GLR Control Charts for Monitoring a Proportion

The generalized likelihood ratio (GLR) control charts are studied for monitoring a process proportion of defective or nonconforming items. The type of process change considered is an abrupt sustained increase in the process proportion, which implies deterioration of the process quality. The objectiv...

Full description

Bibliographic Details
Main Author: Huang, Wandi
Other Authors: Statistics
Format: Others
Published: Virginia Tech 2014
Subjects:
Online Access:http://hdl.handle.net/10919/40405
http://scholar.lib.vt.edu/theses/available/etd-12132011-084926/
id ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-40405
record_format oai_dc
spelling ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-404052020-09-26T05:32:44Z GLR Control Charts for Monitoring a Proportion Huang, Wandi Statistics Reynolds, Marion R. Jr. Woodall, William H. Kim, Inyoung Du, Pang Continuous inspection CUSUM chart Moving window Shewhart chart Statistical process control Steady state average number of observations to sig Subgroup The generalized likelihood ratio (GLR) control charts are studied for monitoring a process proportion of defective or nonconforming items. The type of process change considered is an abrupt sustained increase in the process proportion, which implies deterioration of the process quality. The objective is to effectively detect a wide range of shift sizes. For the first part of this research, we assume samples are collected using rational subgrouping with sample size n>1, and the binomial GLR statistic is constructed based on a moving window of past sample statistics that follow a binomial distribution. Steady state performance is evaluated for the binomial GLR chart and the other widely used binomial charts. We find that in terms of the overall performance, the binomial GLR chart is at least as good as the other charts. In addition, since it has only two charting parameters that both can be easily obtained based on the approach we propose, less effort is required to design the binomial GLR chart for practical applications. The second part of this research develops a Bernoulli GLR chart to monitor processes based on the continuous inspection, in which case samples of size n=1 are observed. A constant upper bound is imposed on the estimate of the process shift, preventing the corresponding Bernoulli GLR statistic from being undefined. Performance comparisons between the Bernoulli GLR chart and the other charts show that the Bernoulli GLR chart has better overall performance than its competitors, especially for detecting small shifts. Ph. D. 2014-03-14T21:23:21Z 2014-03-14T21:23:21Z 2011-12-06 2011-12-13 2011-12-19 2011-12-19 Dissertation etd-12132011-084926 http://hdl.handle.net/10919/40405 http://scholar.lib.vt.edu/theses/available/etd-12132011-084926/ Huang_W_D_2011.pdf In Copyright http://rightsstatements.org/vocab/InC/1.0/ application/pdf Virginia Tech
collection NDLTD
format Others
sources NDLTD
topic Continuous inspection
CUSUM chart
Moving window
Shewhart chart
Statistical process control
Steady state average number of observations to sig
Subgroup
spellingShingle Continuous inspection
CUSUM chart
Moving window
Shewhart chart
Statistical process control
Steady state average number of observations to sig
Subgroup
Huang, Wandi
GLR Control Charts for Monitoring a Proportion
description The generalized likelihood ratio (GLR) control charts are studied for monitoring a process proportion of defective or nonconforming items. The type of process change considered is an abrupt sustained increase in the process proportion, which implies deterioration of the process quality. The objective is to effectively detect a wide range of shift sizes. For the first part of this research, we assume samples are collected using rational subgrouping with sample size n>1, and the binomial GLR statistic is constructed based on a moving window of past sample statistics that follow a binomial distribution. Steady state performance is evaluated for the binomial GLR chart and the other widely used binomial charts. We find that in terms of the overall performance, the binomial GLR chart is at least as good as the other charts. In addition, since it has only two charting parameters that both can be easily obtained based on the approach we propose, less effort is required to design the binomial GLR chart for practical applications. The second part of this research develops a Bernoulli GLR chart to monitor processes based on the continuous inspection, in which case samples of size n=1 are observed. A constant upper bound is imposed on the estimate of the process shift, preventing the corresponding Bernoulli GLR statistic from being undefined. Performance comparisons between the Bernoulli GLR chart and the other charts show that the Bernoulli GLR chart has better overall performance than its competitors, especially for detecting small shifts. === Ph. D.
author2 Statistics
author_facet Statistics
Huang, Wandi
author Huang, Wandi
author_sort Huang, Wandi
title GLR Control Charts for Monitoring a Proportion
title_short GLR Control Charts for Monitoring a Proportion
title_full GLR Control Charts for Monitoring a Proportion
title_fullStr GLR Control Charts for Monitoring a Proportion
title_full_unstemmed GLR Control Charts for Monitoring a Proportion
title_sort glr control charts for monitoring a proportion
publisher Virginia Tech
publishDate 2014
url http://hdl.handle.net/10919/40405
http://scholar.lib.vt.edu/theses/available/etd-12132011-084926/
work_keys_str_mv AT huangwandi glrcontrolchartsformonitoringaproportion
_version_ 1719341375040782336