Analyzing abnormal pattern of hotelling [formula omitted] control chart for compositional data using artificial neural networks

Abstract

Compositional data (CoDa) has been monitored in statistical process monitoring, where multivariate control charts (CCs) such as Hotelling TC2, MEWMA-CoDa, and MCUSUM-CoDa are commonly used to determine if a process is in-control. However, these charts can encounter problems when there is an out-of-control (OOC) process due to various factors such as shifts in variables, outliers, or trends. To address this issue, a pattern recognition (PR) tool using multilayer feed-forward neural networks (MLFFNN) is proposed to accurately recognize CoDa patterns. In the simulation study, six different models in simplex sample space are used to induce trends and shifts in CoDa, and sufficient samples are generated to evaluate the proposed PR model’s performance. The isometric log-ratio (ilr) transformation is applied to CoDa to convert the data from simplex sample space to real space. The Hotelling TC2 statistic is obtained from the generated values after applying the ilr transformation. TC2 statistic is then standardized for MLFFNN, and a back-propagation learning algorithm is used to accurately fit the PR model. Results show the proposed model accurately identifies the CCs pattern, even during OOC processes. A time budget CoDa is analyzed to demonstrate the proposed model’s effectiveness in recognizing patterns.