Gestão & Produção
https://www.gestaoeproducao.com/article/doi/10.1590/1806-9649-2022v29e6822
Gestão & Produção
Artigo Original

Monitoring bivariate processes with synthetic control charts based on sample ranges

Marcela Machado; Antonio Costa; Felipe Domingues Simões

Downloads: 1
Views: 351

Abstract

Abstract: The RMAX chart was proposed to control the covariance matrix of two quality characteristics. The monitoring statistic of the RMAX chart is the maximum of two standardized sample ranges from bivariate observations of two quality characteristics. In this article, we investigate the performance of two synthetic RMAX charts. The first synthetic chart signals when a second point, not far from the first one, falls beyond the warning limit. The second synthetic chart additionally signals when a sample point falls beyond the control limit. The performance of the synthetic RMAX charts are compared with the performance of the standard RMAX chart and the generalized variance S chart. The proposed charts are the best option to detect moderate or even small changes in the covariance matrix. To detect large changes in the covariance matrix, additional run rules are not necessary.

Keywords

RMAX chart, Bivariate processes, Synthetic run rules

Referências

Abujiya, M. R., Lee, M. H., & Riaz, M. (2016). Combined application of Shewhart and cumulative sum R chart for monitoring process dispersion. Quality and Reliability Engineering International, 32(1), 51-67. http://dx.doi.org/10.1002/qre.1725.

Acosta-Mejia, C. A., & Pignatiello, J. J., Jr. (2008). Modified R charts for improved performance. Quality Engineering, 20(3), 361-369. http://dx.doi.org/10.1080/08982110802178980.

Alt, F. B. 1985. Multivariate quality control. In S. Kotz & N. L. Johnson (Eds.), Encyclopedia of statistical sciences. Hoboken: Wiley.

Aparisi, F., & Lee Ho, L. (2017). M-ATTRIVAR: an attribute-variable chart to monitor multivariate process means. Quality and Reliability Engineering International, 34(2), 214-228. http://dx.doi.org/10.1002/qre.2250.

Bourke, P. D. (1991). Detecting a shift in fraction nonconforming using run-length control charts with 100-percent inspection. Journal of Quality Technology, 23(3), 225-238. http://dx.doi.org/10.1080/00224065.1991.11979328.

Costa, A. F. B. (2017). The double sampling range chart. Quality and Reliability Engineering International, 33(8), 2739-2745. http://dx.doi.org/10.1002/qre.2232.

Costa, A. F. B., & Machado, M. A. G. (2008). A new chart for monitoring the covariance matrix of bivariate processes. Communications in Statistics. Simulation and Computation, 37(7), 1453-1465. http://dx.doi.org/10.1080/03610910801988987.

Costa, A. F. B., & Machado, M. A. G. (2009). A new chart based on the sample variances for monitoring the covariance matrix of multivariate processes. International Journal of Advanced Manufacturing Technology, 41(7-8), 770-779. http://dx.doi.org/10.1007/s00170-008-1502-9.

Costa, A. F. B., & Machado, M. A. G. (2011). A control chart based on sample ranges for monitoring the covariance matrix of the multivariate processes. Journal of Applied Statistics, 38(2), 233-245. http://dx.doi.org/10.1080/02664760903406413.

Costa, A. F. B., & Machado, M. A. G. (2015). The steady-state behavior of the synthetic and side-sensitive synthetic double sampling x̄ charts. Quality and Reliability Engineering International, 31(2), 297-303. http://dx.doi.org/10.1002/qre.1588.

Costa, A. F. B., & Faria, A., No. (2017). The S chart with variable charting statistic to control bi and trivariate processes. Computers & Industrial Engineering, 113, 27-34. http://dx.doi.org/10.1016/j.cie.2017.09.001.

Davis, R. B., & Woodall, W. H. (2002). Evaluating and improving the synthetic control chart. Journal of Quality Technology, 34(2), 200-208. http://dx.doi.org/10.1080/00224065.2002.11980146.

Haridy, S., Wu, Z., Khoo, M. B. C., & Yu, F.-J. (2012). A combined synthetic and np scheme for detecting increases in fraction nonconforming. Computers & Industrial Engineering, 62(4), 979-988. http://dx.doi.org/10.1016/j.cie.2011.12.024.

Khoo, M. B. C., Wong, V. H., Wu, Z., & Castagliola, P. (2012). Optimal design of the synthetic chart for the process mean based on median run length. IIE Transactions, 44(9), 765-779. http://dx.doi.org/10.1080/0740817X.2011.609526.

Khoo, M. B., Lee, H. C., Wu, Z., Chen, C. H., & Castagliola, P. (2010). A synthetic double sampling control chart for the process mean. IIE Transactions, 43(1), 23-38. http://dx.doi.org/10.1080/0740817X.2010.491503.

Lee Ho, L., & Costa, A. F. B. (2015). Attribute charts for monitoring the mean vector of bivariate processes. Quality and Reliability Engineering International, 31(4), 683-693. http://dx.doi.org/10.1002/qre.1628.

Lee, P. (2011). Adaptive R charts with variable parameters. Computational Statistics & Data Analysis, 55(5), 2003-2010. http://dx.doi.org/10.1016/j.csda.2010.11.026.

Leoni, R. C., & Costa, A. F. B. (2017). Monitoring bivariate and trivariate mean vectors with a Shewhart chart. Quality and Reliability Engineering International, 33(8), 2035-2042. http://dx.doi.org/10.1002/qre.2165.

Leoni, R. C., Costa, A. F. B., Franco, B. C., & Machado, M. A. G. (2015). The skipping strategy to reduce the effect of the autocorrelation on the T 2 chart’s performance. International Journal of Advanced Manufacturing Technology, 80(9-12), 1547-1559. http://dx.doi.org/10.1007/s00170-015-7095-1.

Machado, M. A. G., & Costa, A. F. B. (2008). The double sampling and the EWMA charts based on the sample variances. International Journal of Production Economics, 114(1), 134-148. http://dx.doi.org/10.1016/j.ijpe.2008.01.001.

Machado, M. A. G., & Costa, A. F. B. (2014). Some comments regarding the synthetic chart. Communications in Statistics. Theory and Methods, 43(14), 2897-2906. http://dx.doi.org/10.1080/03610926.2012.683128.

Machado, M. A. G., Costa, A. F. B., & Marins, F. A. S. (2009). Control charts for monitoring the mean vector and the covariance matrix of bivariate processes. International Journal of Advanced Manufacturing Technology, 45(7-8), 772-785. http://dx.doi.org/10.1007/s00170-009-2018-7.

Machado, M. A. G., Costa, A. F. B., & Rahim, M. A. (2008). The synthetic control chart based on two sample variances for monitoring the covariance matrix. Quality and Reliability Engineering International, 25(5), 595-606. http://dx.doi.org/10.1002/qre.992.

Machado, M. A. G., Lee Ho, L., & Costa, A. F. B. (2018). Attribute control charts for monitoring the covariance matrix of bivariate processes. Quality and Reliability Engineering International, 34(2), 257-264. http://dx.doi.org/10.1002/qre.2253.

Melo, M. S., Lee Ho, L., & Medeiros, P. G. (2017a). A 2-stage attribute-variable control chart to monitor a vector of process means. Quality and Reliability Engineering International, 33(7), 1589-1599. http://dx.doi.org/10.1002/qre.2127.

Melo, M. S., Lee Ho, L., & Medeiros, P. G. (2017b). Max D: an attribute control chart to monitor a bivariate process mean. International Journal of Advanced Manufacturing Technology, 90(1-4), 489-498. http://dx.doi.org/10.1007/s00170-016-9368-8.

Microsoft Fortran PowerStation 4.0. (1989). Microsoft IMSL: Mathematical and Statistical Libraries. Microsoft Corporation.

Shokrizadeh, R., Saghaei, A., & Amirzadeh, V. (2017). Optimal design of the variable sampling size and sampling interval variable dimension T2 control chart for monitoring the mean vector of a multivariate normal process. Communications in Statistics. Simulation and Computation, 47(2), 329-337. http://dx.doi.org/10.1080/03610918.2016.1152369.

Shongwe, S. C., Malela-Majika, J.-C., Castagliola, P., & Molahloe, T. (2019). Side-sensitive synthetic and runs-rules charts for monitoring AR(1) processes with skipping sampling strategies. Communications in Statistics. Theory and Methods

Simões, F. D., Leoni, R. C., Machado, M. A. G., & Costa, A. F. B. (2016). Synthetic charts to control processes with autocorrelated data. Computers & Industrial Engineering, 97, 15-25. http://dx.doi.org/10.1016/j.cie.2016.04.005.

Sun, L., Wang, B. X., Guo, B., & Xie, M. (2018). Synthetic exponential control charts with unknown parameter. Communications in Statistics. Simulation and Computation, 47(8), 2360-2377. http://dx.doi.org/10.1080/03610918.2017.1343840.

Woodall, W. H. (2016). Bridging the gap between theory and practice in basic statistical process monitoring. Quality Engineering, 29, 2-15. http://dx.doi.org/10.1080/08982112.2016.1210449.

Wu, Z., & Spedding, T. A. (2000). Synthetic control chart for detecting small shifts in the process mean. Journal of Quality Technology, 32(1), 32-38. http://dx.doi.org/10.1080/00224065.2000.11979969.

Wu, Z., Ou, Y., Castagliola, P., & Khoo, M. B. C. (2010). A combined synthetic & X chart for monitoring the process mean. International Journal of Production Research, 48(24), 7423-7436. http://dx.doi.org/10.1080/00207540903496681.

Zhang, Y., Castagliola, P., Wu, Z., & Khoo, M. B. C. (2011). The synthetic X IIE Transactions, 43(9), 676-687. http://dx.doi.org/10.1080/0740817X.2010.549547.
 

6478eaffa95395256b404932 gp Articles

Gest. Prod.

Share this page
Page Sections