Quality Control Charts for Multivariate EWMA Daubechies Discrete Wavelet Transformation Coefficients
Abstract
Multivariate exponential weighted moving averages (MEWMA) are used to control several qualitative properties together of production processes. This article proposes the creation of new charts to control and monitor multivariate qualitative property exponential weighted moving averages, as well as variance through wavelet analysis based on the discrete wavelet transform (Daubechies). Wavelet analysis breaks down multivariate data into approximation and detail coefficients, which are used to construct the Exponential Weighted Moving Averages for approximation coefficients (MAEWMA) chart (to control and monitor the average) and the Exponential Weighted Moving Averages for detail coefficients (MDEWMA) chart (to control and monitor the variance). The proposed charts were more efficient than the conventional chart and more sensitive to slight changes, that can occur in the production processes at several values of the tuning parameter and for different sample sizes and numbers of variables through simulation studies and real data.
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