Development of novel quality control charts for individual observations using Haar and Dmey wavelet transforms

Source abstract

Introduction Traditional individual control charts primarily monitor process location and provide limited information regarding dispersion. This study proposes discrete wavelet-based quality control charts using Haar and discrete Meyer (Dmey) wavelets to separately monitor mean and variance through approximation and detail coefficients. Methods Discrete wavelet transform (DWT) is applied to Phase I data to obtain approximation and detail coefficients. Control charts are constructed for normalized coefficients and evaluated against the classical individuals chart. Performance is assessed via Monte Carlo simulation and a real healthcare application involving neonatal serum iron levels. Results The proposed charts produce narrower control limits and improved sensitivity compared with the traditional individuals chart. In simulation, control-limit width decreases from D = 6.2974 (individuals chart) to D = 3.9867 (Dmey detail chart), a reduction of approximately 36.7%. In real data, the individuals chart yields D = 92.0192, while the Haar detail chart reduces it to D = 59.4071 (about 35.4% narrower). Detail-based charts demonstrate superior variance monitoring performance. Discussion Integrating wavelet decomposition within statistical process control enables separate monitoring of location and scale changes, enhancing detection sensitivity for individual-observation processes.