Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales
ilustraciones, gráficas, tablas
- Autores:
-
Espinosa Moreno, Juan Carlos
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/80801
- Palabra clave:
- 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Análisis de datos funcionales
Método de Montecarlo
Fuynctional data analysis
Monte-Carlo method
Outlyingness
Monitoring
Functional
Profiles
MFPCA
Claeskens
Mahalanobis
Monitoreo
Funcional
Perfiles
Análisis estadístico
Statistical analysis
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
| id |
UNACIONAL2_9056991deb285efa38b5c36da2c47315 |
|---|---|
| oai_identifier_str |
oai:repositorio.unal.edu.co:unal/80801 |
| network_acronym_str |
UNACIONAL2 |
| network_name_str |
Universidad Nacional de Colombia |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales |
| dc.title.translated.eng.fl_str_mv |
Multivariate nonlinear profiles monitoring using a functional data approach |
| title |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales |
| spellingShingle |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Análisis de datos funcionales Método de Montecarlo Fuynctional data analysis Monte-Carlo method Outlyingness Monitoring Functional Profiles MFPCA Claeskens Mahalanobis Monitoreo Funcional Perfiles Análisis estadístico Statistical analysis |
| title_short |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales |
| title_full |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales |
| title_fullStr |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales |
| title_full_unstemmed |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales |
| title_sort |
Monitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionales |
| dc.creator.fl_str_mv |
Espinosa Moreno, Juan Carlos |
| dc.contributor.advisor.spa.fl_str_mv |
Guevara González, Rubén Darío |
| dc.contributor.author.spa.fl_str_mv |
Espinosa Moreno, Juan Carlos |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas |
| topic |
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Análisis de datos funcionales Método de Montecarlo Fuynctional data analysis Monte-Carlo method Outlyingness Monitoring Functional Profiles MFPCA Claeskens Mahalanobis Monitoreo Funcional Perfiles Análisis estadístico Statistical analysis |
| dc.subject.lemb.spa.fl_str_mv |
Análisis de datos funcionales Método de Montecarlo |
| dc.subject.lemb.eng.fl_str_mv |
Fuynctional data analysis Monte-Carlo method |
| dc.subject.proposal.eng.fl_str_mv |
Outlyingness Monitoring Functional Profiles MFPCA Claeskens |
| dc.subject.proposal.spa.fl_str_mv |
Mahalanobis Monitoreo Funcional Perfiles |
| dc.subject.unesco.spa.fl_str_mv |
Análisis estadístico |
| dc.subject.unesco.eng.fl_str_mv |
Statistical analysis |
| description |
ilustraciones, gráficas, tablas |
| publishDate |
2021 |
| dc.date.issued.none.fl_str_mv |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2022-01-11T20:24:29Z |
| dc.date.available.none.fl_str_mv |
2022-01-11T20:24:29Z |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
| dc.type.content.spa.fl_str_mv |
Text |
| dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
| status_str |
acceptedVersion |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/80801 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.unal.edu.co/ |
| url |
https://repositorio.unal.edu.co/handle/unal/80801 https://repositorio.unal.edu.co/ |
| identifier_str_mv |
Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
| dc.language.iso.spa.fl_str_mv |
spa |
| language |
spa |
| dc.relation.references.spa.fl_str_mv |
Atashgar, K. and Zargarabadi, O. Monitoring multivariate pro le data in plastic parts manufacturing industries: An intelligently data processing. Journal of Industrial In- formation Integration, 8:38 { 48, 2017. ISSN 2452-414X. doi: https://doi.org/10. 1016/j.jii.2017.06.003. URL http://www.sciencedirect.com/science/article/pii/ S2452414X16300942. Berrendero, J. R., Justel, A., and Svarc, M. Principal components for multivariate functional data. Computational Statistics & Data Analysis, 55(9):2619{2634, 2011. Boone, J. and Chakraborti, S. Two simple shewhart-type multivariate nonparametric control charts. Applied Stochastic Models in Business and Industry, 28(2):130{140, 2012. Brys, G., Hubert, M., and Rousseeuw, P. J. A robusti cation of independent component analysis. Journal of Chemometrics, 19(5-7):364{375, 2005. doi: https://doi.org/10. 1002/cem.940. URL https://analyticalsciencejournals.onlinelibrary.wiley. com/doi/abs/10.1002/cem.940. Chuang, S. C., Hung, Y. C., Tsai, W.-C., and Yang, S.-F. A framework for nonparametric pro le monitoring. Computers & Industrial Engineering, 64(1):482 { 491, 2013. ISSN 0360-8352. doi: https://doi.org/10.1016/j.cie.2012.08.006. URL http: //www.sciencedirect.com/science/article/pii/S0360835212002057. Claeskens, G., Hubert, M., Slaets, L., and Vakili, K. Multivariate functional halfspace depth. Journal of the American Statistical Association, 109(505):411{423, 2014. doi: 10.1080/01621459.2013.856795. URL https://doi.org/10.1080/01621459. 2013.856795. Crosier, R. B. Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3):291{303, 1988. Cuevas, A., Febrero, M., and Fraiman, R. On the use of the bootstrap for estimating functions with functional data. Computational Statistics & Data Analysis, 51(2):1063 { 1074, 2006. ISSN 0167-9473. doi: https://doi.org/10.1016/j.csda.2005.10.012. URL http://www.sciencedirect.com/science/article/pii/S0167947305002793. Cuevas, A., Febrero, M., and Fraiman, R. Robust estimation and classi cation for functional data via projection-based depth notions. Computational Statistics, 22(3): 481{496, Sep 2007. ISSN 1613-9658. doi: 10.1007/s00180-007-0053-0. URL https: //doi.org/10.1007/s00180-007-0053-0. Dai, W. and Genton, M. Directional outlyingness for multivariate functional data. Computational Statistics and Data Analysis, 131:50 { 65, 2019. ISSN 0167-9473. doi: https://doi.org/10.1016/j.csda.2018.03.017. URL http://www.sciencedirect. com/science/article/pii/S016794731830077X. High-dimensional and functional data analysis. Fass o, A., Toccu, M., and Magno, M. Functional control charts and health monitoring of steam sterilizers. Quality and Reliability Engineering International, 32(6):2081{2091, 2016. Ferraty, F. and Vieu, P. Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics. Springer New York, 2010. ISBN 9781441921413. URL https://books.google.com.co/books?id=SlVWcgAACAAJ. Galeano, P., Joseph, E., and Lillo, R. E. The Mahalanobis distance for functional data with applications to classi cation. Technometrics, 57(2):281{291, 2015. Ghosh, M., Li, Y., Zeng, L., Zhang, Z., and Zhou, Q. Modeling multivariate pro les using gaussian process-controlled B-splines. IISE Transactions, 0(0):1{12, 2020. doi: 10.1080/ 24725854.2020.1798038. URL https://doi.org/10.1080/24725854.2020.1798038. G orecki, T., Krzy sko, M., Waszak, L., and Wo ly nski, W. Selected statistical methods of data analysis for multivariate functional data. Statistical Papers, pages 1{30, 2016. Grasso, M., Colosimo, B., and Pacella, M. Pro le monitoring via sensor fusion: The use of PCA methods for multi-channel data. International Journal of Production Research, 02 2014. doi: 10.1080/00207543.2014.916431. Guevara, R. and Vargas, J. Evaluation of process capability in multivariate nonlinear pro les. Journal of Statistical Computation and Simulation, 86(12):2411{2428, 2016. Happ, C. and Greven, S. Multivariate functional principal component analysis for data observed on di erent (dimensional) domains. Journal of the American Statisti- cal Association, 113(522):649{659, 2018. doi: 10.1080/01621459.2016.1273115. URL https://doi.org/10.1080/01621459.2016.1273115. Horv ath, L. and Kokoszka, P. Inference for Functional Data with Applications. Springer Series in Statistics. Springer New York, 2012. ISBN 9781461436546. URL https: //books.google.com.co/books?id=PGOCtgAACAAJ. Hubert, M. Data depth: Robust multivariate analysis, computational geometry and applications by Liu, R., Ser ing, R., and Souvaine, D. L. Biometrics, 64(2):655{656, 2008. doi: 10.1111/j.1541-0420.2008.01026n 6.x. URL https://onlinelibrary.wiley.com/ doi/abs/10.1111/j.1541-0420.2008.01026_6.x. Hubert, M., Rousseeuw, P., and Segaert, P. Multivariate functional outlier detection. Statistical Methods & Applications, 24:177{202, 2015. Hubert, M., Rousseeuw, P., and Segaert, P. Multivariate and functional classi cation using depth and distance. Advances in Data Analysis and Classi cation, 11(3):445{466, Sep 2017. ISSN 1862-5355. doi: 10.1007/s11634-016-0269-3. URL https://doi.org/10. 1007/s11634-016-0269-3. Ieva, F. and Paganoni, A. M. Depth measures for multivariate functional data. Com- munications in Statistics - Theory and Methods, 42(7):1265{1276, 2013. doi: 10.1080/ 03610926.2012.746368. URL https://doi.org/10.1080/03610926.2012.746368. Jacques, J. and Preda, C. Model-based clustering for multivariate functional data. Compu- tational Statistics & Data Analysis, 71:92{106, 2014. Jahani, S., Kontar, R., Veeramani, D., and Zhou, S. Statistical monitoring of multiple pro les simultaneously using gaussian processes. Quality and Reliability Engi- neering International, 34(8):1510{1529, 2018. doi: 10.1002/qre.2326. URL https: //onlinelibrary.wiley.com/doi/abs/10.1002/qre.2326. Jones-Farmer, L. A., Woodall, W. H., Steiner, S. H., and Champ, C. W. An overview of Phase I analysis for process improvement and monitoring. Journal of Qua- lity Technology, 46(3):265{280, 2014. doi: 10.1080/00224065.2014.11917969. URL https://doi.org/10.1080/00224065.2014.11917969. Kang, L. and Albin, S. L. On-line monitoring when the process yields a linear pro le. Journal of Quality Technology, 32(4):418, 2000. Kokoszka, P. and Reimherrm, M. Introduction to Functional Data Analysis. Chapman & Hall / CRC numerical analysis and scienti c computing. CRC Press, 2017. ISBN 9781498746342. URL https://books.google.com.co/books?id=HIxIvgAACAAJ. Li, Z., Dai, Y., and Wang, Z. Multivariate change point control chart based on data depth for Phase I analysis. Communications in Statistics - Simulation and Computation, 43 (6):1490{1507, 2014. doi: 10.1080/03610918.2012.735319. URL https://doi.org/10. 1080/03610918.2012.735319. Liu, R. Y., Parelius, J. M., and Singh, K. Multivariate analysis by data depth: descriptive statistics, graphics and inference, (with discussion and a rejoinder by liu and singh). Ann. Statist., 27(3):783{858, 06 1999. doi: 10.1214/aos/1018031260. URL https:// doi.org/10.1214/aos/1018031260. L opez-Pintado, S. and Romo, J. On the concept of depth for functional data. Journal of the American Statistical Association, 104(486):718{734, 2009. doi: 10.1198/jasa.2009.0108. URL https://doi.org/10.1198/jasa.2009.0108. Lowry, C. A., Woodall, W. H., Champ, C. W., and Rigdon, S. E. A multivariate exponentially weighted moving average control chart. Technometrics, 34(1):46{53, 1992. Maleki, M., Amiri, A., and Castagliola, P. An overview on recent pro le monitoring papers (2008-2018) based on conceptual classi cation scheme. Computers & Industrial Engineering, 126:705 { 728, 2018. ISSN 0360-8352. Montgomery, D. C. Introduction to statistical quality control. John Wiley & Sons, 2007. Munck, L., Norgaard, L., Engelsen, S., Bro, R., and Andersson, C. Chemometrics in food science-a demonstration of the feasibility of a highly exploratory, inductive evaluation strategy of fundamental scienti c signi cance. Chemometrics and Intelligent Laboratory Systems, 44(1):31{60, 1998. ISSN 0169-7439. doi: https://doi.org/10.1016/ S0169-7439(98)00074-4. URL https://www.sciencedirect.com/science/article/ pii/S0169743998000744. Noorossana, R., Saghaei, A., and Amiri, A. Statistical analysis of pro le monitoring, volume 865. John Wiley & Sons, 2011. Pan, J.-N., Li, C.-I., and Lu, M. Z. Detecting the process changes for multivariate nonlinear pro le data. Quality and Reliability Engineering International, 35(6):1890{1910, 2019. doi: 10.1002/qre.2482. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/ qre.2482. Paynabar, K., Zou, C., and Qiu, P. A change-point approach for Phase-I analysis in multivariate pro le monitoring and diagnosis. Technometrics, 58(2):191{204, 2016. doi: 10.1080/00401706.2015.1042168. URL https://doi.org/10.1080/00401706.2015. 1042168. Pe~na, D. An alisis multivariante de datos. McGraw-Hill Interamericana de Espa~na S.L., 2002. ISBN 9788448136109. Pignatiello, J. J. and Runger, G. C. Comparisons of multivariate cusum charts. Journal of quality technology, 22(3):173{186, 1990. Qiu, P. Introduction to statistical process control. CRC Press, 2013. Qiu, P., Zou, C., and Wang, Z. Nonparametric pro le monitoring by mixed e ects modeling. Technometrics, 52(3):265{277, 2010. R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2016. URL https://www.R-project.org/. Ramsay, J. and Silverman, B. Functional data analysis. Springer Series in Statistics. Springer, 2ed edition, 2005. ISBN 038740080X,9780387400808. Schabenberger, O. and Pierce, F. J. Contemporary statistical models for the plant and soil sciences. CRC press, 2001. Sheu, S. H., Ouyoung, C. W., and Hsu, T. S. Phase II statistical process control for functional data. Journal of Statistical Computation and Simulation, 83(11):2144{2159, 2013. Shiau, J.-J. H., Huang, H.-L., Lin, S.-H., and Tsai, M.-Y. Monitoring nonlinear pro les with random e ects by nonparametric regression. Communications in Statistics Theory and Methods, 38(10):1664{1679, 2009. Tarabelloni, N., Biasi, R., Paganoni, A., and Ieva, F. Multivariate functional data depth measure based on variance-covariance operators. 07 2014. Wang, K. and Tsung, F. Hierarchical sparse functional principal component analysis for multistage multivariate pro le data. IISE Transactions, 0(0):1{16, 2020. doi: 10.1080/ 24725854.2020.1738599. URL https://doi.org/10.1080/24725854.2020.1738599. Wang, Y., Mei, Y., and Paynabar, K. Thresholded multivariate principal component analysis for Phase I multichannel pro le monitoring. Technometrics, 0(0):1{13, 2018. doi: 10.1080/00401706.2017.1375993. URL https://doi.org/10.1080/00401706.2017. 1375993. Williams, J. D., Woodall, W. H., and Birch, J. B. Statistical monitoring of nonlinear product and process quality pro les. Quality and Reliability Engineering International, 23(8):925{941, 2007. Yeh, A. B., Huwang, L., and Li, Y.-M. Pro le monitoring for a binary response. IIE Transactions, 41(11):931{941, 2009. Zhang, C., Yan, H., Lee, S., and Shi, J. Weakly correlated pro le monitoring based on sparse multi-channel functional principal component analysis. IISE Transactions, 50 (10):878{891, 2018. doi: 10.1080/24725854.2018.1451012. URL https://doi.org/10. 1080/24725854.2018.1451012 Zhang, J., Ren, H., Yao, R., Zou, C., and Wang, Z. Phase I analysis of multivariate pro les based on regression adjustment. Comput. Ind. Eng., 85(C):132{144, July 2015. ISSN 0360-8352. doi: 10.1016/j.cie.2015.02.025. URL http://dx.doi.org/10.1016/j.cie. 2015.02.025. Zou, C., Tsung, F., and Wang, Z. Monitoring pro les based on nonparametric regression methods. Technometrics, 50(4):512{526, 2008. doi: 10.1198/004017008000000433. URL https://doi.org/10.1198/004017008000000433. Zou, C., Wang, Z., and Tsung, F. A spatial rank-based multivariate EWMA control chart. Naval Research Logistics (NRL), 59(2):91{110, 2012. |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.license.spa.fl_str_mv |
Reconocimiento 4.0 Internacional |
| dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by/4.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Reconocimiento 4.0 Internacional http://creativecommons.org/licenses/by/4.0/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.spa.fl_str_mv |
xi, 60 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.publisher.program.spa.fl_str_mv |
Bogotá - Ciencias - Maestría en Ciencias - Estadística |
| dc.publisher.department.spa.fl_str_mv |
Departamento de Estadística |
| dc.publisher.faculty.spa.fl_str_mv |
Facultad de Ciencias |
| dc.publisher.place.spa.fl_str_mv |
Bogotá, Colombia |
| dc.publisher.branch.spa.fl_str_mv |
Universidad Nacional de Colombia - Sede Bogotá |
| institution |
Universidad Nacional de Colombia |
| bitstream.url.fl_str_mv |
https://repositorio.unal.edu.co/bitstream/unal/80801/1/license.txt https://repositorio.unal.edu.co/bitstream/unal/80801/3/1073161990.2021.pdf https://repositorio.unal.edu.co/bitstream/unal/80801/4/1073161990.2021.pdf.jpg |
| bitstream.checksum.fl_str_mv |
8153f7789df02f0a4c9e079953658ab2 1881e26c63e26e36e637fedc05547db0 dd96df4377b5a9269a7984f4235af9c1 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| repository.mail.fl_str_mv |
repositorio_nal@unal.edu.co |
| _version_ |
1806886664478392320 |
| spelling |
Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Guevara González, Rubén Darío2db6446b3a559b33e7b356835d8a92f2600Espinosa Moreno, Juan Carlos31643765f4872dd5dac328a7e9c12f216002022-01-11T20:24:29Z2022-01-11T20:24:29Z2021https://repositorio.unal.edu.co/handle/unal/80801Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficas, tablasEn este trabajo se presentan algunas propuestas para monitorear perfiles no lineales multivariados en fase II, usando métodos provenientes del análisis de datos funcionales. El desempeño de las cartas de control propuestas se evalúa usando simulaciones de Monte Carlo bajo diferentes escenarios. Para ilustrar el uso de la cartas propuestas se presentan ejemplos con datos reales. (Texto tomado de la fuente).In this work, some proposals for the monitoring of multivariate non-linear pro files in phase II will be presented using statistical control charts, using an approach from the Functional Data Analysis. To evaluate the performance of the proposed charts, Monte Carlo simulations will be carried out under different scenarios. To illustrate the use of the proposed letters, examples with real data will be presented.MaestríaMagíster en Ciencias - EstadísticaControl de calidadAnálisis de datos funcionalesxi, 60 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - EstadísticaDepartamento de EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasAnálisis de datos funcionalesMétodo de MontecarloFuynctional data analysisMonte-Carlo methodOutlyingnessMonitoringFunctionalProfilesMFPCAClaeskensMahalanobisMonitoreoFuncionalPerfilesAnálisis estadísticoStatistical analysisMonitoreo de perfiles no lineales multivariados usando un enfoque de datos funcionalesMultivariate nonlinear profiles monitoring using a functional data approachTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAtashgar, K. and Zargarabadi, O. Monitoring multivariate pro le data in plastic parts manufacturing industries: An intelligently data processing. Journal of Industrial In- formation Integration, 8:38 { 48, 2017. ISSN 2452-414X. doi: https://doi.org/10. 1016/j.jii.2017.06.003. URL http://www.sciencedirect.com/science/article/pii/ S2452414X16300942.Berrendero, J. R., Justel, A., and Svarc, M. Principal components for multivariate functional data. Computational Statistics & Data Analysis, 55(9):2619{2634, 2011.Boone, J. and Chakraborti, S. Two simple shewhart-type multivariate nonparametric control charts. Applied Stochastic Models in Business and Industry, 28(2):130{140, 2012.Brys, G., Hubert, M., and Rousseeuw, P. J. A robusti cation of independent component analysis. Journal of Chemometrics, 19(5-7):364{375, 2005. doi: https://doi.org/10. 1002/cem.940. URL https://analyticalsciencejournals.onlinelibrary.wiley. com/doi/abs/10.1002/cem.940.Chuang, S. C., Hung, Y. C., Tsai, W.-C., and Yang, S.-F. A framework for nonparametric pro le monitoring. Computers & Industrial Engineering, 64(1):482 { 491, 2013. ISSN 0360-8352. doi: https://doi.org/10.1016/j.cie.2012.08.006. URL http: //www.sciencedirect.com/science/article/pii/S0360835212002057.Claeskens, G., Hubert, M., Slaets, L., and Vakili, K. Multivariate functional halfspace depth. Journal of the American Statistical Association, 109(505):411{423, 2014. doi: 10.1080/01621459.2013.856795. URL https://doi.org/10.1080/01621459. 2013.856795.Crosier, R. B. Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3):291{303, 1988.Cuevas, A., Febrero, M., and Fraiman, R. On the use of the bootstrap for estimating functions with functional data. Computational Statistics & Data Analysis, 51(2):1063 { 1074, 2006. ISSN 0167-9473. doi: https://doi.org/10.1016/j.csda.2005.10.012. URL http://www.sciencedirect.com/science/article/pii/S0167947305002793.Cuevas, A., Febrero, M., and Fraiman, R. Robust estimation and classi cation for functional data via projection-based depth notions. Computational Statistics, 22(3): 481{496, Sep 2007. ISSN 1613-9658. doi: 10.1007/s00180-007-0053-0. URL https: //doi.org/10.1007/s00180-007-0053-0.Dai, W. and Genton, M. Directional outlyingness for multivariate functional data. Computational Statistics and Data Analysis, 131:50 { 65, 2019. ISSN 0167-9473. doi: https://doi.org/10.1016/j.csda.2018.03.017. URL http://www.sciencedirect. com/science/article/pii/S016794731830077X. High-dimensional and functional data analysis.Fass o, A., Toccu, M., and Magno, M. Functional control charts and health monitoring of steam sterilizers. Quality and Reliability Engineering International, 32(6):2081{2091, 2016.Ferraty, F. and Vieu, P. Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics. Springer New York, 2010. ISBN 9781441921413. URL https://books.google.com.co/books?id=SlVWcgAACAAJ.Galeano, P., Joseph, E., and Lillo, R. E. The Mahalanobis distance for functional data with applications to classi cation. Technometrics, 57(2):281{291, 2015.Ghosh, M., Li, Y., Zeng, L., Zhang, Z., and Zhou, Q. Modeling multivariate pro les using gaussian process-controlled B-splines. IISE Transactions, 0(0):1{12, 2020. doi: 10.1080/ 24725854.2020.1798038. URL https://doi.org/10.1080/24725854.2020.1798038.G orecki, T., Krzy sko, M., Waszak, L., and Wo ly nski, W. Selected statistical methods of data analysis for multivariate functional data. Statistical Papers, pages 1{30, 2016.Grasso, M., Colosimo, B., and Pacella, M. Pro le monitoring via sensor fusion: The use of PCA methods for multi-channel data. International Journal of Production Research, 02 2014. doi: 10.1080/00207543.2014.916431.Guevara, R. and Vargas, J. Evaluation of process capability in multivariate nonlinear pro les. Journal of Statistical Computation and Simulation, 86(12):2411{2428, 2016.Happ, C. and Greven, S. Multivariate functional principal component analysis for data observed on di erent (dimensional) domains. Journal of the American Statisti- cal Association, 113(522):649{659, 2018. doi: 10.1080/01621459.2016.1273115. URL https://doi.org/10.1080/01621459.2016.1273115.Horv ath, L. and Kokoszka, P. Inference for Functional Data with Applications. Springer Series in Statistics. Springer New York, 2012. ISBN 9781461436546. URL https: //books.google.com.co/books?id=PGOCtgAACAAJ.Hubert, M. Data depth: Robust multivariate analysis, computational geometry and applications by Liu, R., Ser ing, R., and Souvaine, D. L. Biometrics, 64(2):655{656, 2008. doi: 10.1111/j.1541-0420.2008.01026n 6.x. URL https://onlinelibrary.wiley.com/ doi/abs/10.1111/j.1541-0420.2008.01026_6.x.Hubert, M., Rousseeuw, P., and Segaert, P. Multivariate functional outlier detection. Statistical Methods & Applications, 24:177{202, 2015.Hubert, M., Rousseeuw, P., and Segaert, P. Multivariate and functional classi cation using depth and distance. Advances in Data Analysis and Classi cation, 11(3):445{466, Sep 2017. ISSN 1862-5355. doi: 10.1007/s11634-016-0269-3. URL https://doi.org/10. 1007/s11634-016-0269-3.Ieva, F. and Paganoni, A. M. Depth measures for multivariate functional data. Com- munications in Statistics - Theory and Methods, 42(7):1265{1276, 2013. doi: 10.1080/ 03610926.2012.746368. URL https://doi.org/10.1080/03610926.2012.746368.Jacques, J. and Preda, C. Model-based clustering for multivariate functional data. Compu- tational Statistics & Data Analysis, 71:92{106, 2014.Jahani, S., Kontar, R., Veeramani, D., and Zhou, S. Statistical monitoring of multiple pro les simultaneously using gaussian processes. Quality and Reliability Engi- neering International, 34(8):1510{1529, 2018. doi: 10.1002/qre.2326. URL https: //onlinelibrary.wiley.com/doi/abs/10.1002/qre.2326.Jones-Farmer, L. A., Woodall, W. H., Steiner, S. H., and Champ, C. W. An overview of Phase I analysis for process improvement and monitoring. Journal of Qua- lity Technology, 46(3):265{280, 2014. doi: 10.1080/00224065.2014.11917969. URL https://doi.org/10.1080/00224065.2014.11917969.Kang, L. and Albin, S. L. On-line monitoring when the process yields a linear pro le. Journal of Quality Technology, 32(4):418, 2000.Kokoszka, P. and Reimherrm, M. Introduction to Functional Data Analysis. Chapman & Hall / CRC numerical analysis and scienti c computing. CRC Press, 2017. ISBN 9781498746342. URL https://books.google.com.co/books?id=HIxIvgAACAAJ.Li, Z., Dai, Y., and Wang, Z. Multivariate change point control chart based on data depth for Phase I analysis. Communications in Statistics - Simulation and Computation, 43 (6):1490{1507, 2014. doi: 10.1080/03610918.2012.735319. URL https://doi.org/10. 1080/03610918.2012.735319.Liu, R. Y., Parelius, J. M., and Singh, K. Multivariate analysis by data depth: descriptive statistics, graphics and inference, (with discussion and a rejoinder by liu and singh). Ann. Statist., 27(3):783{858, 06 1999. doi: 10.1214/aos/1018031260. URL https:// doi.org/10.1214/aos/1018031260.L opez-Pintado, S. and Romo, J. On the concept of depth for functional data. Journal of the American Statistical Association, 104(486):718{734, 2009. doi: 10.1198/jasa.2009.0108. URL https://doi.org/10.1198/jasa.2009.0108.Lowry, C. A., Woodall, W. H., Champ, C. W., and Rigdon, S. E. A multivariate exponentially weighted moving average control chart. Technometrics, 34(1):46{53, 1992.Maleki, M., Amiri, A., and Castagliola, P. An overview on recent pro le monitoring papers (2008-2018) based on conceptual classi cation scheme. Computers & Industrial Engineering, 126:705 { 728, 2018. ISSN 0360-8352.Montgomery, D. C. Introduction to statistical quality control. John Wiley & Sons, 2007.Munck, L., Norgaard, L., Engelsen, S., Bro, R., and Andersson, C. Chemometrics in food science-a demonstration of the feasibility of a highly exploratory, inductive evaluation strategy of fundamental scienti c signi cance. Chemometrics and Intelligent Laboratory Systems, 44(1):31{60, 1998. ISSN 0169-7439. doi: https://doi.org/10.1016/ S0169-7439(98)00074-4. URL https://www.sciencedirect.com/science/article/ pii/S0169743998000744.Noorossana, R., Saghaei, A., and Amiri, A. Statistical analysis of pro le monitoring, volume 865. John Wiley & Sons, 2011.Pan, J.-N., Li, C.-I., and Lu, M. Z. Detecting the process changes for multivariate nonlinear pro le data. Quality and Reliability Engineering International, 35(6):1890{1910, 2019. doi: 10.1002/qre.2482. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/ qre.2482.Paynabar, K., Zou, C., and Qiu, P. A change-point approach for Phase-I analysis in multivariate pro le monitoring and diagnosis. Technometrics, 58(2):191{204, 2016. doi: 10.1080/00401706.2015.1042168. URL https://doi.org/10.1080/00401706.2015. 1042168.Pe~na, D. An alisis multivariante de datos. McGraw-Hill Interamericana de Espa~na S.L., 2002. ISBN 9788448136109.Pignatiello, J. J. and Runger, G. C. Comparisons of multivariate cusum charts. Journal of quality technology, 22(3):173{186, 1990.Qiu, P. Introduction to statistical process control. CRC Press, 2013.Qiu, P., Zou, C., and Wang, Z. Nonparametric pro le monitoring by mixed e ects modeling. Technometrics, 52(3):265{277, 2010.R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2016. URL https://www.R-project.org/.Ramsay, J. and Silverman, B. Functional data analysis. Springer Series in Statistics. Springer, 2ed edition, 2005. ISBN 038740080X,9780387400808.Schabenberger, O. and Pierce, F. J. Contemporary statistical models for the plant and soil sciences. CRC press, 2001.Sheu, S. H., Ouyoung, C. W., and Hsu, T. S. Phase II statistical process control for functional data. Journal of Statistical Computation and Simulation, 83(11):2144{2159, 2013.Shiau, J.-J. H., Huang, H.-L., Lin, S.-H., and Tsai, M.-Y. Monitoring nonlinear pro les with random e ects by nonparametric regression. Communications in Statistics Theory and Methods, 38(10):1664{1679, 2009.Tarabelloni, N., Biasi, R., Paganoni, A., and Ieva, F. Multivariate functional data depth measure based on variance-covariance operators. 07 2014.Wang, K. and Tsung, F. Hierarchical sparse functional principal component analysis for multistage multivariate pro le data. IISE Transactions, 0(0):1{16, 2020. doi: 10.1080/ 24725854.2020.1738599. URL https://doi.org/10.1080/24725854.2020.1738599.Wang, Y., Mei, Y., and Paynabar, K. Thresholded multivariate principal component analysis for Phase I multichannel pro le monitoring. Technometrics, 0(0):1{13, 2018. doi: 10.1080/00401706.2017.1375993. URL https://doi.org/10.1080/00401706.2017. 1375993.Williams, J. D., Woodall, W. H., and Birch, J. B. Statistical monitoring of nonlinear product and process quality pro les. Quality and Reliability Engineering International, 23(8):925{941, 2007.Yeh, A. B., Huwang, L., and Li, Y.-M. Pro le monitoring for a binary response. IIE Transactions, 41(11):931{941, 2009.Zhang, C., Yan, H., Lee, S., and Shi, J. Weakly correlated pro le monitoring based on sparse multi-channel functional principal component analysis. IISE Transactions, 50 (10):878{891, 2018. doi: 10.1080/24725854.2018.1451012. URL https://doi.org/10. 1080/24725854.2018.1451012Zhang, J., Ren, H., Yao, R., Zou, C., and Wang, Z. Phase I analysis of multivariate pro les based on regression adjustment. Comput. Ind. Eng., 85(C):132{144, July 2015. ISSN 0360-8352. doi: 10.1016/j.cie.2015.02.025. URL http://dx.doi.org/10.1016/j.cie. 2015.02.025.Zou, C., Tsung, F., and Wang, Z. Monitoring pro les based on nonparametric regression methods. Technometrics, 50(4):512{526, 2008. doi: 10.1198/004017008000000433. URL https://doi.org/10.1198/004017008000000433.Zou, C., Wang, Z., and Tsung, F. A spatial rank-based multivariate EWMA control chart. Naval Research Logistics (NRL), 59(2):91{110, 2012.Público generalLICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/80801/1/license.txt8153f7789df02f0a4c9e079953658ab2MD51ORIGINAL1073161990.2021.pdf1073161990.2021.pdfTesis de Maestría en Ciencias - Estadísticaapplication/pdf1144364https://repositorio.unal.edu.co/bitstream/unal/80801/3/1073161990.2021.pdf1881e26c63e26e36e637fedc05547db0MD53THUMBNAIL1073161990.2021.pdf.jpg1073161990.2021.pdf.jpgGenerated Thumbnailimage/jpeg3989https://repositorio.unal.edu.co/bitstream/unal/80801/4/1073161990.2021.pdf.jpgdd96df4377b5a9269a7984f4235af9c1MD54unal/80801oai:repositorio.unal.edu.co:unal/808012024-08-02 23:10:33.855Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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 |