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239 – Advances in Statistical Process Control

GLR Charts for Monitoring Multiple Proportions

Sponsor: Quality and Productivity Section
Keywords: Average Run Length, Generalized Likelihood Ratio Chart, Multinomial Distribution, Multiple Categories, Statistical Process Control

Jaeheon Lee

Chung-Ang University

Yiming Peng

Virginia Tech

Marion R. Reynolds Jr.

Virginia Tech

Lei Sun

Virginia Tech

Ning Wang

Virginia Tech

This paper develops a multi-nomial generalized likelihood ratio (GLR) chart for detecting shifts in category probabilities. This chart can be used when all items from the process are inspected continuously and classified into more than two categories. It is shown that the multi-nomial 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 multi-nomial cumulative sum (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 multi-nomial GLR chart provides a very attractive option for detecting shifts in category probabilities.

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