An effective approach to detect the source(s) of out-of-control signals in productive processes by vector error correction (VEC) residual and Hotelling’s T2 decomposition techniques

Abstract

One of the biggest challenges in the industrial sector is to simultaneously control quality characteristics. Multivariate control charts (MCC) are an efficient method to detect process variability, although they cannot signal the source responsible for variability to cause target deviation, especially in the presence of serial autocorrelation. Thus, this study proposes an approach to point out the source of variability of the process based on the vector error correction (VEC) residual and Hotelling’s T2 decomposition technique. The Design Research Methodology (DRM) was used to guide this study, and the accuracy and efficiency of the proposed approach were analyzed using simulated and real data from an extrusion machine operation, being: pressure (Pr), heating power (Hp), and temperature (Tp). Each of the monitored variables has 763 observations measured every 10 min of operation. An outlier was incorporated into each of the three variables: Pr - observation 91, Hp - observation 473, and Tp - observation 352. A VEC (3) model was fit and the residuals were plotted on a Hotelling’s T2 chart, which pointed the intentionally incorporated outliers. The Hotelling’s T2 decomposition of observation 91 showed thatT(Pr)2 = 14.4053 > 9.9187, and the variable Pr contributed significantly to the outlier. The variable Tp was identified as the source of variability for outlier 352 (p-value = 0.002). For observation 473, T(Hp)2=11.7202 > 9.9187; that is, Hp contributed significantly to the out-of-control point. Hotelling’s T2 chart was based on the VEC residual accurately identified the outliers, and the Hotelling’s T2 decomposition technique could identify the source of process variability.