Multivariate control charts based on Bayesian state space models

TL;DR

This paper introduces a Bayesian multivariate control charting method for autocorrelated processes, utilizing a local level model and log Bayes' factors to effectively monitor mean, covariance, and distributional changes.

Contribution

It proposes a novel Bayesian multivariate control chart based on local level models and log Bayes' factors, handling autocorrelation and non-normality in process monitoring.

Findings

Effective in detecting shifts in mean and covariance.

Handles autocorrelation and non-normality.

Demonstrated on real industrial and financial data.

Abstract

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.