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...
Main Author: | |
---|---|
Other Authors: | |
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 |