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A Bernoulli GLR chart based on Bayes estimator
Journal of the Korean Data & Information Science Society 2018;29:37-47
Published online January 31, 2018
© 2018 Korean Data and Information Science Society.

Sung Won Han1 · Jaeheon Lee2 · Jongtae Park3

12Department of Applied Statistics, Chung-Ang University
3Department of Digital Information and Statistics, Pyeongtaek University
Correspondence to: Professor, Department of Applied Statistics, Chung-Ang University, Seoul 06974, Korea. E-mail: jaeheon@cau.ac.kr
Received November 10, 2017; Revised December 14, 2017; Accepted December 21, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
It is known that the overall performance of Bernoulli GLR (generalized likelihood ratio) chart is better when we monitor the proportion p of nonconforming items. The GLR chart has the advantage that the value of control parameter does not need to be specified unlike CUSUM or EWMA charts, and it can be estimated from the process data. In the Bernoulli GLR chart proposed in Huang et al. (2013), there is a possibility that the MLE (maximum likelihood estimator) of p becomes 1, which would lead to an undefined Bernoulli GLR statistic. Thus, they put an upper bound on the MLE of p so that the estimate can not be 1. However, this restriction can make the performance of the GLR chart worse. In this paper, we proposed a Bernoulli GLR chart based on Bayes estimator to avoid such a restriction. We compared the performance of the proposed GLR chart based on Bayes estimator with the GLR chart based on the MLE by using ARL (average run length). Simulation results showed that the performance of the GLR chart based on Bayes estimator depends on the parameters of prior distribution, and is generally better than the GLR chart based on the MLE when the actual shift that occurs is not close to the specified upper bound.
Keywords : Average run length, Bayes estimator, Bernoulli distribution, GLR control chart, Maximum likelihood estimator.