OWave control chart for monitoring the process mean. (September 2016) - Cohen, Achraf; Tiplica, Teodor; Kobi, Abdessamad
Abstract: In this paper a control chart for monitoring the process mean, called OWave (Orthogonal Wavelets), is proposed. The statistic that is plotted in the proposed control chart is based on weighted wavelets coefficients, which are provided through the Discrete Wavelets Transform using Daubechies db 2 wavelets family. The statistical behavior of the wavelets coefficients when the mean shifts are occurring is presented, and the distribution of wavelets coefficients in the case of normality and independence assumptions is provided. The on-line algorithm of implementing the proposed method is also provided. The detection performance is based on simulation studies, and the comparison result shows that OWave control chart performs slightly better than Fixed Sample Size and Sampling Intervals control charts ( X ¯, 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. Abstract : Highlights: A new control chart called OWave (Orthogonal Wavelets) in order to monitor the process mean is proposed. OWave control chart performs slightly better than Fixed Sample Size and Sampling Intervals control charts (X-bar, EWMA, CUSUM). Probability distribution of wavelets coefficients, in the case of discrete wavelets (Orthogonal and Biorthogonal), is derived. The on-line algorithm for implementing the proposed control chart is provided.