Gestão & Produção
Gestão & Produção
Seção Temática: Monitoramento e Controle Estatístico de Processos

An EWMA control chart for the mean of individual streams in multiple stream processes

Bruno Francisco Teixeira Simões; Eugenio Kahn Epprecht

Downloads: 0
Views: 51


Abstract:: In a multiple stream process (MSP) a product is manufactured in a number of streams in parallel. The traditional tool for monitoring MSPs, the group control chart (GCC), does not take into account that typically the value of the quality variable in each stream is the sum of a component common to all streams and an individual component, of the particular stream. This may render the GCC ineffective in detecting shifts in the mean of individual streams. Based on this two-components model, we propose an exponentially weighted moving average (EWMA) GCC to monitor the means of the individual streams components. We optimize its design (minimizing the ARL for given shifts in the mean of a stream) and compare their ARLs with the ones of other existing charts devised for two-components MSPs. For this comparison, we needed to obtain optimal designs of these previous charts too, which were not available in the literature; this is an additional contribution of our work. The ARLs of the charts were obtained by simulation, with a number of runs sufficiently large to ensure precise results. The results show that the proposed chart outperforms the previous ones, becoming thus recommended for the statistical control of MSPs.


Multiple stream processes, Group control chart, Components of variance, Exponentially weighted moving average


Amin, R. W., & Li, K. (2000). The MaxMin EWMA tolerance limits. International Journal of Quality & Reliability Management, 17(1), 27-41.

Boyd, B. F. (1950). Applying the group chart for and R. Industrial Quality Control, 3, 22-25.

Crowder, S. V. (1989). Design of Exponentially Weighted Moving Average Schemes. Journal of Quality Technology, 21(3), 155-162.

Epprecht, E. K. (2015). Statistical control of multiple-stream processes: a literature review. In S. Knoth & W. Schmid, (Eds.), Frontiers in statistical quality control 11 (p. 49-64). Springer International Publishing, Switzerland.

Epprecht, E. K., Barbosa, L. F. M., & Simões, B. F. T. (2011a). SPC of multiple stream processes – a chart for enhanced detection of shifts in one stream. Produção, 21(2), 242-253.

Epprecht, E. K., de Luna, M. A., & Aparisi, F. (2011b). Joint EWMA charts for multivariate process control: markov chain and optimal design. International Journal of Production Research, 49(23), 7151-7169.

Kiefer, J. (1953). Sequential minimax search for a maximum. Proceedings of the American Mathematical Society, 4(3), 502-506.

Lanning, J. W., Montgomery, D. C., & Runger, G. C. (2002). Monitoring a multiple stream filling operation using fractional samples. Quality Engineering, 15(2), 183-195.

Liu, X., Mackay, R. J., & Steiner, S. H. (2008). Monitoring multiple stream processes. Quality Engineering, 20(3), 296-308.

Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control chart. Technometrics, 34(1), 46-53.

Meneces, N. S., Olivera, S. A., Saccone, C. D., & Tessore, J. (2008). Statistical control of multiple-stream processes: a shewhart control chart for each stream. Quality Engineering, 20(2), 185-194.

Mortell, R. R., & Runger, G. C. (1995). Statistical process control of multiple stream processes. Journal of Quality Technology, 27(1), 1-12.

Nelson, L. S. (1986). Control charts for multiple stream processes. Journal of Quality Technology, 18(4), 255-256.

Runger, G. C., Alt, F. B., & Montgomery, D. C. (1996). Controlling multiple stream processes with principal components. International Journal of Production Research, 34(11), 2991-2999.

Simões, B. F. T. (2010). Controle estatístico de processos multicanal (Tese de doutorado). Pontifícia Universidade Católica do Rio de Janeiro - PUC-Rio, Rio de Janeiro.

Xiang, L., & Tsung, F. (2008). Statistical monitoring of multi-stage processes based on engineering models. IIE Transactions, 40(10), 957-970.

6113df1ea9539543a7553b42 gp Articles

Gest. Prod.

Share this page
Page Sections