ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Statistics and Probability
Development of Novel Quality Control Charts for Individual Observations Using Haar and Dmey Wavelet Transforms
Provisionally accepted
- 1University of Mosul, Mosul, Iraq
- 2Akre University, Duhok, Iraq
- 3Salahaddin University, Erbil, Iraq
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These are discrete-wavelet quality control charts that are proposed for tracking individual observations. The Haar wavelets and the discrete Meyer (Dmey) wavelets are used to reduce the Phase I process data into approximation and detail coefficients, which describe both the average process and local variability, i.e., dispersion. Control charts are created for both normalized approximation and detail coefficients so that the mean and variance can be analyzed separately with no intervention from one observation. Performance is assessed by Monte Carlo simulation and areal healthcare practice involving neonatal serum iron levels at Valia Hospital, Erbil, Iraq. In general, the wavelet-based charts achieve tighter control limits and higher sensitivity than the traditional Individuals chart, and the detail-based charts make for excellent monitoring of variability. For example, in a representative simulation setting, the control-limit width D=UCL-LCL is reduced from 6.2974 for the Individuals chart to 3.9867 for the Dmey detail chart (about 36.7% narrower). Similarly, in the real-data application, the Individuals chart yields D=92.0192, whereas the Haar detail chart reduces this width to D=59.4071 (about 35.4% narrower), indicating improved detection sensitivity. These results suggest that the integration of wavelet decomposition within statistical process control will enable detecting both locational and scale changes.
Keywords: Discrete wavelet transform, Dmey wavelet, Haar wavelet, Individual observations, process monitoring, Quality control charts
Received: 10 Dec 2025; Accepted: 11 Feb 2026.
Copyright: © 2026 Abdulqader, Salih and Ali. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Taha Hussein Ali
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