Economic design of and R charts under Weibull shock models
Main Author: | |
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Publication Date: | 2013 |
Other Authors: | |
Format: | Article |
Language: | eng |
Source: | Repositório Institucional da UNESP |
Download full: | http://dx.doi.org/10.1080/03610926.2012.748914 http://hdl.handle.net/11449/219941 |
Summary: | This article considers the problem of a continuous production process, whose mean and variance are simultaneously monitored by and R control charts, respectively. The product variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as, tool wear-out, overheating, or vibration). One changes the process mean and the other the process variance. The occurrence of one kind of the assignable causes does not preclude the occurrence of the other kind. The occurrence times of the assignable causes are described by Weibull distributions having increasing failure rates. A cost model is developed for determining the economic design parameters. A non uniform decreasing sampling interval scheme is adopted to incorporate the effects of process deterioration. A two-step search procedure is employed to determine the economically optimum design parameters. The relative contribution of this article over the results obtained in Costa (1993) is addressed. This article introduces a few new assumptions and provides some theoretical derivations and results. These results may serve as readily available references for future studies. The article shows through numerical examples that ignoring the true (by assumption) Weibull shock model and incorrectly assuming exponential distributions of times to occurrences of assignable causes (and using constant sampling schemes), results in sizeable cost penalties. A sensitivity analysis of the model with respect to Weibull distribution parameters is performed. © 2013 Copyright Taylor and Francis Group, LLC. |
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Economic design of and R charts under Weibull shock modelsIncreasing hazard rateIntegrated hazard criterionNon uniform sampling intervalOptimum design parametersThis article considers the problem of a continuous production process, whose mean and variance are simultaneously monitored by and R control charts, respectively. The product variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as, tool wear-out, overheating, or vibration). One changes the process mean and the other the process variance. The occurrence of one kind of the assignable causes does not preclude the occurrence of the other kind. The occurrence times of the assignable causes are described by Weibull distributions having increasing failure rates. A cost model is developed for determining the economic design parameters. A non uniform decreasing sampling interval scheme is adopted to incorporate the effects of process deterioration. A two-step search procedure is employed to determine the economically optimum design parameters. The relative contribution of this article over the results obtained in Costa (1993) is addressed. This article introduces a few new assumptions and provides some theoretical derivations and results. These results may serve as readily available references for future studies. The article shows through numerical examples that ignoring the true (by assumption) Weibull shock model and incorrectly assuming exponential distributions of times to occurrences of assignable causes (and using constant sampling schemes), results in sizeable cost penalties. A sensitivity analysis of the model with respect to Weibull distribution parameters is performed. © 2013 Copyright Taylor and Francis Group, LLC.Natural Sciences and Engineering Research Council of CanadaFEG-UNESP, GuaratinguetáFaculty of Administration University of New Brunswick, Fredericton, NB E3B 5A3FEG-UNESP, GuaratinguetáUniversidade Estadual Paulista (UNESP)University of New BrunswickCosta, Antonio F. B. [UNESP]Rahim, M. A.2022-04-28T18:58:34Z2022-04-28T18:58:34Z2013-11-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article3902-3925http://dx.doi.org/10.1080/03610926.2012.748914Communications in Statistics - Theory and Methods, v. 42, n. 21, p. 3902-3925, 2013.0361-09261532-415Xhttp://hdl.handle.net/11449/21994110.1080/03610926.2012.7489142-s2.0-84885572686Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCommunications in Statistics - Theory and Methodsinfo:eu-repo/semantics/openAccess2022-04-28T18:58:34Zoai:repositorio.unesp.br:11449/219941Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-28T18:58:34Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Economic design of and R charts under Weibull shock models |
title |
Economic design of and R charts under Weibull shock models |
spellingShingle |
Economic design of and R charts under Weibull shock models Costa, Antonio F. B. [UNESP] Increasing hazard rate Integrated hazard criterion Non uniform sampling interval Optimum design parameters |
title_short |
Economic design of and R charts under Weibull shock models |
title_full |
Economic design of and R charts under Weibull shock models |
title_fullStr |
Economic design of and R charts under Weibull shock models |
title_full_unstemmed |
Economic design of and R charts under Weibull shock models |
title_sort |
Economic design of and R charts under Weibull shock models |
author |
Costa, Antonio F. B. [UNESP] |
author_facet |
Costa, Antonio F. B. [UNESP] Rahim, M. A. |
author_role |
author |
author2 |
Rahim, M. A. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) University of New Brunswick |
dc.contributor.author.fl_str_mv |
Costa, Antonio F. B. [UNESP] Rahim, M. A. |
dc.subject.por.fl_str_mv |
Increasing hazard rate Integrated hazard criterion Non uniform sampling interval Optimum design parameters |
topic |
Increasing hazard rate Integrated hazard criterion Non uniform sampling interval Optimum design parameters |
description |
This article considers the problem of a continuous production process, whose mean and variance are simultaneously monitored by and R control charts, respectively. The product variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as, tool wear-out, overheating, or vibration). One changes the process mean and the other the process variance. The occurrence of one kind of the assignable causes does not preclude the occurrence of the other kind. The occurrence times of the assignable causes are described by Weibull distributions having increasing failure rates. A cost model is developed for determining the economic design parameters. A non uniform decreasing sampling interval scheme is adopted to incorporate the effects of process deterioration. A two-step search procedure is employed to determine the economically optimum design parameters. The relative contribution of this article over the results obtained in Costa (1993) is addressed. This article introduces a few new assumptions and provides some theoretical derivations and results. These results may serve as readily available references for future studies. The article shows through numerical examples that ignoring the true (by assumption) Weibull shock model and incorrectly assuming exponential distributions of times to occurrences of assignable causes (and using constant sampling schemes), results in sizeable cost penalties. A sensitivity analysis of the model with respect to Weibull distribution parameters is performed. © 2013 Copyright Taylor and Francis Group, LLC. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-11-02 2022-04-28T18:58:34Z 2022-04-28T18:58:34Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1080/03610926.2012.748914 Communications in Statistics - Theory and Methods, v. 42, n. 21, p. 3902-3925, 2013. 0361-0926 1532-415X http://hdl.handle.net/11449/219941 10.1080/03610926.2012.748914 2-s2.0-84885572686 |
url |
http://dx.doi.org/10.1080/03610926.2012.748914 http://hdl.handle.net/11449/219941 |
identifier_str_mv |
Communications in Statistics - Theory and Methods, v. 42, n. 21, p. 3902-3925, 2013. 0361-0926 1532-415X 10.1080/03610926.2012.748914 2-s2.0-84885572686 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Communications in Statistics - Theory and Methods |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
3902-3925 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1797789714616418304 |