Design of experiments and statistical process control using wavelets analysis

• Discrete Wavelet Transform, using the Haar wavelet, is equivalent to the Xbar-R control scheme.
• New method to estimate change time (fault isolation), based on Continuous Wavelet Transform, is proposed. We show that it is equivalent to the maximum likelihood estimator.
• Discrete Wavelet Transform, using the Haar wavelet, is an equivalent representation of 2k2k factorial Design Of Experiments.
• New control chart, called DeWave, is proposed, in order to monitor the variability of the process.

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.