GLR Charts for Monitoring Multiple Proportions

• Activity Number: 239
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Jaeheon Lee*+ and Ning Wang and Yiming Peng and Lei Sun and Marion R. Reynolds, Jr.
• Companies: Chung-Ang University and Virginia Tech and Virginia Tech and Virginia Tech and Virginia Tech
• Keywords: Average Run Length ; Generalized Likelihood Ratio Chart ; Multinomial Distribution ; Multiple Categories ; Statistical Process Control

Abstract

This paper develops a multinomial generalized likelihood ratio (GLR) chart for detecting shifts in category probabilities. This chart can be used when all items from the process are inspected and classified into more than two categories. It is shown that the multinomial GLR chart has a very significant advantage relative to some other charts when the direction of the out-of-control shift in the parameter vector can not be specified. Some charts such as the multinomial cumulative (CUSUM) chart give a good performance when the shifts in parameters can be specified, but give a very poor performance when the shifts are not in anticipated directions or the shift direction is unknown. Because there may not be too many applications with multiple categories where the shifts in parameters can be specified or there is only one specific direction of interest, the multinomial GLR chart provides a ve