Nonparametric Threshold Estimation of Autocorrelated Statistics in Multivariate Statistical Process Monitoring

Abstract

Multivariate statistical process monitoring is commonly used to detect abnormal process behavior in real time. Multiple process variables are monitored simultaneously, and alarms are issued when monitoring statistics exceed a predetermined threshold. Traditional approaches use a parametric threshold based on the assumptions of independence and multivariate normality of the process data, which are often violated in complex processes with high sampling frequencies, leading to excessive false alarms. Some approaches for improved threshold selection have been proposed, but they assume independence of the monitoring statistics, which are often autocorrelated. In this paper, we compare the performance of nonparametric estimators for computing thresholds from autocorrelated monitoring statistics through simulation. The false alarm rate and in-control average run length of each estimator under different distributions, sample sizes, and autocorrelation levels and types are found. Estimator performance is found to depend on sample size and the strength of autocorrelation. The class of kernel density estimation (KDE) methods tends to perform better than estimators that use bootstrapping, and the proposed adjusted KDE methods that account for autocorrelation are recommended for general use. A case study to monitor a wastewater treatment facility further illustrates the performance of nonparametric and parametric thresholds when applied to real-world systems.