Gráficos de control estadístico para variables Poisson y multinomial en el contexto multivariado: una revisión de la literatura
Resumen
La necesidad de controlar la variabilidad cuando se tienen variables de calidad discretas Poisson y multinomiales en el contexto multivariante nos condujo a realizar una revisión muy general e introductoria de las propuestas más relevantes que se han hecho para monitorear gráficos de control multivariantes para este tipo de variables. Es mucha la investigación que se ha hecho en el contexto paramétrico y no paramétrico en este campo, que en este artículo tratamos de resaltar. Sin embargo, bajo el enfoque de la teoría difusa son pocos los trabajos dedicados al estudio de este tipo de gráficos. La teoría difusa puede ser una herramienta muy útil para modelar situaciones de control multivariantes donde se tengan variables correlacionadas y de diferentes categorías. Esperamos que este artículo pueda orientar y ser de ayuda a quiénes están buscando información en el campo de los gráficos de control multivariantes para variables tipo Poissson y multinomial.
Citas
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Aparisi, F., García-Bustos, S., y Epprecht, E. K. (2014). Optimum Multiple and Multivariate Poisson Statistical Control Charts. Quality and Reliability Engineering International, 30(2), 221–234. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/qre.1490 doi: 10.1002/qre.1490
Benjamini, Y., y Hochberg, Y. (2000). On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics. Journal of educational and Behavioral Statistics, 25(1), 60–83. doi: 10.3102/10769986025001060
Benjamini, Y., y Liu, W. (1999). A step-down multiple hypotheses testing procedure that controls the false discovery rate under independence. Journal of statistical planning and inference, 82(1-2), 163–170. Descargado de http://www.sciencedirect.com/science/article/pii/S0378375899000403 doi: 10.1016/S0378-3758(99)00040-3
Chen, N., Li, Z., y Ou, Y. (2015). Multivariate Exponentially Weighted Moving-Average Chart for Monitoring Poisson Observations. Journal of Quality Technology, 47(3), 252–263. doi: 10.1080/00224065.2015.11918131
Cheng, C.-B. (2005). Fuzzy process control: construction of control charts with fuzzy numbers. Fuzzy Sets and Systems, 154(2), 287–303. Descargado de http://www.sciencedirect.com/science/article/pii/S0165011405001107 doi: 10.1016/j.fss.2005.03.002
Chiu, J.-E., y Kuo, T.-I. (2007). Attribute Control Chart for Multivariate Poisson Distribution. Communications in Statistics-Theory and Methods, 37(1), 146–158. doi: 10.1080/03610920701648771
Coppi, R., Gil, M. A., y Kiers, H. A. L. (2006). The fuzzy approach to statistical analysis. Computational Statistics & Data Analysis, 51(1), 1–14. doi: 10.1016/j.csda.2006.05.012
Epprecht, E. K., Aparisi, F., y García-Bustos, S. (2013). Optimal linear combination of Poisson variables for multivariate statistical process control. Computers & operations research, 40(12), 3021–3032. Descargado de http://www.sciencedirect.com/science/article/pii/S030505481300186X doi: 10.1016/j.cor.2013.07.007
García-Bustos, S., Aparisi, F., y Epprecht, E. K. (2015). Optimal EWMA of linear combination of Poisson variables for multivariate statistical process control. International Journal of Production Research, 53(14), 4141–4159. doi: 10.1080/00207543.2014.975863
García-Bustos, S., Mite, M., y Vera, F. (2016). Control Charts with Variable Dimension for Linear Combination of Poisson Variables. Quality and Reliability Engineering International, 32(5), 1741–1755. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/qre.1910 doi: 10.1002/qre.1910
Ho, L. L., y Costa, A. F. B. (2009). Control charts for individual observations of a bivariate Poisson process. The International Journal of Advanced Manufacturing Technology, 43(7-8), 744–755. doi: 10.1007/s00170-008-1746-4
Holgate, P. (1964). Estimation for the bivariate Poisson distribution. Biometrika, 51(1-2), 241–287. doi: 10.1093/biomet/51.1-2.241
Karlis, D., y Meligkotsidou, L. (2005). Multivariate Poisson regression with covariance structure. Statistics and Computing, 15(4), 255–265.
Karlis, D., y Ntzoufras, I. (2005). Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R. Journal of Statistical Software, 14(10), 1–36. doi: 10.18637/jss.v014.i10
Kumar, A., y Mohapatra, P. (2012). A new Approach to Design of Fuzzy Multi-Attribute Control Charts. En POMS 23rd Annual Conference (Vol. 1, pp.1–5). Chicago, Illinois, U.S.A.
Laungrungrong, B., Borror, C. M., y Montgomery, D. C. (2011). EWMA control charts for multivariate Poisson-distributed data. International Journal of Quality Engineering and Technology, 2(3), 185–211. doi: 10.1504/IJQET.2011.041227
Laviolette, M., Seaman, J. W., Barrett, J. D., y Woodall, W. H. (1995). A Probabilistic and Statistical View of Fuzzy Methods. Technometrics, 37(3), 249–261. Descargado de https://www.tandfonline.com/doi/abs/10.1080/00401706.1995.10484327 doi: 10.1080/00401706.1995.10484327
Li, J., Tsung, F., y Zou, C. (2014). Multivariate binomial/multinomial control chart. IIE Transactions, 46(5), 526–542. doi: 10.1080/0740817X.2013.849830
Li, Y., y Tsung, F. (2012). Multiple Attribute Control Charts with False Discovery Rate Control. Quality and Reliability Engineering International, 28(8), 857–871. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/qre.1276 doi: 10.1002/qre.1276
Lowry, C. A., Woodall, W. H., Champ, C. W., y Rigdon, S. E. (1992). A Multivariate Exponentially Weighted Moving Average Control Chart. Technometrics, 34(1), 46–53. Descargado de https://amstat.tandfonline.com/doi/abs/10.1080/00401706.1992.10485232 doi: 10.1080/00401706.1992.10485232
Lu, X. (1998). Control chart for multivariate attribute processes. International Journal of Production Research, 36(12), 3477–3489. doi: 10.1080/002075498192166
Montgomery, D. C. (2004). Control estadístico de la calidad (3.ed.). México: Limusa-Wiley.
Montgomery, D. C. (2009). Statistical Quality Control: A Modern Introduction (6.ed.). Hoboken, New Jersey: John Whiley & Sons, Inc.
Pastuizaca Fernández, M. N. (2016). Diseño y mejora de gráficos de control multivariantes para atributos. Un enfoque basado en teoría difusa. (Tesis Doctoral, Universitat Politécnica de València). doi: 10.4995/Thesis/10251/65073
Pastuizaca Fernández, M. N., Carrión García, A., y Ruiz-Barzola, O. (2015). Multivariate multinomial T2 control chart using fuzzy approach. International Journal of Production Research, 53(7), 2225–2238. doi: 10.1080/00207543.2014.983617
Qiu, P. (2008). Distribution-free multivariate process control based on log-linear modeling. IIE Transactions, 40(7), 664–677. doi: 10.1080/07408170701744843
Qiu, P., He, Z., y Wang, Z. (2019). Nonparametric monitoring of multiple count data. IISE Transactions, 51(9), 972–984. doi: 10.1080/24725854.2018.1530486
Raza, M. A., y Aslam, M. (2019). Design of control charts for multivariate Poisson distribution using generalized multiple dependent state sampling. Quality Technology & Quantitative Management, 16(6), 629–650. doi: 10.1080/16843703.2018.1497935
Rowlands, H., y Wang, L. R. (2000). An approach of fuzzy logic evaluation and control in SPC. Quality and Reliability Engineering International, 16(2), 91–98. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-1638%28200003/04%2916%3A2%3C91%3A%3AAID-QRE307%3E3.0.CO%3B2-9 doi: 10.1002/(SICI)1099-1638(200003/04)16:2h91::AID-QRE307i3.0.CO;2-9
Saghir, A., y Lin, Z. (2014). Control chart for monitoring multivariate COM-Poisson attributes. Journal of Applied Statistics, 41(1), 200–214. doi: 10.1080/02664763.2013.838666
Smith, J. L. (2009). Remembering Walter A. Shewhart’s Contribution to the Quality World. Quality Magazine. Descargado de https://www.qualitymag.com/articles/85973-remembering-walter-a-shewharts-contribution-to-the-quality-world
Sorooshian, S. (2013). Fuzzy Approach to Statistical Control Charts. Journal of Applied Mathematics, Special Issue. doi: 10.1155/2013/745153
Taleb, H., y Limam, M. (2005). Fuzzy Multinomial Control Charts. En S. Bandini y S. Manzoni (Eds.), Congress of the Italian Association for Artificial Intelligence 2005. AI*IA 2005: Advances in Artificial Intelligence (pp. 553–563). Springer Berlin Heidelberg. doi: 10.1007/11558590_56
Taleb, H., Limam, M., y Hirota, K. (2006). Multivariate Fuzzy Multinomial Control Charts. Quality Technology & Quantitative Management, 3(4), 437–453. doi:10.1080/16843703.2006.11673125
Wang, J.-H., y Raz, T. (1990). On the construction of control charts using linguistic variables. The International Journal of Production Research, 28(3), 477–487. doi: 10.1080/00207549008942731
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. Descargado de http://www.sciencedirect.com/science/article/pii/S001999586590241X doi: 10.1016/S0019-9958(65)90241-X
Aparisi, F., García-Bustos, S., y Epprecht, E. K. (2014). Optimum Multiple and Multivariate Poisson Statistical Control Charts. Quality and Reliability Engineering International, 30(2), 221–234. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/qre.1490 doi: 10.1002/qre.1490
Benjamini, Y., y Hochberg, Y. (2000). On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics. Journal of educational and Behavioral Statistics, 25(1), 60–83. doi: 10.3102/10769986025001060
Benjamini, Y., y Liu, W. (1999). A step-down multiple hypotheses testing procedure that controls the false discovery rate under independence. Journal of statistical planning and inference, 82(1-2), 163–170. Descargado de http://www.sciencedirect.com/science/article/pii/S0378375899000403 doi: 10.1016/S0378-3758(99)00040-3
Chen, N., Li, Z., y Ou, Y. (2015). Multivariate Exponentially Weighted Moving-Average Chart for Monitoring Poisson Observations. Journal of Quality Technology, 47(3), 252–263. doi: 10.1080/00224065.2015.11918131
Cheng, C.-B. (2005). Fuzzy process control: construction of control charts with fuzzy numbers. Fuzzy Sets and Systems, 154(2), 287–303. Descargado de http://www.sciencedirect.com/science/article/pii/S0165011405001107 doi: 10.1016/j.fss.2005.03.002
Chiu, J.-E., y Kuo, T.-I. (2007). Attribute Control Chart for Multivariate Poisson Distribution. Communications in Statistics-Theory and Methods, 37(1), 146–158. doi: 10.1080/03610920701648771
Coppi, R., Gil, M. A., y Kiers, H. A. L. (2006). The fuzzy approach to statistical analysis. Computational Statistics & Data Analysis, 51(1), 1–14. doi: 10.1016/j.csda.2006.05.012
Epprecht, E. K., Aparisi, F., y García-Bustos, S. (2013). Optimal linear combination of Poisson variables for multivariate statistical process control. Computers & operations research, 40(12), 3021–3032. Descargado de http://www.sciencedirect.com/science/article/pii/S030505481300186X doi: 10.1016/j.cor.2013.07.007
García-Bustos, S., Aparisi, F., y Epprecht, E. K. (2015). Optimal EWMA of linear combination of Poisson variables for multivariate statistical process control. International Journal of Production Research, 53(14), 4141–4159. doi: 10.1080/00207543.2014.975863
García-Bustos, S., Mite, M., y Vera, F. (2016). Control Charts with Variable Dimension for Linear Combination of Poisson Variables. Quality and Reliability Engineering International, 32(5), 1741–1755. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/qre.1910 doi: 10.1002/qre.1910
Ho, L. L., y Costa, A. F. B. (2009). Control charts for individual observations of a bivariate Poisson process. The International Journal of Advanced Manufacturing Technology, 43(7-8), 744–755. doi: 10.1007/s00170-008-1746-4
Holgate, P. (1964). Estimation for the bivariate Poisson distribution. Biometrika, 51(1-2), 241–287. doi: 10.1093/biomet/51.1-2.241
Karlis, D., y Meligkotsidou, L. (2005). Multivariate Poisson regression with covariance structure. Statistics and Computing, 15(4), 255–265.
Karlis, D., y Ntzoufras, I. (2005). Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R. Journal of Statistical Software, 14(10), 1–36. doi: 10.18637/jss.v014.i10
Kumar, A., y Mohapatra, P. (2012). A new Approach to Design of Fuzzy Multi-Attribute Control Charts. En POMS 23rd Annual Conference (Vol. 1, pp.1–5). Chicago, Illinois, U.S.A.
Laungrungrong, B., Borror, C. M., y Montgomery, D. C. (2011). EWMA control charts for multivariate Poisson-distributed data. International Journal of Quality Engineering and Technology, 2(3), 185–211. doi: 10.1504/IJQET.2011.041227
Laviolette, M., Seaman, J. W., Barrett, J. D., y Woodall, W. H. (1995). A Probabilistic and Statistical View of Fuzzy Methods. Technometrics, 37(3), 249–261. Descargado de https://www.tandfonline.com/doi/abs/10.1080/00401706.1995.10484327 doi: 10.1080/00401706.1995.10484327
Li, J., Tsung, F., y Zou, C. (2014). Multivariate binomial/multinomial control chart. IIE Transactions, 46(5), 526–542. doi: 10.1080/0740817X.2013.849830
Li, Y., y Tsung, F. (2012). Multiple Attribute Control Charts with False Discovery Rate Control. Quality and Reliability Engineering International, 28(8), 857–871. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/qre.1276 doi: 10.1002/qre.1276
Lowry, C. A., Woodall, W. H., Champ, C. W., y Rigdon, S. E. (1992). A Multivariate Exponentially Weighted Moving Average Control Chart. Technometrics, 34(1), 46–53. Descargado de https://amstat.tandfonline.com/doi/abs/10.1080/00401706.1992.10485232 doi: 10.1080/00401706.1992.10485232
Lu, X. (1998). Control chart for multivariate attribute processes. International Journal of Production Research, 36(12), 3477–3489. doi: 10.1080/002075498192166
Montgomery, D. C. (2004). Control estadístico de la calidad (3.ed.). México: Limusa-Wiley.
Montgomery, D. C. (2009). Statistical Quality Control: A Modern Introduction (6.ed.). Hoboken, New Jersey: John Whiley & Sons, Inc.
Pastuizaca Fernández, M. N. (2016). Diseño y mejora de gráficos de control multivariantes para atributos. Un enfoque basado en teoría difusa. (Tesis Doctoral, Universitat Politécnica de València). doi: 10.4995/Thesis/10251/65073
Pastuizaca Fernández, M. N., Carrión García, A., y Ruiz-Barzola, O. (2015). Multivariate multinomial T2 control chart using fuzzy approach. International Journal of Production Research, 53(7), 2225–2238. doi: 10.1080/00207543.2014.983617
Qiu, P. (2008). Distribution-free multivariate process control based on log-linear modeling. IIE Transactions, 40(7), 664–677. doi: 10.1080/07408170701744843
Qiu, P., He, Z., y Wang, Z. (2019). Nonparametric monitoring of multiple count data. IISE Transactions, 51(9), 972–984. doi: 10.1080/24725854.2018.1530486
Raza, M. A., y Aslam, M. (2019). Design of control charts for multivariate Poisson distribution using generalized multiple dependent state sampling. Quality Technology & Quantitative Management, 16(6), 629–650. doi: 10.1080/16843703.2018.1497935
Rowlands, H., y Wang, L. R. (2000). An approach of fuzzy logic evaluation and control in SPC. Quality and Reliability Engineering International, 16(2), 91–98. Descargado de https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-1638%28200003/04%2916%3A2%3C91%3A%3AAID-QRE307%3E3.0.CO%3B2-9 doi: 10.1002/(SICI)1099-1638(200003/04)16:2h91::AID-QRE307i3.0.CO;2-9
Saghir, A., y Lin, Z. (2014). Control chart for monitoring multivariate COM-Poisson attributes. Journal of Applied Statistics, 41(1), 200–214. doi: 10.1080/02664763.2013.838666
Smith, J. L. (2009). Remembering Walter A. Shewhart’s Contribution to the Quality World. Quality Magazine. Descargado de https://www.qualitymag.com/articles/85973-remembering-walter-a-shewharts-contribution-to-the-quality-world
Sorooshian, S. (2013). Fuzzy Approach to Statistical Control Charts. Journal of Applied Mathematics, Special Issue. doi: 10.1155/2013/745153
Taleb, H., y Limam, M. (2005). Fuzzy Multinomial Control Charts. En S. Bandini y S. Manzoni (Eds.), Congress of the Italian Association for Artificial Intelligence 2005. AI*IA 2005: Advances in Artificial Intelligence (pp. 553–563). Springer Berlin Heidelberg. doi: 10.1007/11558590_56
Taleb, H., Limam, M., y Hirota, K. (2006). Multivariate Fuzzy Multinomial Control Charts. Quality Technology & Quantitative Management, 3(4), 437–453. doi:10.1080/16843703.2006.11673125
Wang, J.-H., y Raz, T. (1990). On the construction of control charts using linguistic variables. The International Journal of Production Research, 28(3), 477–487. doi: 10.1080/00207549008942731
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. Descargado de http://www.sciencedirect.com/science/article/pii/S001999586590241X doi: 10.1016/S0019-9958(65)90241-X
Publicado
2020-10-14
Sección
Articulos
