Discrete Wavelet Transformation Coefficients Charts for Quality Control on Multivariate Individual Observations

The multivariable individual observations chart is based only on values of the views, and it does not account for changes that may occur in production. Thus, the researchers proposed producing new charts that could control and monitor equivalence and variance of multivariate individual observations using discrete wavelet transforms of approximation and detail coefficients for Daubechies wavelets across orders to measure production by monitoring the development process. The target line in the approximation and detail coefficients chart was estimated to be an average of the approximation and detail coefficients at the mean of the approximation and detail coefficients curve. In both cases, the upper and lower control limits are the target line added (or subtracted) by three multiplied by the square root of the factor in the variance-covariance matrix between the approximation and detail coefficients. The simulation and real data were used to make the proposed charts in the MATLAB program intended for this purpose. The findings of this study presented the effectiveness of the proposed charts and the possibility of using them to control and monitor the quality of the production process.