Notre-Dame-de-Mésage, France
Notre-Dame-de-Mésage, France

Time filter

Source Type

Cohen A.,LARIS Systems Engineering Research Laboratory | Tiplica T.,LARIS Systems Engineering Research Laboratory | Kobi A.,LARIS Systems Engineering Research Laboratory
Control Engineering Practice | Year: 2015

In this paper, three new connections between Wavelets analysis and Statistical Quality Control are proposed. Firstly, we show that the Discrete Wavelet Transform, using Haar wavelet, is equivalent to the Xbar-R control scheme. Results concerning the distribution of wavelets coefficients, using others wavelets families, are presented, and then a new control chart, called DeWave, is proposed, in order to monitor the variability of the process. 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. © 2015 Elsevier Ltd.


Cohen A.,LARIS systems engineering research laboratory | Tiplica T.,LARIS systems engineering research laboratory | Kobi A.,LARIS systems engineering research laboratory
Control Engineering Practice | Year: 2016

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 db2 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. © 2016 Elsevier Ltd


Cohen A.,LARIS Systems Engineering Research Laboratory | Tiplica T.,LARIS Systems Engineering Research Laboratory | Kobi A.,LARIS Systems Engineering Research Laboratory
Journal of Physics: Conference Series | Year: 2015

Autocorrelation and non-normality of process characteristic variables are two main difficulties that industrial engineers must face when they should implement control charting techniques. This paper presents new issues regarding the probability distribution of wavelets coefficients. Firstly, we highlight that wavelets coefficients have capacities to strongly decrease autocorrelation degree of original data and are normally-like distributed, especially in the case of Haar wavelet. We used AR(1) model with positive autoregressive parameters to simulate autocorrelated data. Illustrative examples are presented to show wavelets coefficients properties. Secondly, the distributional parameters of wavelets coefficients are derived, it shows that wavelets coefficients reflect an interesting statistical properties for SPC purposes. © Published under licence by IOP Publishing Ltd.


Cohen A.,LARIS Systems Engineering Research Laboratory | Tiplica T.,LARIS Systems Engineering Research Laboratory | Kobi A.,LARIS Systems Engineering Research Laboratory
IFAC-PapersOnLine | Year: 2016

In this paper, we present a result regarding the probability distribution of wavelets coefficients. It extends the Theorem 1 that is presented in our previous work-Cohen, A. et al. Design of experiments and statistical process control using wavelets analysis. Control Engineering Practice. 2015- to include Biorthogonal wavelets. Then, a new control chart, called OWave (Orthogonal Wavelets), is proposed in order to detect mean change in the process. The statistic of the proposed control chart is based on weighted wavelets coefficients. Performance study shows that OWave control chart performs slightly better than the optimal version of EWMA control chart. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Loading LARIS systems engineering research laboratory collaborators
Loading LARIS systems engineering research laboratory collaborators