Multilevel spatial randomness approach for monitoring changes in 3D topographic surfaces

The 3D surface topography of finished products is a key characteristic for monitoring the quality of products and manufacturing processes. The topography has unique properties in which the topographic values are spatially autocorrelated with their neighbours and the locations of topographic values randomly change from one surface to another under the in-control process behaviour, making the online detection of local topographic changes challenging. Due to the complex structure of topographic data, the existing monitoring approaches lack the detection of local changes. Therefore, we develop a novel online monitoring approach for detecting local changes in 3D topographic surfaces. We introduce a multilevel surface thresholding algorithm for enhancing the representation of topographic values by slicing the 3D surface topography into cumulative levels in reference to the characteristics of the in-control surfaces. The spatial and random properties of topographic values are quantified at each surface level through the proposed spatial randomness profile. After obtaining the spatial randomness profile, an effective monitoring statistic based on the functional principal component analysis is developed for detecting anomaly surfaces. The proposed approach shows superior performance in identifying a wide range of fault patterns and outperforms the existing approaches in both simulated and real-life topographic data.