Monitoring Parametric, Nonparametric, and Semiparametric Linear Regression Models Using a Multivariate EWMA Bayesian Control Chart

• Activity Number: 269 - Statistical Process Monitoring Methods
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Chelsea Jones* and D'Arcy Mays and AbdelSalam AbdelSalam
• Companies: Virginia Commonwealth University and Virginia Commonwealth University and Qatar University
• Keywords: Bayesian; mEWMA; P-spline; MRR1; Count data; Squared Error

Abstract

We explore the multivariate exponentially weighted moving average (mEWMA) control chart under a Bayesian approach that allows for monitoring of data with mulitple trackable variables. The Bayesian chart is informed by the squared error loss function and applied to multivariate data whose models are fit using parametric, nonparametric, and semiparametric regression methods. The penalized spline (p-spline) and model robust regression 1 (MRR1) are the respective nonparametic and semiparametric methods of interest and our mehtods of model comparison are the mean squared error (MSE), Akaike information criterion (AIC) and Bayesion information criterion (BIC). The chart's capability to detect out-of-control occurrences is assessed with simulation studies under both a hyper-parameter and sample size sensitivty analyses. We are interested in the use of our methods on count data, and utilize our methods on suicide count data made available by the World Health Organization (WHO) to predict and monitor global suicide rates.