Bayesian change point estimation in Poisson-based control charts

Abstract

Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change, a linear trend and a known multiple number of changes in the Poisson rate. The Markov chain Monte Carlo is used to obtain posterior distributions of the change point parameters and corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the well-known c-, Poisson exponentially weighted moving average (EWMA) and Poisson cumulative sum (CUSUM) control charts for different change type scenarios. We also apply the Deviance Information Criterion as a model selection criterion in the Bayesian context, to find the best change point model for a given dataset where there is no prior knowledge about the change type in the process. In comparison with built-in estimators of EWMA and CUSUM charts and ML based estimators, the Bayesian estimator performs reasonably well and remains a strong alternative. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Anomaly Detection in Activities of Daily Living with Linear Drift

“…After detecting an abrupt change, the next step is to estimate the time when the change has happened. Different approaches have been presented for change point estimation: neural networks [55][56][57], fuzzy sets [58-60, 49, 61] and the bayesian approach [62,63], among others. Nevertheless, most existing approaches are based on MLE [64][65][66].…”

Bayesian Multiple Change Point Estimation of Poisson Rates in Control Charts

“…The ML framework has also been applied for di erent change scenarios in correlated Poisson observations [14][15][16] and other attributes [17][18][19][20][21][22]. A Bayesian modeling and computation framework has recently been proposed as an alternative platform for both attribute [3,23] and variable characteristics [24][25][26]. They were found highly exible in incorporation of process complexity (e.g.…”

On the use of multi-agent systems for the monitoring of industrial systems

“…Many researches have used the control charts for process monitoring (Yu-Chang et al 2015;Xia 2015;Ehsan and Sadigh 2014;Vijayababu and Rukmini 2014;Assareh et al 2013). To identify the variables that make an out-ofcontrol in T 2 , a decomposition of the statistic T 2 into independent terms has been suggested by Jing et al (2008).…”