Registration‐free monitoring of multimode near‐circular shape profiles

Traditional shape profile monitoring of product geometric features mostly focuses on one type or mode of shapes in the discrete‐part manufacturing. Little attention has been paid to monitoring of multimode shape profiles, where different modes of shapes appear in a sample in the batch production process. Motivated by a real example of a powder material production process, we exploit the statistical process monitoring of multimode near‐circular shape profiles. First, we develop a feature extraction approach that is invariant to shape rotation and thus requires no registration for a mixture of different modes of shape profiles. The extracted feature vectors capture shape features well, based on which different modes of shape profiles are separated into several clusters. This enables us to build a Gaussian mixture model for the multimodality in the feature vector space. In process surveillance, a control chart is constructed based on the likelihood ratio test for detecting shifts in both the proportions and the shape features of multimode near‐circular shape profiles. Numerical simulations and real case studies demonstrate the effectiveness of our proposed chart.