Multi-scale diagnosis of spatial point interaction via decomposition of the K function-based T² statistic

Data in the form of spatial point distribution are commonly encountered in manufacturing processes such as nanoparticles in composite materials. By analyzing their distributional characteristics which are often related to product quality, we can monitor and diagnose the fabrication processes. Based on modeling the K function of point patterns using a Gaussian process, this paper proposes diagnosing point patterns through decomposition of the K function-based T² statistic. The decomposition provides a novel way for independently analyzing point interactions at multiple spatial scales, which is particularly useful for fault diagnosis when the process is out of control. Effectiveness of the proposed method has been verified through several simulated examples and real data.