Probabilidade do alarme falso no gráfico de controle EWMA para o monitoramento de processo autocorrelacionado

• Ano de defesa: 2012
• Autor(a) principal: Rosa, Lidiane Maria Ferraz
• Orientador(a): Ribeiro Junior, José Ivo
• Banca de defesa: Ferreira, Eric Batista
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Viçosa
• Programa de Pós-Graduação: Mestrado em Estatística Aplicada e Biometria
• Departamento: Estatística Aplicada e Biometria
• País: BR
• Palavras-chave em Português: Controle de qualidade; Desempenho; Auto-regressivo
• Palavras-chave em Inglês: Quality control; Performance, Auto-regressive
• Área do conhecimento CNPq: CNPQ::CIENCIAS AGRARIAS
• Link de acesso: http://locus.ufv.br/handle/123456789/4057

This work aimed to estimate the probability of false alarm caused by the control graph of the exponentially weighted moving average (EWMA) in an autocorrelated process along rational subgroups, using different combinations of the values of the following terms: number of standard deviations (2 ≤ k ≤ 6), weight of the rational subgroup (0.01 ≤ λ ≤ 1) and first order correlation (ρ). To study these values, data of a random variable Y were simulated, under normal distribution with average μ0 = 0 and standard deviation σ0 = 1 for a statistically-controlled process of up to 50 rational subgroups , with individual observations (n = 1). To obtain the values of Y along the 50 rational subgroups, 10 different situations were performed, according to the following first order autocorrelations (ρ = 0; 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9). A total of 1.000 simulations were carried out for each situation. A probability of false alarm (α) decreased with the respective increase of k and λ. On the other hand, this probability increassed with the increase of ρ. Thus, in case the response variable Y is monitored by the EWMA control graph under an autocorrelated process, it is necessary to increase the values of k and λ, as the autocorrelation increases in degree. This requires widening the control limits by adopting values of k above three, so that the false alarm probabilities may be found at low levels, such as values lower than 0.01. To confirm α equal or lower than 0.1, 0.05, or 0.01, according to the first order autocorrealation, different combinations of k and λ are recommended. For ρ ≤ 0.6, λ = 0.01 was recommended , combined with values of k aproximately equal to 2.5 (ρ = 0), 2.7 (ρ = 0.1), 3.0 (ρ = 0.2), 3.3 (ρ = 0.3), 3.7 (ρ = 0.4), 4.4 (ρ = 0.5) and 5.3 (ρ = 0.6).Under these situations, the effect of λ on the decrese of α was small. Thus, one could use any value up to the unit, without the need to change the magnitude of k too much. However, despite the fact that the decrease of λ leads to the increase of k in order to maintain the same false alarm probability, such decision to indicate λ = 0.01 was taken to search for a greater distancing from the Shewhart control graph, which is equal to EWMA for λ = 1. On the other hand, for 0.7 ≤ ρ ≤ 0.9, it was also necessary to increase the values of λ, together with that of k, to obtain a low false alarm probability. In such cases,the following recommendations approximate of λ, were established for k = 6: 0.5 (ρ = 0.7), 0.6 (ρ = 0.8) and 0.95 (ρ = 0.9). Such conclusions agree with those by Costa et al. (2004), who proposed widening the control limits, since autocorrealation provides an estimate of the random variability caused by the process. In this work, widening the control limits occurred due to the imposition of k values higher than three during the design of the EWMA control graph.