Construction of the Daubechies Wavelet Chart for Quality Control of the Single Value

Abstract

In this paper, it was proposed to create a new quality control chart for the single value of the Daubechies wavelet to address the problem of data contamination before creating the single value chart and comparing it with the classical Shewhart single value chart. The proposed charts are an application of wavelet shrinkage and a universal threshold estimation method with a soft threshold rule to address the contamination problem and de-noise data to obtain a more efficient chart in controlling the single value and increasing the sensitivity of the chart in detecting minor changes that may occur in the production process. Accordingly, a single chart for the Daubechies wavelet with orders (1, 2, and 3) was proposed and applied to randomly generated data (simulated) for several cases, then real data and some efficiency indicators of the proposed charts were calculated and compared with the classical chart based on the MATLAB program. The paper results showed that all proposed charts were better than the classical chart for single values for all simulation cases and real data.

Keywords

• shewhart control chart for individual values
• wavelets
• shrinkage
• daubechies wavelet. universal thresholding