Wavelet Daubechies Enhanced Average Chart Incorporating Classical Shewhart and Bayesian Techniques

Abstract

This article aims to improve tools in monitoring processes of production by presenting four new control charts based on the wavelet analysis with the Daubechies wavelet. The proposed charts consist of the classical average chart with approximate coefficients, the Bayesian average chart with approximate coefficients, the classical average chart with detailed coefficients and the Bayesian average chart with detailed coefficients. These charts were used on actual data of body temperatures of newborns in Valia Hospital, Erbil, Kurdistan, Iraq. The proposed charts resist noise because low-pass and high-pass filtering is performed in the wavelet transformation to separate smooth trends from noise. The new charts were evaluated against classical Shewhart average and Bayesian average charts using simulations under control and various mean shift situations. Average Run Length and Control Limit Width, as performance measures, were obtained as the new charts show a better performance than traditional average charts for the case of small to medium size shifts in temperature. This improves the ability to supervise the production process, for example, in medicine by tracking newborns’ temperatures at hospitals.