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合并到系统中。两者都需要将部件故障造成的系统损坏与整个系统的故障联系起来。在这里，我们采取了新的方法来解决这些问题。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，对于承受不断增加的载荷的机械系统，例如承受拉伸载荷的纤维复合材料(其中纤维段是部件)，或者对于处于不断增加的“流量”(其中节点是部件)的布线系统，负载分担规则描述了如何将拉伸载荷或流量从故障部件转移/重新分配到工作部件。第二种方法是基于熵/信息形式论，其中系统中的损害/破坏是根据危险函数和反向危险函数来量化的。这些新的方法应该导致更现实的随机或概率模型的一般系统的故障，如所提到的。此外，许多复杂的系统或设备在发生故障之前会随着时间的推移或在不断增加的负载下退化，对这种退化进行建模以预测故障是本项目的重要组成部分。工程降级试验通常可以定期进行，以衡量此类系统的降级过程的程度。所得到的退化数据以及任何实际的故障数据可用于拟合模型，所述模型提供对故障分布的估计或为预测导致系统故障的退化阈值提供基础。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，在这一研究项目中，将开发退化和失效模型，涉及累积损伤概念，并根据已知但可能很少使用的分布，如逆高斯型或Birnbaum-Saunders型分布，得出易于处理的统计推断方法。特别是，模型中将包括协变量或加速变量，并将针对这些一般情况进行经典推理和贝叶斯分析。准确预测设备或一般系统的故障，对于此类系统的维护或更换策略的决策至关重要。这是防止关键系统或设备在关键操作期间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)在更现实的条件和关于系统的假设下开发新的系统故障数学模型，考虑到故障物理因素；(2)开发新的程序，以根据观察到的此类系统的故障或观察到的系统随时间退化的水平，或两者兼而有之地对系统故障做出推断。

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.