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In this work, a two level hierarchical approach was proposed and used to analyze cockle phenomena found in the paper manufacturing process. The hierarchy is general for process that produces 3D data sets. The first level performs as a 3D decomposition (Tucker3) while the second level employs a 2D analysis (PLS) of the loadings supplied by the first level. The analysis showed that the important sections of the paper machine that contributed to cockle were Kraft refiners, etc. These are the locations that are expected to contribute to cockle from process knowledge. A calibration model was then developed. The predictive nature of the model was shown to be satisfactory to predict cockle index for reel data that were not a part of the calibration data. Online monitoring and detection applications are possible with this two-level hierarchical structure. It is necessary to use PARAFAC to detect when to recalibrate because the core is unique and every new decomposition is similar to a projection onto the same core. With respect to the use of two-level hierarchical approach to similar processes, such as fiber spinning or continuous casting. It is believed that the two-level hierarchy may be used successfully, at least for diagnosis. However, it should be carefully assessed if the assumptions made in the present case hold in other cases. Additional research is needed to confirm the two-level hierarchy for other processes.