A Process Capability Index for Multivariate Normal and Non-Normal Distributions of Correlated and Uncorrelated Variables
Keywords:
Multivariate process capability index, Univariate capability index, Non-normal distribution, Normal distribution, Statistical methodsAbstract
DOI: https://doi.org/10.26439/ing.ind2020.n038.4814
The multivariate process capability analysis includes many indices that are only used when the data is normal and others, when the data is not normal. The same occurs with correlated and uncorrelated quality variables. In this research work, a CPME multivariate capability index was developed by initially using a univariate index—depending on whether the data was o not normal—and any correlation between variables, and then through a characteristic function for the multivariate data. This index may be used in all the aforementioned cases. Some examples of this alternative are presented on a set of real and simulated data, where a broad performance of our proposed index was found against other similar capability indices.
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References
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Wang, F. K., Hubele, N. F., Lawrence, F. P., Miskulin, J. D., y Shahriari, H. (2000). Comparison for three multivariate process capability indices. Journal of Quality Technology, 32(3), 263-275. <a href="https://doi.org/10.1080/00224065.2000.11980002" target="_blank">https://doi.org/10.1080/00224065.2000.11980002</a>
Yeh, A., y Chen, H. (2001). A nonparametric multivariate process capability index. International Journal of Modelling and Simulation, 21(3), 218-223. <a href="https://doi.org/10.1080/02286203.2001.11442205" target="_blank">https://doi.org/10.1080/02286203.2001.11442205</a>
Castagliola, P., y Castellanos, J. V. G. (2005). Capability indices dedicated to the two quality characteristics case. Quality Technology and Quantitative Management, 2(2), 201-220. <a href="https://doi.org/10.1080/16843703.2005.11673094" target="_blank">https://doi.org/10.1080/16843703.2005.11673094</a>
Castagliola, P., y Castellanos, J. V. G. (2008). Process capability indices dedicated to bivariate non-normal distributions. Journal of Quality in Maintenance Engineering, 14(1), 87-101. <a href="https://doi.org/10.1108/13552510810861969" target="_blank">https://doi.org/10.1108/13552510810861969</a>
Chen, H. (1994). A multivariate process capability index over a rectangular solid tolerance zone. Statistica Sinica, 4(2), 749-758.
Chou, Y., Polansky, A., y Mason, R. (1998). Transforming non-normal data to normality in statistical process control. Journal of Quality Technology, 30(2), 133-141. <a href="https://doi.org/10.1080/00224065.1998.11979832" target="_blank">https://doi.org/10.1080/00224065.1998.11979832</a>
Cuamea, G., y Anaya, C. (2009). Evaluación de la calidad en productos o procesos con múltiples características de calidad correlacionadas. Epistemus, 6, 12-16.
Cuamea, G., y Rodríguez, M. (2014). Propuesta para evaluar la capacidad de procesos de manufactura multivariados. Revista Ingeniería Industrial, 13(2), 35-47.
Foster, E. J., Barton, R. R., y Gautam, N. (2005). The process-oriented multivariate capability index, International Journal of Production Research, 43(10), 2135-2148. <a href="https://doi.org/10.1080/00207540412331530158" target="_blank">https://doi.org/10.1080/00207540412331530158</a>
Hubele, N., Shahiari, H., y Cheng, C. (1991). A bivariate capability vector. En J. B. Keats y D. C. Montgomery (Eds.), Statistics and design in process control: Keeping pace with automated manufacturing (pp. 229-310). Marcel Dekker.
Johnson, N. L. (1949). System of frequency curves generated by methods of translation. Biometrika, 36(2), 149-176. doi:10.2307/2332539
Liu, P. H. y Chen, F. L. (2006). Process capability analysis of non-normal process data using the Burr XII distribution. International Journal of Advanced Manufacturing Technology, 27(9), 975-984. <a href="https://doi.org/10.1007/s00170-004-2263-8" target="_blank">https://doi.org/10.1007/s00170-004-2263-8</a>
Montgomery, D. (2009). Statistical quality control. A modern introduction (6. a ed.). John Wiley and Sons, Inc.
Polansky, A. M., Chou, Y. M., y Mason, R. L. (1998). Estimating process capability indices for a truncated distribution. Quality Engineering, 11(2), 257-265. <a href="https://doi.org/10.1080/08982119808919237" target="_blank">https://doi.org/10.1080/08982119808919237</a>
Salazar, E., y Fermín, J. (2016). Un índice de capacidad de procesos para distribuciones multivariadas normales de variables correlacionadas y no correlacionadas. Ingeniería Industrial, (34), 57-73. doi:10.26439/ing.ind2016.n034.1337
Salazar, E., y Fermín, J. (2017). Un índice de capacidad de procesos para distribuciones multivariadas no normales de variables correlacionadas y no correlacionadas. Ingeniería Industrial, (35), 55-75. doi:10.26439/ing.ind2017.n035.1790
Shahriari, H., y Abdollahzadeh, M. (2009). A new multivariate process capability vector. Quality Engineering, 21(3), 290-299. <a href="https://doi.org/10.1080/08982110902873605" target="_blank">https://doi.org/10.1080/08982110902873605</a>
Shinde, R. L., y Khadse, K. G. (2009). Multivariate process capability using principal component analysis. Quality and Reliability Engineering International, 25(1), 69-77. <a href="https://doi.org/10.1002/qre.954" target="_blank">https://doi.org/10.1002/qre.954</a>
Somerville, S., y Montgomery, D. (1996). Process capability indices and non-normal distributions. Quality Engieneering, 9(2), 305-316. <a href="https://doi.org/10.1080/08982119608919047" target="_blank">https://doi.org/10.1080/08982119608919047</a>
Statgraphics (16.1.15) [Software] (2015). Recuperado de <a href="https://statgraphics.net/" target="_blank">https://statgraphics.net/</a>
Taam, W., Subbaiah, P., y Liddy, J. W. (1993). A note of multivariate capability indices. Journal of Applied Statistics, 20(3), 339-351. <a href="https://doi.org/10.1080/02664769300000035" target="_blank">https://doi.org/10.1080/02664769300000035</a>
Tang, L. C., y Than, S. E. (1999). Computing process capability indices for non-normal data: a review and comparative study. Quality and Reliability Engineering International, 15(5), 339-353. <a href="https://doi.org/10.1002/(SICI)1099-1638(199909/10)15:5<339::AID-QRE259>3.0.CO;2-A" target="_blank">https://doi.org/10.1002/(SICI)1099-1638(199909/10)15:5<339::AID-QRE259>3.0.CO;2-A</a>
Wang, F. K. (2006). Quality evaluations of a manufactured Product with multiple characteristics. Quality and Reliability Engineering International, 22(2), 225-236. <a href="https://doi.org/10.1002/qre.712" target="_blank">https://doi.org/10.1002/qre.712</a>
Wang, F. K., y Du, T. C. (2000) Using principal component analysis in process performance for multivariate data. Omega, 28(2), 185-194. <a href="https://doi.org/10.1016/S0305-0483(99)00036-5" target="_blank">https://doi.org/10.1016/S0305-0483(99)00036-5</a>
Wang, F. K., Hubele, N. F., Lawrence, F. P., Miskulin, J. D., y Shahriari, H. (2000). Comparison for three multivariate process capability indices. Journal of Quality Technology, 32(3), 263-275. <a href="https://doi.org/10.1080/00224065.2000.11980002" target="_blank">https://doi.org/10.1080/00224065.2000.11980002</a>
Yeh, A., y Chen, H. (2001). A nonparametric multivariate process capability index. International Journal of Modelling and Simulation, 21(3), 218-223. <a href="https://doi.org/10.1080/02286203.2001.11442205" target="_blank">https://doi.org/10.1080/02286203.2001.11442205</a>
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Published
2020-07-06
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Section
Quality and environment
How to Cite
A Process Capability Index for Multivariate Normal and Non-Normal Distributions of Correlated and Uncorrelated Variables. (2020). Ingeniería Industrial, 38(038), 67-92. https://revistas.ulima.edu.pe/index.php/Ingenieria_industrial/article/view/4765
