Statistical process control for AR(1) or non-Gaussian processes using wavelets coefficients

Abstract

Autocorrelation and non-normality of process characteristic variables are two main difficulties that industrial engineers must face when they should implement control charting techniques. This paper presents new issues regarding the probability distribution of wavelets coefficients. Firstly, we highlight that wavelets coefficients have capacities to strongly decrease autocorrelation degree of original data and are normally-like distributed, especially in the case of Haar wavelet. We used AR(1) model with positive autoregressive parameters to simulate autocorrelated data. Illustrative examples are presented to show wavelets coefficients properties. Secondly, the distributional parameters of wavelets coefficients are derived, it shows that wavelets coefficients reflect an interesting statistical properties for SPC purposes.