Gestão & Produção
https://gestaoeproducao.com/article/doi/10.1590/1806-9649-2021v28e43
Gestão & Produção
Seção Temática: Monitoramento e Controle Estatístico de Processos

Monitoring multinomial processes based on a weighted chi-square control chart

Achouri Ali; Emira Khedhiri; Ramzi Talmoudi; Hassen Taleb

Downloads: 0
Views: 26

Abstract

Abstract: : Interpreting an out-of-control signal is a crucial step in monitoring categorical processes. For the Chi-Square Control Chart (CSCC), an out-of control situation does not specify if it was a process deterioration or a process improvement. For this reason, a weighted chi-square statistical control chart WSCC is proposed with different weighting categories in order to enable an accelerated disclosure of a control situation after a shift due to a deterioration of quality and on the other hand, decelerate an out of control situation after a shift due to a quality improvement. Furthermore, in comparison with Marcucci’s method, the new procedure provides an accurate and easier way to interpret several signals. In other words, the WSCC allows a faster detection of an out-of control situation in the case of a quality deterioration, however, an out-of control situation is not quickly detected in the case of a quality improvement. Indeed, comparative studies have been performed to find the best control chart for each combination. Concluding remarks with comments and recommendations are given based on Average Run Length (ARL) and standard deviation run length (SDRL).

Keywords

Multinomial processes, Categorical processes, Chi-square control chart, Weighted chi-square statistic, ARL and SDRL

Referências

Duncan, A. J. (1950). A chi-square chart for controlling a set of percentages. Industrial Quality Control, 7, 11-15.

Duncan, A. J. (1974). Quality control and industrial statistics (4th ed.). Homewood, IL: Richard D. Irwin.

Feiveson, A. H., & Delaney, F. C. (1968). A chi-square chart for controlling a set of percentages. industrial quality control (Vol. 38). Washington: National Aeronautics and Space Administration.

Kanagawa, A., Tamaki, F., & Ohta, H. (1993). Control charts for process average and variability based on linguistic data. International Journal of Production Research, 31(4), 913-922. http://dx.doi.org/10.1080/00207549308956765.

Marcucci, M. (1985). Monitoring multinomial processes. Journal of Quality Technology, 17(2), 86-91. http://dx.doi.org/10.1080/00224065.1985.11978941.

Nelson, L. S. (1987). A chi-square control chart for several proportions. Journal of Quality Technology, 19(4), 229-231. http://dx.doi.org/10.1080/00224065.1987.11979069.

Raz, T., & Wang, J. (1990). On the construction of control charts using linguistic variables. International Journal of Production Research, 28(3), 477-487. http://dx.doi.org/10.1080/00207549008942731.

Shewhart, W. A. (1925). The application of statistics as an aid in maintaining quality of a manufactured product. Journal of the American Statistical Association, 20(152), 546-548. http://dx.doi.org/10.1080/01621459.1925.10502930.

Shewhart, W. A., & Deming, W. E. (1939). Statistical method from the viewpoint of quality control. Washington: The Graduate School, The Department of Agriculture.

Steiner, S. H., Geyer, P. L., & Wesolowsky, G. O. (1996). Shewhart control charts to detect mean and standard deviation shifts based on grouped data. Quality and Reliability Engineering International, 12(5), 345-353. http://dx.doi.org/10.1002/(SICI)1099-1638(199609)12:5<345::AID-QRE11>3.0.CO;2-M.

Taleb, H., Limam, M., & Hirota, H. (2006). Multivariate fuzzy multinomial control charts. Quality Technology & Quantitative Management, 3(4), 437-453. http://dx.doi.org/10.1080/16843703.2006.11673125.

Taleb, M., & Limam, M. (2002). H.and Limam. On fuzzy and probabilistic control charts. International Journal of Production Research, 40(12), 2849-2863. http://dx.doi.org/10.1080/00207540210137602.

Topalidou, E., & Psarakis’, S. (2009). Review of multinomial and multi attribute quality control charts. Quality and Reliability Engineering International, 25(7), 773-804. http://dx.doi.org/10.1002/qre.999.

Tucker, G. R., Woodall, W. H., & Tsui, K. L. (2002). control chart method for ordinal data. American Journal of Mathematical and Management Sciences, 22(1-2), 31-48. http://dx.doi.org/10.1080/01966324.2002.10737574.

Woodall, W. H. (1997). Control charts based on attribute data: bibliography and review. Journal of Quality Technology, 29(2), 172-183. http://dx.doi.org/10.1080/00224065.1997.11979748.
 

61380864a953955e9f125764 gp Articles

Gest. Prod.

Share this page
Page Sections