Anomaly Detection for Compositional Data using VSI MEWMA control chart

TL;DR

This paper introduces a new control chart method for monitoring compositional data, utilizing variable sampling intervals and isometric log-ratio transformation, with optimized parameters for improved detection performance.

Contribution

The study develops a Phase II MEWMA control chart with variable sampling intervals tailored for compositional data, including an optimal procedure for parameter selection and performance comparison.

Findings

Proposed chart outperforms standard MEWMA in detection speed.

Optimal control limits and smoothing constants are effectively determined.

The method demonstrates improved Average Time to Signal for various shifts.

Abstract

In recent years, the monitoring of compositional data using control charts has been investigated in the Statistical Process Control field. In this study, we will design a Phase II Multivariate Exponentially Weighted Moving Average (MEWMA) control chart with variable sampling intervals to monitor compositional data based on isometric log-ratio transformation. The Average Time to Signal will be computed based on the Markov chain approach to investigate the performance of proposed chart. We also propose an optimal procedure to obtain the optimal control limit, smoothing constant, and out-of-control Average Time to Signal for different shift sizes and short sampling intervals. The performance of proposed chart in comparison with the standard MEWMA chart for monitoring compositional data is also provided. Finally, we end the paper with a conclusion and some recommendations for future research.