A Novel Dmey Wavelet Charts for Controlling and Monitoring the Average and Variance of Quality Characteristics

Abstract

Shewhart charts for quality control of the average and variance of quality characteristics and their monitoring can be affected by data noise. This article proposes the creation of novel charts based on wavelet analysis, specifically the Dmey wavelet, to handle data noise. The discrete wavelet transformation of the Dmey wavelet, which divides the data into two halves, is the foundation of the suggested charts. In contrast, the detail coefficients are proportional to the variance of the observations or the differences between the observations. Through them, the D chart is constructed, which corresponds to the Shewhart chart for the variance. The approximation coefficients are proportional to the average of the observations, and through them the A chart is constructed, which corresponds to the Shewhart chart for the average. Both simulated data and actual data about the weights of infants at Valia Hospital in Erbil were utilized to illustrate the effectiveness of the suggested charts and compare them with Shewhart charts. According to the simulation results, the weights of the infants at Valia Hospital were under control, the suggested charts were effective at treating noise, and were more responsive to even small changes in the Shewhart charts’ quality attributes.