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Marcelo Azevedo Costahttp://lattes.cnpq.br/0843501351619189Anderson Laécio Galindo TrindadeMagno Silvério CamposLinda Lee Hohttp://lattes.cnpq.br/5310110080398573Víctor Brito Quinino2024-03-13T18:00:41Z2024-03-13T18:00:41Z2023-12-21http://hdl.handle.net/1843/657720000-0002-8007-6202Supplementary run-rules have been used since the 1950s to improve the performance of control charts. In a prior publication, Quinino et al.(QUININO et al., 2023), we have suggested an improvement for a procedure known as Klein’s 2-of-2, a simple and efficient supplementary rule which signals that the process is out-of-control only when two sequential sample averages are observed above the upper control limit (UCL) or below the lower control limit (LCL). The use of this rule results in a substantial reduction of the average run length (ARL) in detecting small process shifts, although this improvement has only been attested when compared to the traditional x-bar control chart, which aims to only monitor a process’s mean. This work proposes to implement Klein’s 2-of-2 for a more complex type of control chart, the x-bar −S2 joint control chart, which aims to monitor both the mean and the variance of a process simultaneously, an important application in high quality processes. The use of this rule for the x-bar − S2 control chart results in a substantial reduction of the average run length (ARL) in detecting small process shifts when compared to the traditional x-bar − S2 control chart while also maintaining a high level of applicability due to the 2-of-2 rule’s ease of use in practical environments. The implementation of Klein’s run rule for the x-bar − S2 control chart was done through a 15 state Markov Chain, and its performance was compared to both the basic x-bar −S2 control chart as well as two applications of the exponentially weighted moving average (EWMA), known to have excellent capabilities in detecting small process average shifts at the cost of a more complex control scheme, providing a competitive performance even when compared to the more complex EWMA control chart.Regras suplementares de execução têm sido utilizadas desde a década de 1950 para melhorar o desempenho de cartas de controle. Em uma publicação anterior, Quinino et al.(QUININO et al., 2023), sugerimos uma melhoria para um procedimento conhecido como "Klein's 2-of-2", uma regra suplementar simples e eficiente que sinaliza que o processo está fora de controle apenas quando duas médias sequenciais de amostras são observadas acima do limite de controle superior (UCL) ou abaixo do limite de controle inferior (LCL). O uso dessa regra resulta em uma redução substancial no average run length (ARL) na detecção de pequenos deslocamentos no processo, embora essa melhoria tenha sido atestada apenas em comparação com a carta de controle tradicional x-bar, que visa apenas monitorar a média de um processo. Este trabalho propõe implementar o "Klein's 2-of-2" para um tipo mais complexo de carta de controle, a carta de controle conjunta x-bar −S2, que visa monitorar simultaneamente a média e a variância de um processo, uma aplicação importante em processos de alta qualidade. O uso dessa regra para a carta x-bar −S2 resulta em uma redução substancial no average run length (ARL) na detecção de pequenos deslocamentos no processo, em comparação com a carta de controle tradicional x-bar −S2, mantendo também um alto nível de aplicabilidade devido à facilidade de uso da regra 2-of-2 em ambientes práticos. A implementação da regra de execução de Klein para a carta x-bar −S2 foi realizada por meio de uma Cadeia de Markov de 15 estados, e seu desempenho foi comparado tanto com a carta de controle básica x-bar −S2 quanto com duas aplicações da média móvel ponderada exponencialmente (EWMA), conhecida por ter excelentes capacidades na detecção de pequenos deslocamentos médios do processo, ao custo de um esquema de controle mais complexo, proporcionando um desempenho competitivo mesmo em comparação com a carta de controle EWMA mais complexa.CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em Engenharia de ProduçãoUFMGBrasilENG - DEPARTAMENTO DE ENGENHARIA PRODUÇÃOEngenharia de produçãoEngenharia de controleEstatística industrial - MetodologiaControle estatístico do processoCartas, diagramas etc.Processo estocásticoMarkov, Processos deControl chartsRun rulesARLMarkov chainA control chart for the joint monitoring of mean and variance with Klein's supplementary ruleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALDissertação de mestrado- Víctor Brito Quinino.pdfDissertação de mestrado- Víctor Brito Quinino.pdfapplication/pdf29824749https://repositorio.ufmg.br/bitstream/1843/65772/1/Disserta%c3%a7%c3%a3o%20de%20mestrado-%20V%c3%adctor%20Brito%20Quinino.pdfe572000682546c089388c941a6b144d5MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/65772/2/license.txtcda590c95a0b51b4d15f60c9642ca272MD521843/657722024-03-13 15:00:41.874oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2024-03-13T18:00:41Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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