Dynamic Models and Decision Making for Complex Reliability Systems

评估系统可靠性或关于维护或替换策略的决策的主要挑战是，许多系统由组件（或子系统）的复杂系统组成，或者可以被视为这些组件（或子系统）的复杂系统，由于组件的交互和依赖关系，这些组件在系统中的行为可能相当复杂。这一挑战要求模型选择将“故障物理”考虑纳入模型，将组件可靠性信息集成到系统可靠性模型中，该模型实际模拟了这些类型系统的审查，并考虑了模型中的不确定性。决策过程的关键是正确的模型选择（模型选择）以及将部件可靠性信息集成到系统可靠性评估中，在许多情况下，从系统数据中获得的部件信息涉及复杂的审查机制。本课题的主要目标是研究动态负荷分担可靠性模型及其决策与模型选择。具体来说，这个项目的目的是：1。提出可靠性系统的动态负载共享模型，该模型考虑了“故障物理”因素以及组件或子系统之间的动态交互和依赖关系；2. 得到了这些负荷共享系统的概率性质，特别是导出了系统的寿命分布；3. 审查这类系统的数据应计制，并为这些负荷分担系统制订统计推断程序，其中也考虑到审查；和4。在可靠性系统的背景下，当有几个相互竞争的模型时，制定决策策略，特别是与模型选择或可能的模型平均相关的决策。系统可靠性评估需要对系统故障进行准确的预测。这对于维护或更换政策的决策也是必不可少的，对于关键系统或设备在关键操作期间试图防止灾难性故障尤其重要。该项目的优点在于动态负载共享可靠性模型将考虑模型组件的交互和依赖关系。这些通用可靠性模型也将用于其他复杂系统，如物理、生物和医学科学。例如，对于负载不断增加的机械系统，（例如在拉伸载荷下的复合材料，其中光纤段是组件，或者在流量不断增加的路由系统，其中节点是组件），负载共享规则描述了负载或流量如何从故障组件转移/重新分配到工作组件，并考虑了“物理故障”。所提出的模型具有综合“故障物理”和“统计可靠性”概念的潜力，以描述对系统的损坏如何导致系统故障。本项目的统计推断方面，包括模型选择和决策部分，将解决与基于这些动态模型的复杂数据的模型参数估计有关的重要问题。这个推理问题在可靠性文献中还没有得到广泛的讨论，因此这个项目有望在这个方向上取得重大进展。研究结果预计将影响工程和其他科学，为系统故障提供新颖和更现实的模型，并为预测故障和做出维护和更换决策提供推理程序。

The major challenge for assessing system reliability or decision-making regarding maintenance or replacement policies is that many systems are composed of, or can be viewed as, complex systems of components (or of subsystems) whose behavior within the system can be quite complicated due to omponent interactions and dependencies. This challenge requires model selection that incorporates "physics-of-failure" considerations into the model, integrates component reliability information into system reliability models that realistically models the censoring for these types of systems, and accounts for uncertainties in the model. Crucial to the decision making process is the proper model choice (model selection) as well as the integration of component reliability information into the system reliability assessment where in many cases the component information obtained from system data involves complicated censoring mechanisms. The major goal of this proposed project is to study dynamic load-sharing reliability models and decision-making with model selection for such models. Specifically, the aims of this project are: 1. to propose dynamic load-sharing models for reliability systems that incorporate "physics-of-failure" considerations and the dynamic interactions and dependencies among components or subsystems; 2. to obtain probabilistic properties of these load-sharing systems, in particular, to derive the system life distribution; 3. to examine data-accrual schemes for such systems and to develop statistical inference procedures for these load-sharing systems that also account for censoring; and 4. to develop decision-making strategies in the context of reliability systems when there are several competing models, leading in particular to decision-making with model selection or, possibly, model-averaging.The assessment of system reliability requires accurate prediction of system failure. This is also essential to decision making regarding maintenance or replacement policies and is especially important for key systems or equipment in attempting to prevent catastrophic failures during critical operations. The merit of this proposed project emanates from the fact that the dynamic load-sharing reliability models will take into account model component interactions and dependencies. These generic reliability models will also be useful for other complex systems, such as in physical, biological, and medical sciences. For example, for a mechanical system under increasing load, (such as a composite under tensile loading where fiber segments are components or a routing system under increasing traffic, where the nodes are components) the load-sharing rule describes how the load or traffic is transferred/redistributed from failed components to working components and takes into consideration the "physics-of-failure." The proposed models have the potential to synthesize "physics-of-failure" and "statistical reliability" concepts to describe how damage to the system contributes to system failure. The statistical inference aspects of this project, including the model selection and the decision-making portion, will address important problems pertaining to the estimation of model parameters based on complex data for these dynamic models. This inference problem has not been dealt with extensively in the reliability literature, hence this project is expected to provide significant advances on this direction. The results of the investigations are expected to impact engineering and other sciences by providing novel and more realistic models for system failure and inference procedures for prediction of failure and for making maintenance and replacement decisions.