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.
