Monitoramento de processo seis sigma por gráficos de controle de Shewhart
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Data
2013-08-02
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Universidade Federal de Viçosa
Resumo
Desenvolvida em 1987 na Motorola, a metodologia Seis Sigma busca, mediante redução na variabilidade dos processos-chave, obter características críticas para a qualidade (CTQs) com probabilidades de defeitos próximas de zero. Tem-se um processo Seis Sigma quando a distância entre o valor-alvo (VN) da CTQ e o limite de especificação mais próximo for igual ou superior a seis desvios-padrão (σ). Na prática, por maior que seja a atenção dispensada ao processo, a média da distribuição de probabilidades da CTQ pode deslocar em até 1,5σ do valor-alvo, que ainda assim o processo será considerado Seis Sigma. Então existe um intervalo de 4,5 a 6σ, no qual o processo pode variar sem que perca o nível de qualidade considerado de classe mundial . Desta forma, neste trabalho, buscou-se estabelecer recomendações para o planejamento de gráficos de controle de Shewhart ̅ e R para o monitoramento de processos Seis Sigma. Para tanto, estabeleceu-se um desempenho de referência no qual se admitiu a probabilidade do alarme falso conjunto igual ou inferior a 0,01; e a probabilidade do alarme verdadeiro conjunto crescendo de acordo com a redução do nível Sigma do processo, passando de 0 em processos 6σ para 0,10 naqueles 5σ, atingindo 0,90 em processos 4,5σ até atingir a unidade para processos 3σ e inferiores. Nesse sentido, investigou-se planejamentos com combinações entre n = 2, 3, 4 e 5 e k = 2,5, 2,6, 2,7, 2,8, 2,9 e 3,0. Identificou-se que o par de gráficos em questão apresentou bom desempenho quando o processo esteve sob efeito somente do deslocamento da média e perdeu desempenho à medida que ocorreu o aumento da variação como única perturbação ou quando as duas anomalias estiveram atuando. Foi possível identificar que o deslocamento da média é o problema mais observado, a ocorrência simultânea das duas anomalias é menos frequente e a presença exclusiva do aumento da variação é rara. Logo, recomendou-se o planejamento com n = 5 e k = 2,9, para o monitoramento de processos Seis Sigma Práticos (isto é, com nível sigma entre 4,5 e 6σ), que apresentou bom desempenho apenas quando o processo esteve principalmente sob efeito do deslocamento da média. Portanto, é provável que o nível de qualidade dos processos caia sem que os gráficos de controle em questão sinalizem a perda da qualidade em função do aumento da variação, com ou sem a presença do deslocamento da média.
Developed at Motorola in 1987 the Six Sigma methodology seeks, by reducing the variability of key-processes, obtain critical to quality characteristics (CTQs) with defect probabilities close to zero. It has a Six Sigma process when the distance between the CTQ s target value (VN) and its nearest specification limit, is equal or greater than six standards-deviations (σ). In practice, despite the big attention being paid to the process, the average of the CTQ s probabilities distribution is able to shift until 1,5σ from the target value which even so, the process will be considered Six Sigma. So there is an interval between 4,5 and 6σ in which the process can vary without losing the quality level considered as world class . Thus, in this study, aimed establishes recommendations for planning the Shewhart control charts ̅ and R for monitoring Six Sigma processes. To do so, it was established a reference performance in which it was assumed the joint probability of false alarm equal to or less than 0.01; and the joint probability of true alarm growing according the reduction of the process Sigma level, from 0 in 6σ processes to 0.10 in those 5σ, reaching 0.90 at 4.5σ processes until reaches the unit for 3σ processes and inferior. Accordingly, it were investigated plannings with combinations between n = 2, 3, 4 and 5 and k = 2.5, 2.6, 2.7, 2.8, 2.9 and 3.0. It was identified that the pair of graphs in question performed well when the process was only under the effect of average displacement and lost performance occurred the increase of the variation as the only disturbance present or when the two anomalies were acting. It was possibly identify that the average displacement is the most observed problem, the simultaneous occurrence of both anomalies is less frequent and exclusive presence of increased variation is rare. Therefore, it was recommended that planning with n = 5 and k = 2.9 for monitoring Six Sigma Practical processes (ie, with sigma level between 4.5 and 6σ), which performed well only when the process was mainly under the effect of the average displacement. However, it is expected a good performance of this planning when the process is mainly under the effect of the average displacement. Thus, it is likely that the processes quality level falls without any signal from the control charts in question to indicate quality loss due to the increase of the variation, with or without the presence of the average displacement.
Developed at Motorola in 1987 the Six Sigma methodology seeks, by reducing the variability of key-processes, obtain critical to quality characteristics (CTQs) with defect probabilities close to zero. It has a Six Sigma process when the distance between the CTQ s target value (VN) and its nearest specification limit, is equal or greater than six standards-deviations (σ). In practice, despite the big attention being paid to the process, the average of the CTQ s probabilities distribution is able to shift until 1,5σ from the target value which even so, the process will be considered Six Sigma. So there is an interval between 4,5 and 6σ in which the process can vary without losing the quality level considered as world class . Thus, in this study, aimed establishes recommendations for planning the Shewhart control charts ̅ and R for monitoring Six Sigma processes. To do so, it was established a reference performance in which it was assumed the joint probability of false alarm equal to or less than 0.01; and the joint probability of true alarm growing according the reduction of the process Sigma level, from 0 in 6σ processes to 0.10 in those 5σ, reaching 0.90 at 4.5σ processes until reaches the unit for 3σ processes and inferior. Accordingly, it were investigated plannings with combinations between n = 2, 3, 4 and 5 and k = 2.5, 2.6, 2.7, 2.8, 2.9 and 3.0. It was identified that the pair of graphs in question performed well when the process was only under the effect of average displacement and lost performance occurred the increase of the variation as the only disturbance present or when the two anomalies were acting. It was possibly identify that the average displacement is the most observed problem, the simultaneous occurrence of both anomalies is less frequent and exclusive presence of increased variation is rare. Therefore, it was recommended that planning with n = 5 and k = 2.9 for monitoring Six Sigma Practical processes (ie, with sigma level between 4.5 and 6σ), which performed well only when the process was mainly under the effect of the average displacement. However, it is expected a good performance of this planning when the process is mainly under the effect of the average displacement. Thus, it is likely that the processes quality level falls without any signal from the control charts in question to indicate quality loss due to the increase of the variation, with or without the presence of the average displacement.
Descrição
Palavras-chave
Qualidade, Alarme falso, Alarme verdadeiro, Quality, False alarm, True alarm
Citação
MARQUES, Caio Augusto Nunes. Monitoring of six sigma process by Shewhart control charts. 2013. 80 f. Dissertação (Mestrado em Estatística Aplicada e Biometria) - Universidade Federal de Viçosa, Viçosa, 2013.