Wavelet-Assisted Regression Control Charts for Monitoring Predictions and Residuals

This study proposes a multiresolution wavelet-based framework for improving process monitoring in regression-based quality control systems. The proposed approach integrates the discrete wavelet transform (DWT) with regression control charts by decomposing the fitted-value and residual series into approximation and detail coefficients, thereby enabling the simultaneous monitoring of global process behavior and localized variations. An independent sensitivity analysis compared Daubechies orders db4, db8, db11, db20, and db41 at Decomposition Levels 1 and 2. Among the configurations suitable for the full simulated sample-size range, db11 at Level 1 achieved the highest mean detection probability and was retained for the primary simulation; db41 at Level 1 was retained for the real-data illustration on the basis of a separate development-subset comparison. The performance of the proposed framework was assessed through simulation experiments conducted under different sample sizes, noise levels, and process-shift magnitudes. The evaluation was based on detection probability, false-alarm probability, and conditional average detection delay. The results showed that the wavelet-based charts generally produced narrower control limits, higher detection probabilities, lower false-alarm probabilities, and shorter detection delays than the classical regression control chart, particularly for small process shifts. A real-data application involving the regression modeling of hemoglobin using hematocrit and mean corpuscular volume was also presented. In this application, the wavelet approximation residual chart detected three out-of-control observations, whereas the classical residual chart and the wavelet detail residual chart each detected two. These findings indicate that multiresolution wavelet analysis can enhance the sensitivity of regression-based monitoring schemes and provide a useful statistical framework for detecting global and localized process changes.