Stochastic Models and Inference for the Reliability of Complex Systems

对复杂系统的故障或可靠性进行建模的重要方面是（i）组件交互的建模和（ii）将有关每个组件的信息纳入系统。 两者都需要将组件故障引起的系统损坏与整个系统的故障联系起来。 在这里，对这些问题采取了新的方法。 第一种方法是基于组件的负载共享系统，其中组件之间的交互由负载共享规则建模。 例如，对于经受增加的负载的机械系统，诸如在拉伸负载下的纤维复合材料，其中纤维段是部件，或者在增加的“业务”下的路由系统，其中节点是部件，负载分担规则描述拉伸负载或业务如何从故障部件转移/重新分布到工作部件。 第二种方法是基于熵/信息的形式主义，在系统中的损害/破坏量化的危险和反向危险函数。 这些新的方法应导致更现实的随机或概率模型，如上述一般系统的故障。 此外，许多复杂的系统或设备在失效前会随着时间的推移或负载的增加而退化，因此对这种退化进行建模以预测失效是该项目的重要组成部分。 工程退化测试通常可以定期进行，以测量这些系统的退化过程的水平。 所得到的退化数据，沿着任何实际的故障数据，可用于拟合模型，该模型提供故障分布的估计或给出用于预测导致系统故障的退化阈值的基础。 类似地，同样的退化建模方法可以用于疾病向医疗或健康环境中有意义的终点的进展。 因此，在本研究项目中，退化和故障模型的开发将涉及累积损伤的概念，并导致基于已知的，但可能很少使用的分布，如逆高斯型或Birnbaum-Saunders型分布的统计推断的易于处理的方法。 特别是，协变量，或加速变量，将包括在模型中，和经典的推理，以及贝叶斯分析，将调查这些一般cases.Accurate预测的故障件的设备或一般系统是必不可少的决策有关的维护或更换政策，这样的系统。 这是防止关键操作期间关键系统或设备发生灾难性故障的一个特别重要的因素。 本研究项目的总体目标是通过以下方式解决上述问题：（1）在更现实的条件下开发新的系统故障数学模型，并对系统进行假设，同时考虑到故障物理因素，以及（2）开发新的程序，根据观察到的此类系统故障或观察到的系统随时间推移的退化水平对系统故障进行推断，或两者

Important aspects of modeling the failure or reliability of complex systems are (i) the modeling of the component interactions and (ii) incorporating information about each component into the system. Both are needed to relate the system damage caused by component failure to the failure of the entire system. Here, new approaches to these problems are taken. The first approach is based on load-sharing systems of components, where the interactions among components are modeled by load-sharing rules. For examples, for a mechanical system undergoing an increasing load, such as a fibrous composite material under tensile loading where fiber segments are the components, or a routing system under increasing "traffic" where the nodes are components, the load-sharing rule describes how the tensile load or traffic is transferred/redistributed from failed components to working components. The second approach is based on an entropy/information formalism where damage/destruction in the system is quantified in terms of hazard and reverse hazard functions. These new approaches should lead to more realistic stochastic or probabilistic models for the failure of general systems such as those mentioned. In addition, many complex systems, or pieces of equipment, degrade over time or under increasing load before they fail, and modeling such degradation for prediction of failure is an important part of this project. Engineering degradation tests can often be performed at regular intervals to measure the levels of the degradation processes of such systems. The resulting degradation data, along with any actual failure data, can be used to fit models which provide estimates of the failure distributions or give a basis for prediction of a degradation threshold that causes system failure. Analogously, the same approaches to degradation modeling can be utilized in the progression of a disease toward a meaningful endpoint in medical or health settings. Hence, in this research project, development of models for degradation and failure will be undertaken that involve cumulative damage concepts and result in tractable approaches for statistical inference based on known, but perhaps little-used, distributions, such as inverse Gaussian-type or Birnbaum-Saunders-type distributions. In particular, covariates, or acceleration variables, will be included in the models, and classical inference, as well as Bayesian analysis, will be investigated for these general cases.Accurate prediction of the failure of pieces of equipment or general systems is essential in decision making concerning maintenance or replacement policies for such systems. This is an especially important factor in preventing catastrophic failures of key systems or equipment during critical operations. The overall objective of this research project is to address the above issue by (1) developing new mathematical models for system failure under more realistic conditions and assumptions about the system, taking into account physics-of-failure considerations, and (2) developing new procedures to make inferences about system failure based on either observed failures of such systems or observed levels of the degradation of the system over time, or both.