A Study of the Robustness of the AEWMA Chart

• Activity Number: 430
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Rong Zheng* and Subha Chakraborti
• Companies: The University of Alabama and The University of Alabama
• Keywords: Nonparametric ; AEWMA ; ARL ; Robustness

Abstract

The in-control average run-length (ICARL) robustness is crucial for the application and the interpretation of any control chart. In this paper, in an extensive simulation study, the ICARL robustness of the well-known adaptive exponentially weighted moving average (AEWMA) chart of Capizzi and Masarotto (2003) is examined with respect to the underlying assumption of normality. The ICARL profiles of the AEWMA chart are calculated for a family of distributions of various shapes, including light-tailed, heavy-tailed, symmetric and skewed distributions. Our results show that the AEWMA chart is quite sensitive to the normality assumption and may not maintain the nominal ICARL well under non-normality. This raises questions about the application of the AEWMA chart in some practical situations. As an alternative, a nonparametric analog of the AEWMA (NPAEWMA) chart is proposed based on average ranks. The NPAEWMA chart shows good ICARL-robustness against non-normality. Performance comparisons are made between the NPAEWMA chart and an available nonparametric EWMA (NEWMA) chart of Li et al. (2010). It is seen that the proposed NPAEWMA has better shift detection properties in some situations. An illustration with some data is provided.