Using Transcripts for Nonparametric Monitoring of Serial Dependence

2026-05-26

AI Summary

This study addresses the well-known limitation of traditional control charts, whose performance deteriorates significantly when process residuals exhibit serial correlation or violate the independent and identically distributed (i.i.d.) assumption. To overcome this challenge, the paper introduces, for the first time, the use of transcripts and algebraic distance in process monitoring, proposing a nonparametric control chart that requires no distributional assumptions. The method constructs transcript representations based on ordinal patterns and employs algebraic distance to detect changes in the temporal dependence structure of time series data, demonstrating high sensitivity across diverse forms of serial dependence. Extensive simulations and real-world case studies from the chemical industry show that the proposed approach substantially outperforms existing methods in detecting shifts in dependence structure, offering both theoretical novelty and practical utility.

Abstract

Control charts for process monitoring are widely used in practice. Most control charts require the monitored (residuals) process to be serially independent (and to satisfy specified distributional assumptions), whereas undetected dependence (or violations of distributional assumptions) may severely affect the charts' performances. Therefore, (distribution-free) control charts for monitoring serial dependence are of utmost relevance for practice. Recently, various nonparametric control charts have been proposed for this purpose, which are based on ordinal patterns, and which showed an appealing performance in detecting different types of serial dependence. In this research, we further progress in this direction and develop novel nonparametric control charts being based on transcripts and algebraic distances (as derived from ordinal patterns). The performance of the newly proposed control charts is evaluated in a simulation study, and their application in practice is illustrated with a real-world data example from chemical industry.

Problem

• serial dependence
• nonparametric control charts
• process monitoring
• distribution-free

Innovation

• transcripts
• algebraic distances
• nonparametric control charts
• serial dependence
• ordinal patterns