A Phase II EWMA Chart for the Random Effects Model

• Activity Number: 615 - Statistical Process Control
• Type: Contributed
• Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Yuhui Yao* and Subhabrata Chakraborti
• Companies: The University of Alabama and University of Alabama
• Keywords: Statistical process control; Random effects model; Analysis of variance; Phase II monitoring; Parameter estimation; Robustness

Abstract

Statistical process control (SPC) and monitoring techniques are often used in applications where multiple sources of variation are present, as for example in a variance components model. The Shewhart ¯X control charts for these situations have been studied by Roes and Does (1995), Woodall and Thomas (1995) and other researchers, but Montgomery (2009) argued that the Shewhart ¯X control charts are less useful in Phase II and recommended the exponentially weighted moving average (EWMA) chart which is more sensitive to small process mean shifts. We study refinements and adaptations of these charts for the variance components model taking proper account of the effects of parameter estimation while designing and implementing the control charts. In the sequel, we derive and calculate the corrected (adjusted) control limits for Phase II applications. Two types of corrected limits are provided, following the recent literature, one based on the unconditional perspective and the other on the conditional perspective and the exceedance probability criterion (EPC). Tabulations of the charting constants and illustrations with data are provided. An R package is provided to help deployment of the new methodology in practice.