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Determinação de Parâmetros das Cartas CUSUM−𝒍𝒏(𝑺 𝟐 ) e EWMA−𝒍𝒏(𝑺 𝟐 ) e Desenvolvimento de Software de Apoio ao Controlo Estatístico do Processo
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Orientador(es)
Resumo(s)
No âmbito do Controlo Estatístico do Processo (SPC), são utilizadas diversas cartas de controlo
para monitorizar tanto a média como a dispersão de um processo produtivo. As cartas de controlo
baseadas nos princípios de Shewhart apresentam sensibilidade reduzida na deteção de
pequenas ou moderadas alterações dos parâmetros do processo, média e dispersão. Para
contornar esta falta de sensibilidade, são utilizadas as cartas CUSUM (Somas Acumuladas) ou
EWMA (Média Móvel Exponencialmente Amortecida), que analisam o processo considerando
toda a informação histórica disponível. A utilização eficaz destas cartas pressupõe a escolha
correta dos seus parâmetros. Nesse sentido, foram desenvolvidas tabelas e ábacos para a
consulta destes parâmetros para as cartas EWMA, CUSUM, EWMA−ln(𝑆
2
) e CUSUM−ln(𝑆
2
),
por Crowder (1989), Gan (1991), Chang e Gan (1994) e Chang e Gan (1995), respetivamente, e
ainda alguns trabalhos inseridos em dissertações de mestrado de alunos da FCT/UNL.
As tabelas e ábacos, embora bastante úteis, apresentam alguns inconvenientes, especialmente
no que concerne a erros de leitura e à diversidade de cenários. Assim, este estudo apresenta
um procedimento baseado nos desenvolvimentos dos autores mencionados anteriormente, em
particular o dos mestrandos da FCT/UNL, que contempla uma gama mais abrangente de
cenários, para estas cartas. O autor realizou simulações para as dimensões de amostra 7,15 e
20, para as cartas EWMA−ln(𝑆
2
) e 10, 15 e 20 para a carta CUSUM−ln(𝑆
2
), completando os
estudos de Cardoso (2016) e Afonso (2012) para a carta CUSUM−ln(𝑆
2
) e de Nogueira (2015)
para a carta EWMA−ln(𝑆
2
). Os parâmetros das cartas EWMA e CUSUM, referentes à média do
processo, foram obtidos por Alves (2009) e Cardoso (2016).
Por fim, desenvolveu-se um software para a obtenção rápida dos parâmetros destas cartas,
assim como para agilizar o controlo estatístico de processos, incluindo parâmetros para as cartas
de Shewhart, nomeadamente para as cartas de controlo de variáveis, 𝑋̅/𝑅, 𝑋̅/𝑆 e 𝑋/𝑀𝑅 contendo
os parâmetros destas para a aplicação na Fase 1 e Fase 2 do SPC.
O trabalho de investigação realizado contempla uma mais-valia importante no âmbito das cartas
de controlo CUSUM e EWMA, em virtude de agregar os desenvolvimentos em anos anteriores
conseguidos com a investigação na FCT/UNL e completá-los com a presente investigação, assim
como o desenvolvimento de um software que agiliza a obtenção dos parâmetros das cartas
CUSUM e EWMA.
Regarding Statistical Process Control (SPC), several control charts are used to monitor both the mean and the dispersion of a productive process. Charts based on the Shewhart principles have reduced sensitivity in detecting small or moderate changes in process parameters, mean and dispersion. To overcome this lack of sensitivity, the CUSUM and EWMA charts are used, which analyze the process considering all available historical information. The effective use of these cards implies the correct choice of their parameters. In this sense, tables and nomograms were developed to query these parameters for the EWMA, CUSUM, EWMA-ln(𝑆 2 ) and CUSUM-ln(𝑆 2 ) charts by Crowder (1989), Gan (1991), Chang and Gan (1994) and Chang and Gan (1995), respectively. Although quite useful, tables and abacuses have some drawbacks, especially with regard to reading errors and the diversity of scenarios. Thus, this study presents a procedure based on the one followed by these authors, which contemplates a wider range of scenarios, for these charts. The author performed simulations for sample sizes 7,15 and 20 for EWMA- ln(𝑆 2 ) and 10, 15 and 20 for CUSUM-ln(𝑆 2 ), completing the studies made in this institution by Cardoso ( 2016) and Afonso (2012) for the CUSUM−ln(𝑆 2 ) chart and Nogueira (2015) for the EWMA−ln(𝑆 2 ) chart. The parameters of the EWMA and CUSUM charts, referring to the mean of the process, were obtained by Alves (2009) and Cardoso (2016). Finally, a software was developed to quickly obtain the parameters of these charts, as well as to streamline statistical process control, including parameters for Shewhart charts, namely 𝑋̅/𝑅, 𝑋̅/𝑆 and 𝑋/𝑀𝑅 containing the parameters of these charts for Phase 1 and Phase 2 application. The research work carried out contemplates an important added value within the CUSUM and EWMA control charts, by aggregating the developments in previous years achieved with the research in the FCT / UNL and completing them with the present investigation, as well as the development of software that makes it easier to obtain the parameters of the CUSUM and EWMA charts.
Regarding Statistical Process Control (SPC), several control charts are used to monitor both the mean and the dispersion of a productive process. Charts based on the Shewhart principles have reduced sensitivity in detecting small or moderate changes in process parameters, mean and dispersion. To overcome this lack of sensitivity, the CUSUM and EWMA charts are used, which analyze the process considering all available historical information. The effective use of these cards implies the correct choice of their parameters. In this sense, tables and nomograms were developed to query these parameters for the EWMA, CUSUM, EWMA-ln(𝑆 2 ) and CUSUM-ln(𝑆 2 ) charts by Crowder (1989), Gan (1991), Chang and Gan (1994) and Chang and Gan (1995), respectively. Although quite useful, tables and abacuses have some drawbacks, especially with regard to reading errors and the diversity of scenarios. Thus, this study presents a procedure based on the one followed by these authors, which contemplates a wider range of scenarios, for these charts. The author performed simulations for sample sizes 7,15 and 20 for EWMA- ln(𝑆 2 ) and 10, 15 and 20 for CUSUM-ln(𝑆 2 ), completing the studies made in this institution by Cardoso ( 2016) and Afonso (2012) for the CUSUM−ln(𝑆 2 ) chart and Nogueira (2015) for the EWMA−ln(𝑆 2 ) chart. The parameters of the EWMA and CUSUM charts, referring to the mean of the process, were obtained by Alves (2009) and Cardoso (2016). Finally, a software was developed to quickly obtain the parameters of these charts, as well as to streamline statistical process control, including parameters for Shewhart charts, namely 𝑋̅/𝑅, 𝑋̅/𝑆 and 𝑋/𝑀𝑅 containing the parameters of these charts for Phase 1 and Phase 2 application. The research work carried out contemplates an important added value within the CUSUM and EWMA control charts, by aggregating the developments in previous years achieved with the research in the FCT / UNL and completing them with the present investigation, as well as the development of software that makes it easier to obtain the parameters of the CUSUM and EWMA charts.
Descrição
Palavras-chave
SPC CUSUM EWMA CUSUM−ln(𝑆 2 ) EWMA−ln(𝑆 2 ) Simulação