Collaborative Research: Reliability Analysis of Spatial Systems with Local Interactions

该拨款为现代工程系统和业务流程的空间可靠性/风险分析建模框架的开发提供资金，如微/纳米集成电路和大规模物流系统。在空间可靠性系统中，缺陷以其空间位置、形状和大小为特征。由于结构、环境、地理或经济的限制，空间缺陷经常表现出与其邻近缺陷的局部相互作用。交互缺陷簇在空间上随时间演化，并与网络拓扑相互作用，从而影响整个系统的性能。一个具有局部相互作用的空间马尔可夫点过程将被用来描述空间缺陷在固定时间历元和有限时间范围内的分布。将发展用于空间缺陷建模的随机集的依赖理论，以确定可靠性/风险度量的结构特性并构建其可计算边界。研究了缺陷聚类分类算法及其统计特性。模拟/计算程序将在开发的空间可靠性/风险框架的背景下实施，以准确估计空间可靠性措施。模型和方法将使用可用的微集成电路和供应链数据集进行验证。如果成功，这项研究将导致一个新的空间可靠性/风险建模框架，以及一个新的分析和计算工具，可以应用于不同的领域，如纳米/微集成电路，供应链网络，金融/信贷市场和互联网。该项目的成功完成将提供新的空间可靠性/风险模型和方法，并导致空间系统性能的有效和准确的可靠性估计和预测，从而有助于系统/过程设计，提高系统可靠性和降低风险。

This grant provides funding for the development of a modeling framework for spatial reliability/risk analysis of modern engineering systems and business processes, such as micro/nano integrated circuits and large-scale logistics systems. In a spatial reliability system, defects are featured by their spatial location, shape and size. Spatial defects often exhibit local interactions with their neighboring defects, arising from structural, environmental, geographical, or economic constraints. Clusters of interactive defects evolve in space over time and interact with the network topology, and thereby affect the entire system performance. A spatial Markov point process with local interactions will be used to depict the distribution of spatial defects at a fixed time epoch and over a finite time horizon. A dependence theory of random sets, which are used to model spatial defects, will be developed to determine structural properties of reliability/risk measures and to construct their computable bounds. The algorithms for defect cluster classifications and their statistical properties will be investigated. Simulation/computation procedures will be implemented in the context of the developed spatial reliability/risk framework for accurate estimation of spatial reliability measures. The models and methods will be validated using available micro integrated circuits and supply chain data sets. If successful, this research will lead to a new spatial reliability/risk modeling framework as well as a new analytical and computational tools that can be applied in diverse fields such as nano/micro integrated circuits, supply chain networks, financial/credit markets and the Internet. Successful completion of the project will contribute new spatial reliability/risk models and methods, and lead to efficient and accurate reliability estimation and prediction of spatial system performance, which in turn will aid system/process design, improve system reliability and mitigate risk.