Significance Statement
Modern industrial systems are being more and more complex, and they are often affected by disturbances of the operating conditions, which then can lead to generate faults or assignable/special causes. This research project concerns with data-driven approaches for process monitoring.
We presented three new connections between wavelets analysis and statistical quality control. Firstly, we show that the Discrete Wavelet Transform, using Haar wavelet, is equivalent to the Xbar-R control scheme used to monitor the mean and the variance of processes. Secondly, the equivalence between the Likelihood Ratio and the Continuous Wavelet Transform, in terms of estimating the change time, is presented. Finally, we demonstrate that the Discrete Wavelet Transform is an equivalent representation of factorial Design Of Experiments. In this research work [1-2], the probability distribution of wavelets coefficients using Orthonormal and Biorthogonal compactly supported wavelets (Haar, Daubechies, Symlets, Coiflets, Discrete Meyer, Biorthogonal, Reverse Biorthogonal) is presented.
The knowledge about the probability distribution of wavelets coefficients allows us to understand their behavior and then be able to propose new techniques for statistical process control. Consequently, a new control chart, called DeWave, in order to monitor the variability of the process is proposed. We also proposed the OWave control chart for monitoring the process mean. The statistic that is plotted in the OWave control chart is based on weighted wavelets coefficients, which are provided through the Discrete Wavelets Transform using Daubechies db2 wavelets family. The statistical behavior of the wavelets coefficients when the mean shifts are occurring is presented. The on-line algorithm for implementing the OWave control chart is also provided.
The detection performance shows that OWave control chart performs slightly better than Fixed Sample Size and Sampling Intervals control charts (Xbar, EWMA, CUSUM) in terms of Average Run Length. In addition, illustrative examples of the new control chart are presented, and an application to Tennessee Eastman Process is also proposed.
Reference:
[1] Cohen, A., Tiplica, T., & Kobi, A. (2016). “Design of experiments and statistical process control using wavelets analysis”. Control Engineering Practice, 49, 129-138.
[2] Cohen, A., Tiplica, T., & Kobi, A. (2016). “OWave control chart for monitoring the process mean”. Control Engineering Practice, 54, 223-230.
Journal Reference
Achraf Cohen, Teodor Tiplica, Abdessamad Kobi. Design of experiments and statistical process control using wavelets analysis. Control Engineering Practice, Volume 49, April 2016, Pages 129-138.
L’UNAM, LARIS Systems Engineering Research Laboratory, ISTIA Engineering School, 62 Avenue Notre Dame du Lac 49000 Angers, France
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