Daubechies Wavelet Charts to Control and Monitor Individual Observations

Abstract

Traditional quality control charts, such as the individual observations chart using the moving average, did not provide charts specifically for controlling and monitoring the variation or differences in the produced material. Therefore, the researchers proposed creating new charts for the approximation (low-pass filter) and detail (high-pass filter) coefficients of the Daubechies wavelet for order (N = 2, 3, 4, 5, 6) corresponding to the Shewhart chart for individual observations. Also, the proposed charts are robust to noise data that affects the accuracy of the results of the traditional charts. The proposed charts use Daubechies wavelet analysis based on discrete wavelet transformation. One of the charts highlights approximation coefficients to track individual observations. At the same time, the other focuses on the detailed coefficients to identify the differences between the observations in the material being produced. To create the charts’, simulated data was used as well as real data, specifically from the engineering tests that were done on the strength of the steel that Erbil Steel Factory uses. The results showed that the charts were highly effective not only in terms of accuracy but also in dealing with noisy data. Furthermore, it was proven that they were better than the traditional charts at spotting very small details in the production process. This can make a huge difference in maintaining higher quality.