions between hardware and software during the system performance degradation and failure process. The proposed approach is verified using the Markov-based method. As demonstrated by case studies on systems without and with warm standby sparing, the proposed approach is applicable to arbitrary types of time-to-failure or degradation distributions. Effects of different transition and fault detection/recovery parameters on system performance are also investigated through examples.