Analyzing out-of-control signals of T2 control chart for compositional data using artificial neural networks

Abstract

Various multivariate control charts (CCs) are applied to monitor compositional data (CoDa) processes post an isometric log-ratio (ilr) transformation aimed at assessing in-control or out-of-control (OOC) conditions. While optimal multivariate CCs effectively detect shifts in the overall mean vector, challenges arise when shifts occur in specific variables rather than the overall mean vector. This complexity in signal interpretation using traditional multivariate CCs prompts the need for improved approaches. To address this issue, this study introduces the application of a multilayer perceptron neural network (MLPNN) with back-propagation (BP) learning to interpret OOC signals in Hotelling’s T2 CC for CoDa. The proposed model aids practitioners in identifying atypical variables responsible for OOC situations instead of focusing solely on mean shifts. This capability to detect atypical variables enhances process control strategies, leading to more efficient industrial operations. The model’s performance is assessed through two cases: one involving p=3-part CoDa and another with p=5-part CoDa. Shifts are introduced by altering variable means using various combinations. For comparison, the study also presents results obtained from multivariate data analysis using MLPNN with BP. The results demonstrate that the MLPNN consistently provides more accurate outcomes in the case of CoDa than multivariate data. Applying the ilr transformation improves the MLPNN’s efficacy in accurately interpreting OOC signals within the CoDa domain. An application is reported to interpret the OOC signal during the working hours of machine operators in an industry.