Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales
En el control estadístico de procesos caracterizados por una relación funcional entre dos variables, el supuesto de independencia entre las observaciones de un mismo perfil o entre perfiles es de uso recurrente en una gran cantidad de aplicaciones. La rápida obtención de información, la inercia de l...
- Autores:
-
Cardenas Pineda, David Humberto
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/80213
- Palabra clave:
- 510 - Matemáticas
Análisis multivariante
Multivariate analysis
Functional time series
Control charts
Nonlinear profiles
Functional data
Cartas de Control
Datos Funcionales
Perfiles no Lineales
Series de Tiempo Funcionales
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
| id |
UNACIONAL2_3591e40f4fbc65fb6ed6416ebd5f0730 |
|---|---|
| oai_identifier_str |
oai:repositorio.unal.edu.co:unal/80213 |
| 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 con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales |
| dc.title.translated.eng.fl_str_mv |
Phase II monitoring of nonlinear profiles with temporal dependece using a functional data analysis approach |
| title |
Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales |
| spellingShingle |
Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales 510 - Matemáticas Análisis multivariante Multivariate analysis Functional time series Control charts Nonlinear profiles Functional data Cartas de Control Datos Funcionales Perfiles no Lineales Series de Tiempo Funcionales |
| title_short |
Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales |
| title_full |
Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales |
| title_fullStr |
Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales |
| title_full_unstemmed |
Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales |
| title_sort |
Monitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionales |
| dc.creator.fl_str_mv |
Cardenas Pineda, David Humberto |
| dc.contributor.advisor.none.fl_str_mv |
Guevara Gonzáles, Ruben Darío Calderón Villanueva, Sergio Alejandro |
| dc.contributor.author.none.fl_str_mv |
Cardenas Pineda, David Humberto |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas |
| topic |
510 - Matemáticas Análisis multivariante Multivariate analysis Functional time series Control charts Nonlinear profiles Functional data Cartas de Control Datos Funcionales Perfiles no Lineales Series de Tiempo Funcionales |
| dc.subject.lemb.spa.fl_str_mv |
Análisis multivariante |
| dc.subject.lemb.eng.fl_str_mv |
Multivariate analysis |
| dc.subject.proposal.eng.fl_str_mv |
Functional time series Control charts Nonlinear profiles Functional data |
| dc.subject.proposal.spa.fl_str_mv |
Cartas de Control Datos Funcionales Perfiles no Lineales Series de Tiempo Funcionales |
| description |
En el control estadístico de procesos caracterizados por una relación funcional entre dos variables, el supuesto de independencia entre las observaciones de un mismo perfil o entre perfiles es de uso recurrente en una gran cantidad de aplicaciones. La rápida obtención de información, la inercia de los procedimientos, entre otras causas, propician la violación del anterior supuesto, causando que una proporción considerable de los esquemas de control típicos se presenten como inadecuados. En este trabajo se plantea una propuesta de control para el monitoreo de perfiles no lineales en fase II, vistos como realizaciones de procesos temporales estacionarios en espacios funcionales, mediante un enfoque desde el análisis de datos funcionales. A través de un estudio de simulación el desempeño de la propuesta se evalúa. Además, se ilustra su aplicación usando datos industriales para el monitoreo de perfiles de temperatura en hornos industriales. (Texto tomado de la fuente) |
| publishDate |
2020 |
| dc.date.issued.none.fl_str_mv |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2021-09-16T15:01:04Z |
| dc.date.available.none.fl_str_mv |
2021-09-16T15:01:04Z |
| 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/80213 |
| 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/80213 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 |
Alshraideh, H. & Runger, G. (2014), “Process monitoring using hidden markov models”, Quality and Reliability Engineering International 30(8), 1379-1387. Alwan, L. C. & Roberts, H. V. (1988), “Time-series modeling for statistical process control”, Journal of Business and Economic Statistics 6(1), 87-95. Atienza, O. O., Tang, L. C. & Ang, B. W. (2002), “A CUSUM scheme for autocorrelated observations”, Journal of Quality Technology 34(2), 187-199. URL: https://doi.org/10.1080/00224065.2002.11980145 Aue, A., Norinho, D. D. & Hörmann, S. (2015), “On the prediction of stationary functional time series”, Journal of the American Statistical Association 110(509), 378-392. URL: https://www.tandfonline.com/doi/abs/10.1080/01621459.2014.909317 Bosq, D. (2000), Linear Processes in Function Spaces Theory and Applications, Springer. Box, G. E. P. & Jenkins, G. M. (1976), Time Series Analysis Forecasting and Control., Holden-Day series in time series analysis and digital processing, Holden-Day. Chakraborti, S. (2000), “Run length, average run length and false alarm rate of shewhart x-bar chart: Exact derivations by conditioning”, Communications in Statistics Part B: Simulation and Computation 29(1), 61-81. URL: https://doi.org/10.1080/03610910008813602 Chakraborti, S. (2007), “Run length distribution and percentiles: The shewhart X-bar chart with unknown parameters”, Quality Engineering 19(2), 119-127. URL: https://doi.org/10.1080/08982110701276653 Champ, C. W. & Woodall, W. H. (1987), “Exact results for shewhart control charts with supplementary runs rules”, Technometrics 29(4), 393-399. URL: https://www.tandfonline.com/doi/abs/10.1080/00401706.1987.10488266 Cheng, T., Hsieh, P. & Yang, S. (2014), “Process Control for the Vector Autoregressive Model”, Quality and Reability Engieneering International 30, 57-81 Chiang, J. Y., Lio, Y. L. & Tsai, T. R. (2017), “MEWMA Control Chart and Process Capability Indices for Simple Linear Profiles with Within-profile Autocorrelation”, Quality and Reliability Engineering International 33(5), 1083-1094. Chuang, S. C., Hung, Y. C., Tsai, W. C. & Yang, S. F. (2013), “A framework for nonparametric profile monitoring”, Computers and Industrial Engineering 64(1), 482-491. URL: http://www.sciencedirect.com/science/article/pii/S0360835212002057 Dawod, A., Riaz, M. & Abbasi, S. (2017), “On model selection for autocorrelated processes in statistical process control”, Quality Reliability Engineering International 33, 867-882. De Ketelaere, B., Rato, T., Schmitt, E. & Hubert, M. (2016), “Statistical process monitoring of time-dependent data”, Quality Engineering 28(1), 127-142. Didericksen, D., Kokoszka, P. & Zhang, X. (2012), “Empirical properties of forecast with the functional autoregressive model”, Comput Stat 27(2), 285-298. Faltin, W., Mastrangelo, C., Runger, G. & Ryan, T. (1997), “Considerations in monitoring of autocorrelated and independent data”, Journal of Quality Technology 29(2), 131-133. Fraiman, R. & Muniz, G. (2001), “Trimmed means for functional data”, Test 10(2), 419- 440. Gabrys, R. & Kokoszka, P. (2007), “Portmanteau test of independence for functional observations”, Journal of the American Statistical Association 102(480), 1338-1348. Garthoff, R. & Schmid, W. (2015), “Control charts for multivariate nonlinear time series”, REVSTAT 13(2), 131-144. Garthoff, R. & Schmid, W. (2017), “Monitoring means and covariances of multivariate non linear time series with heavy tails”, Communications in Statistics - Theory and Methods 46(21), 10394-10415. URL: https://doi.org/10.1080/03610926.2015.1085567 Gohberg, Y., Goldberg, S. & Kaashoek, M. A. (1993), Classes of linear operators: advances and applications, Vol. 59, Birkhäuser. Goma, A. & Birch, J. (2019), “A semiparametric nonlinear mixed model approach to phase I profiles monitoring”, Communications in Statistics - Simulation and Computation 48(6), 1677-1693. Haridy, S. & Zhang, W. (2009), “Univariate and multiariate control charts for monitoring dynamic-behavior processes: a case study”, Journal of Industrial Engineering and Management 2(3), 464-498. Hauck, D. J., Runger, G. C. & Montgomery, D. C. (1999), “Multivariate statistical process monitoring and diagnosis with grouped regression-adjusted variables”, Communications in Statistics Part B: Simulation and Computation 28(2), 309-328. URL: https://www.tandfonline.com/doi/abs/10.1080/03610919908813551 Hörmann, S., Kidzi, L. & Hallin, M. (2015), “Dynamic functional principal components”, Journal of the Royal Statistical Society. Series B: Statistical Methodology 77(2), 319- 348. URL: http://doi.wiley.com/10.1111/rssb.12076 Hörmann, S. & Kidzinski, L. (2015), “A note on estimation in hilbertian linear models”, Scandinavian Journal of Statistics 42(1), 43-62. URL: http://doi.wiley.com/10.1111/sjos.12094 Hörmann, S. & Kokoszka, P. (2010), “Weakly dependent functional data”, Annals of Sta- tistics 38(3), 1845-1884. URL: https://projecteuclid.org/euclid.aos/1269452656 Horváth, L. & Kokoszka, P. (2012), Inference for Functional Data with Applications, Springer. Horváth, L., Kokoszka, P. & Rice, G. (2014), “Testing stationarity of functional time series”, Journal of Econometrics 179(1), 66-82. URL: http://www.sciencedirect.com/science/article/pii/S0304407613002327 Human, S. W., Kritzinger, P. & Chakraborti, S. (2011), “Robustness of the EWMA control chart for individual observations”, Journal of Applied Statistics 38(10), 2071-2087. URL: https://doi.org/10.1080/02664763.2010.545114 Hyndman, R. J. & Shahid Ullah, M. (2007), “Robust forecasting of mortality and fertility rates: A functional data approach”, Computational Statistics and Data Analysis 51(10), 4942-4956. Jarrett, J. E. & Pan, X. (2007), “The quality control chart for monitoring multivariate autocorrelated processes”, Computational Statistics and Data Analysis 51(8), 3862-3870. Jensen, W. A. & Birch, J. B. (2011), Correlation and Autocorrelation in Profiles, in R. Noorossana, A. Saghaei & A. Amiri, eds, “Statistical Analysis of Profile Monitoring”, Wiley Series in Probability and Statistics, Jhon Wiley & Sons, Inc, chapter 9, pp. 253-268. Jensen, W. & Birch, J. (2009), “Profile monitoring via nonlinear mixed models”, Journal of Quality Technology 41(1), 18-34. Jensen, W., Birch, J. & Woodal, W. (2008), “Monitoring correlation within linear profiles using mixed models”, Journal of Quality Technology 40(2), 167-183. Jiang, W., Tsui, K. L. & Woodall, W. H. (2000), “A new SPC monitoring method: The ARMA chart”, Technometrics 42(4), 399-410. URL: http://www.jstor.org/stable/1270950 Kazemzadeh, R., Noorossana, R. & Amiri, A. (2010), “Phase II Monitoring of Autocorrelated Polynomial Profiles in AR(1) Processes”, Scientia Iranica 17(1), 12-24. Khedmati, M. & Niaki, S. T. A. (2016), “Phase II monitoring of general linear profiles in the presence of between-profile autocorrelation”, Quality and Reliability Engineering International 32(2), 443-452. Kokoszka, P. & Reimherr, M. (2017), Introduction to functional data analysis, CRC Press. Kokoszka, P. & Zhang, X. (2012), “Functional prediction of intraday cumulative returns”, Statistical Modelling 12(4), 377-398. URL: http://journals.sagepub.com/doi/10.1177/1471082X1201200404 Kramer, H. G. & Schmid, L. V. (1997), “Ewma charts for multivariate time series”, Se- quential Analysis 16(2), 131-154. URL: https://doi.org/10.1080/07474949708836378 Kunsch, H. R. (1989), “The Jackknife and the Bootstrap for General Stationary Observations”, The Annals of Statistics 17(3), 1217-1241. URL: https://doi.org/10.1214/aos/1176347265 Lawler, G. F. (2006), Introduction to Stochastic Processes, 2 edn, Taylor and Francis/CRC Press. Li, Y., Huang, M. & Pan, E. (2018), “Residual chart with hidden Markov model to monitoring the auto-correlated processes”, Journal of Shanghai Jiaotong University (Science) 83(Suppl 1), 103-108. Li, Y., Pan, E. & Xiao, Y. (2020), “On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes”, Quality and Reliability Engineering International 36(7), 2351-2369. Macgregor, J. & Harris, T. (1993), “The Exponentially Weighted Moving Variance”, Jour- nal of Quality Technology 25(2), 106-118. Maleki, M. R., Amiri, A. & Castagliola, P. (2018), “An overview on recent profile monitoring papers (2008-2018) based on conceptual classification scheme”, Computers & Industrial Engineering 126, 705-728. Mingoti, S. A., de Carvalho, J. P. & de Oliveira Lima, J. (2008), “On the estimation of serial correlation in Markov-dependent production processes”, Journal of Applied Statistics 35(7), 763-771. URL: https://doi.org/10.1080/02664760802005688 Montgomery, D. (2013), Introduction to statistical quality control, 7 edn, John Wiley & Sons. Montgomery, D. C. & Mastrangelo, C. M. (1991), “Some Statistical Process Control Methods for Autocorrelated Data”, Journal of Quality Technology 23(3), 179-193. Noorossana, R., Amiri, A. & Soleimani, P. (2008), “On the Monitoring of Autocorrelated Linear Profiles”, Communications in Statistics|Theory and Methods 37(3), 425-442. Noorossana, R., Saghaei, A. & Amiri, A. (2011), Statistical Analysis of Profile Monitoring, Wiley Series in Probability and Statistics, Jhon Wiley & Sons, Inc. Noorossana, R. & Vaghe_, S. (2006), “E_ect of autocorrelation on performance of the MCUSUM control chart”, Quality Reliability Engeenering International 22, 191-197. Osei-Aning, R., Abbasi, S. A. & Riaz, M. (2017a), “Mixed EWMA-CUSUM and mixed CUSUM-EWMA modified control charts for monitoring first order autoregressive processes”, Quality Technology and Quantitative Management 14(4), 429-453. URL: http://dx.doi.org/10.1080/16843703.2017.1304038 Osei-Aning, R., Abbasi, S. A. & Riaz, M. (2017b), “Monitoring of serially correlated processes using residual control charts”, Scientia Iranica 24(3), 1603-1614. Pan, J.-N. & Chen, S.-T. (2008), “Monitoring long-memory air quality data using ARFIMA model”, Environmetrics 19(2), 209-219. Pan, X. & Jarret, J. (2007), “Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation”, International journal of production economics 106, 204-216. Paynabar, K. & Jin, J. (2011), “Characterization of non-linear profiles variations using mixed-effect models and wavelets”, IIE Transactions (Institute of Industrial Engineers) 43(4), 275-290. Pilavakis, D., Paparoditis, E. & Sapatinas, T. (2019), “Moving block and tapered block bootstrap for functional time series with an application to the Ksample mean problem”, Bernoulli 25(4B), 3496-3526. URL: https://doi.org/10.3150/18-BEJ1099 Psarakis, S. & Papaleonida, G. E. A. (2007), “SPC Procedures for Monitoring Autocorrelated Processes”, Quality Technology & Quantitative Management 4(4), 501-540. Qiu, P. (2013), Introduction to statistical process control, CRC Press. Qiu, P., Zou, C. & Wang, Z. (2010), “Nonparametric profile monitoring by mixed effects modeling”, Technometrics 52(3), 265-277. Ramsay, J. & Silverman, B. W. (2005), Functional Data Analysis, Springer Series in Statistics, Springer. Reynolds, M. R., Arnold, J. C. & Baik, J. W. (1996), “Variable sampling interval X charts in the presence of correlation”, Journal of Quality Technology 28(1), 12-30. URL: https://doi.org/10.1080/00224065.1996.11979633 Roberts, S. W. (1959), “Control chart tests based on geometric moving averages”, Techno- metrics 1(3), 239-250. URL: https://www.tandfonline.com/doi/abs/10.1080/00401706.1959.10489860 Ryan, T. P. (2011), Statistical Methods for Quality Improvement: Third Edition, 3 edn, John Wiley & Sons. Sheu, S. H., Ouyoung, C. W. & Hsu, T. S. (2013), “Phase II statistical process control for functional data”, Journal of Statistical Computation and Simulation 83(11), 2144-2159. Shiau, J.-J. H. & Ya-Chen, H. (2005), “Robustness of the EWMA Control Chart to Nonnormality for Autocorrelated Processes”, Quality Technology & Quantitative Management 2(2), 125-146. URL: https://doi.org/10.1080/16843703.2005.11673089 Shongwe, S. & Malela-Majika, J. (2019), “Shewhart-type monitoring schemes with suplementary w-of-w run-rules to monitor the mean of autocorrelated samples”, Communications in Statistics - Simulation and Computation pp. 1-30. Siddiqui, Z. & Abdel-Salam, A. S. G. (2019), “A semiparametric profile monitoring via residuals”, Quality and Reliability Engineering International 35(4), 959-977. Steiner, S., Jensen, W. A., Grimshaw, S. D. & Espen, B. (2016), “Nonlinear profile monitoring for oven-temperature data”, Journal of Quality Technology 48(1), 84-97. Tang, L. C. & Cheong, W. T. (2006), “A control scheme for high-yield correlated production under group inspection”, Journal of Quality Technology 38(1), 45-55. URL: https://doi.org/10.1080/00224065.2006.11918583 Vanbrackle, L. N. & Reynolds, M. R. J. (1997), “EWMA and CUSUM control charts in the presence of correlation”, Communications in Statistics - Simulation and Computation 26(3), 979-1008. URL: https://doi.org/10.1080/03610919708813421 Walker, E. & Wright, S. P. (2002), “Comparing curves using additive models”, Journal of Quality Technology 34(1), 118-129. Wang, H., Kim, S. H., Huo, X., Hur, Y. & Wilson, J. R. (2015), “Monitoring nonlinear profiles adaptively with a wavelet-based distribution-free CUSUM chart”, International Journal of Production Research 53(15), 4648-4667. URL: http://dx.doi.org/10.1080/00207543.2015.1029085 Wardell, D., Moskowitz, H. & Plante, R. (1994), “Control charts in the presence of data autocorrelation”, Management Science 38(8), 1084-1105. Williams, J. D. (2011), Parametric Nonlinear Profiles, in R. Noorossana, A. Saghaei & A. Amiri, eds, “Statistical Analysis of Profile Monitoring”, Wiley Series in Probability and Statistics, Jhon Wiley & Sons, Inc, chapter 5, pp. 129-156. Woodall, W. (2017), “Bridging the gap between theory and practice in basic statistical process monitoring”, Quality Engineering 29(1), 2-15. Woodall, W. H. (2007), “Current research on profile monitoring”, Producao 17(3), 420-425. Woodall, W. H. & Montgomery, D. C. (1999), “Research Issues and Ideas in Statistical Process Control”, Journal of Quality Technology 31(4), 376-386. URL: https://doi.org/10.1080/00224065.1999.11979944 Zhang, J., Ren, H., Yao, R., Zou, C. & Wang, Z. (2015), “Phase I analysis of multivariate profiles based on regression adjustment”, Computers and Industrial Engineering 85, 132- 144. URL: http://www.sciencedirect.com/science/article/pii/S0360835215001047 Zhang, N. (1998), “A statistical control chart for stationary process data”, Technometrics 40(1), 24-39. |
| 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 |
xv, 87 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/80213/1/license.txt https://repositorio.unal.edu.co/bitstream/unal/80213/2/1032470253.2020.pdf https://repositorio.unal.edu.co/bitstream/unal/80213/3/1032470253.2020.pdf.jpg |
| bitstream.checksum.fl_str_mv |
cccfe52f796b7c63423298c2d3365fc6 270cee843a6015e70086d9598768793e 9fc9097c937d493bb87556029223db23 |
| 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_ |
1814089419460706304 |
| spelling |
Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Guevara Gonzáles, Ruben Daríoaa42312186461230e87a1ebb140b3710Calderón Villanueva, Sergio Alejandro4435821363acfcc5a0b97c50464db9d4Cardenas Pineda, David Humberto5b04117d4deaf838a59cfbe2583d48a42021-09-16T15:01:04Z2021-09-16T15:01:04Z2020https://repositorio.unal.edu.co/handle/unal/80213Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/En el control estadístico de procesos caracterizados por una relación funcional entre dos variables, el supuesto de independencia entre las observaciones de un mismo perfil o entre perfiles es de uso recurrente en una gran cantidad de aplicaciones. La rápida obtención de información, la inercia de los procedimientos, entre otras causas, propician la violación del anterior supuesto, causando que una proporción considerable de los esquemas de control típicos se presenten como inadecuados. En este trabajo se plantea una propuesta de control para el monitoreo de perfiles no lineales en fase II, vistos como realizaciones de procesos temporales estacionarios en espacios funcionales, mediante un enfoque desde el análisis de datos funcionales. A través de un estudio de simulación el desempeño de la propuesta se evalúa. Además, se ilustra su aplicación usando datos industriales para el monitoreo de perfiles de temperatura en hornos industriales. (Texto tomado de la fuente)In the statistical control of processes characterized by functional relationships between two variables the independence assumption of observations within a profile or between profiles is commonly used in most of applications. Flows of data at higher speeds, procedures inertia, among other causes, leads to a violation of the former assumption, driving a considerable amount of control schemes to be classified as inadequate. In this thesis, a control schema is proposed for phase II monitoring of nonlinear profiles, treated as realizations of stationary functional processes, using a functional data analysis approach. Through simulation studies the proposal performance is accessed, furthermore, its use is explained within an industrial application in profile monitoring of industrial ovens temperature.MaestríaMagíster en Ciencias - Estadísticaxv, 87 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - EstadísticaDepartamento de EstadísticaFacultad de CienciasBogotá - ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - MatemáticasAnálisis multivarianteMultivariate analysisFunctional time seriesControl chartsNonlinear profilesFunctional dataCartas de ControlDatos FuncionalesPerfiles no LinealesSeries de Tiempo FuncionalesMonitoreo de perfiles no lineales con dependencia temporal en fase II desde un enfoque del análisis de datos funcionalesPhase II monitoring of nonlinear profiles with temporal dependece using a functional data analysis approachTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAlshraideh, H. & Runger, G. (2014), “Process monitoring using hidden markov models”, Quality and Reliability Engineering International 30(8), 1379-1387.Alwan, L. C. & Roberts, H. V. (1988), “Time-series modeling for statistical process control”, Journal of Business and Economic Statistics 6(1), 87-95.Atienza, O. O., Tang, L. C. & Ang, B. W. (2002), “A CUSUM scheme for autocorrelated observations”, Journal of Quality Technology 34(2), 187-199. URL: https://doi.org/10.1080/00224065.2002.11980145Aue, A., Norinho, D. D. & Hörmann, S. (2015), “On the prediction of stationary functional time series”, Journal of the American Statistical Association 110(509), 378-392. URL: https://www.tandfonline.com/doi/abs/10.1080/01621459.2014.909317Bosq, D. (2000), Linear Processes in Function Spaces Theory and Applications, Springer.Box, G. E. P. & Jenkins, G. M. (1976), Time Series Analysis Forecasting and Control., Holden-Day series in time series analysis and digital processing, Holden-Day.Chakraborti, S. (2000), “Run length, average run length and false alarm rate of shewhart x-bar chart: Exact derivations by conditioning”, Communications in Statistics Part B: Simulation and Computation 29(1), 61-81. URL: https://doi.org/10.1080/03610910008813602Chakraborti, S. (2007), “Run length distribution and percentiles: The shewhart X-bar chart with unknown parameters”, Quality Engineering 19(2), 119-127. URL: https://doi.org/10.1080/08982110701276653Champ, C. W. & Woodall, W. H. (1987), “Exact results for shewhart control charts with supplementary runs rules”, Technometrics 29(4), 393-399. URL: https://www.tandfonline.com/doi/abs/10.1080/00401706.1987.10488266Cheng, T., Hsieh, P. & Yang, S. (2014), “Process Control for the Vector Autoregressive Model”, Quality and Reability Engieneering International 30, 57-81Chiang, J. Y., Lio, Y. L. & Tsai, T. R. (2017), “MEWMA Control Chart and Process Capability Indices for Simple Linear Profiles with Within-profile Autocorrelation”, Quality and Reliability Engineering International 33(5), 1083-1094.Chuang, S. C., Hung, Y. C., Tsai, W. C. & Yang, S. F. (2013), “A framework for nonparametric profile monitoring”, Computers and Industrial Engineering 64(1), 482-491. URL: http://www.sciencedirect.com/science/article/pii/S0360835212002057Dawod, A., Riaz, M. & Abbasi, S. (2017), “On model selection for autocorrelated processes in statistical process control”, Quality Reliability Engineering International 33, 867-882.De Ketelaere, B., Rato, T., Schmitt, E. & Hubert, M. (2016), “Statistical process monitoring of time-dependent data”, Quality Engineering 28(1), 127-142.Didericksen, D., Kokoszka, P. & Zhang, X. (2012), “Empirical properties of forecast with the functional autoregressive model”, Comput Stat 27(2), 285-298.Faltin, W., Mastrangelo, C., Runger, G. & Ryan, T. (1997), “Considerations in monitoring of autocorrelated and independent data”, Journal of Quality Technology 29(2), 131-133.Fraiman, R. & Muniz, G. (2001), “Trimmed means for functional data”, Test 10(2), 419- 440.Gabrys, R. & Kokoszka, P. (2007), “Portmanteau test of independence for functional observations”, Journal of the American Statistical Association 102(480), 1338-1348.Garthoff, R. & Schmid, W. (2015), “Control charts for multivariate nonlinear time series”, REVSTAT 13(2), 131-144.Garthoff, R. & Schmid, W. (2017), “Monitoring means and covariances of multivariate non linear time series with heavy tails”, Communications in Statistics - Theory and Methods 46(21), 10394-10415. URL: https://doi.org/10.1080/03610926.2015.1085567Gohberg, Y., Goldberg, S. & Kaashoek, M. A. (1993), Classes of linear operators: advances and applications, Vol. 59, Birkhäuser.Goma, A. & Birch, J. (2019), “A semiparametric nonlinear mixed model approach to phase I profiles monitoring”, Communications in Statistics - Simulation and Computation 48(6), 1677-1693.Haridy, S. & Zhang, W. (2009), “Univariate and multiariate control charts for monitoring dynamic-behavior processes: a case study”, Journal of Industrial Engineering and Management 2(3), 464-498.Hauck, D. J., Runger, G. C. & Montgomery, D. C. (1999), “Multivariate statistical process monitoring and diagnosis with grouped regression-adjusted variables”, Communications in Statistics Part B: Simulation and Computation 28(2), 309-328. URL: https://www.tandfonline.com/doi/abs/10.1080/03610919908813551Hörmann, S., Kidzi, L. & Hallin, M. (2015), “Dynamic functional principal components”, Journal of the Royal Statistical Society. Series B: Statistical Methodology 77(2), 319- 348. URL: http://doi.wiley.com/10.1111/rssb.12076Hörmann, S. & Kidzinski, L. (2015), “A note on estimation in hilbertian linear models”, Scandinavian Journal of Statistics 42(1), 43-62. URL: http://doi.wiley.com/10.1111/sjos.12094Hörmann, S. & Kokoszka, P. (2010), “Weakly dependent functional data”, Annals of Sta- tistics 38(3), 1845-1884. URL: https://projecteuclid.org/euclid.aos/1269452656Horváth, L. & Kokoszka, P. (2012), Inference for Functional Data with Applications, Springer. Horváth, L., Kokoszka, P. & Rice, G. (2014), “Testing stationarity of functional time series”, Journal of Econometrics 179(1), 66-82. URL: http://www.sciencedirect.com/science/article/pii/S0304407613002327Human, S. W., Kritzinger, P. & Chakraborti, S. (2011), “Robustness of the EWMA control chart for individual observations”, Journal of Applied Statistics 38(10), 2071-2087. URL: https://doi.org/10.1080/02664763.2010.545114Hyndman, R. J. & Shahid Ullah, M. (2007), “Robust forecasting of mortality and fertility rates: A functional data approach”, Computational Statistics and Data Analysis 51(10), 4942-4956.Jarrett, J. E. & Pan, X. (2007), “The quality control chart for monitoring multivariate autocorrelated processes”, Computational Statistics and Data Analysis 51(8), 3862-3870.Jensen, W. A. & Birch, J. B. (2011), Correlation and Autocorrelation in Profiles, in R. Noorossana, A. Saghaei & A. Amiri, eds, “Statistical Analysis of Profile Monitoring”, Wiley Series in Probability and Statistics, Jhon Wiley & Sons, Inc, chapter 9, pp. 253-268.Jensen, W. & Birch, J. (2009), “Profile monitoring via nonlinear mixed models”, Journal of Quality Technology 41(1), 18-34.Jensen, W., Birch, J. & Woodal, W. (2008), “Monitoring correlation within linear profiles using mixed models”, Journal of Quality Technology 40(2), 167-183.Jiang, W., Tsui, K. L. & Woodall, W. H. (2000), “A new SPC monitoring method: The ARMA chart”, Technometrics 42(4), 399-410. URL: http://www.jstor.org/stable/1270950Kazemzadeh, R., Noorossana, R. & Amiri, A. (2010), “Phase II Monitoring of Autocorrelated Polynomial Profiles in AR(1) Processes”, Scientia Iranica 17(1), 12-24.Khedmati, M. & Niaki, S. T. A. (2016), “Phase II monitoring of general linear profiles in the presence of between-profile autocorrelation”, Quality and Reliability Engineering International 32(2), 443-452.Kokoszka, P. & Reimherr, M. (2017), Introduction to functional data analysis, CRC Press.Kokoszka, P. & Zhang, X. (2012), “Functional prediction of intraday cumulative returns”, Statistical Modelling 12(4), 377-398. URL: http://journals.sagepub.com/doi/10.1177/1471082X1201200404Kramer, H. G. & Schmid, L. V. (1997), “Ewma charts for multivariate time series”, Se- quential Analysis 16(2), 131-154. URL: https://doi.org/10.1080/07474949708836378Kunsch, H. R. (1989), “The Jackknife and the Bootstrap for General Stationary Observations”, The Annals of Statistics 17(3), 1217-1241. URL: https://doi.org/10.1214/aos/1176347265Lawler, G. F. (2006), Introduction to Stochastic Processes, 2 edn, Taylor and Francis/CRC Press.Li, Y., Huang, M. & Pan, E. (2018), “Residual chart with hidden Markov model to monitoring the auto-correlated processes”, Journal of Shanghai Jiaotong University (Science) 83(Suppl 1), 103-108.Li, Y., Pan, E. & Xiao, Y. (2020), “On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes”, Quality and Reliability Engineering International 36(7), 2351-2369.Macgregor, J. & Harris, T. (1993), “The Exponentially Weighted Moving Variance”, Jour- nal of Quality Technology 25(2), 106-118.Maleki, M. R., Amiri, A. & Castagliola, P. (2018), “An overview on recent profile monitoring papers (2008-2018) based on conceptual classification scheme”, Computers & Industrial Engineering 126, 705-728.Mingoti, S. A., de Carvalho, J. P. & de Oliveira Lima, J. (2008), “On the estimation of serial correlation in Markov-dependent production processes”, Journal of Applied Statistics 35(7), 763-771. URL: https://doi.org/10.1080/02664760802005688Montgomery, D. (2013), Introduction to statistical quality control, 7 edn, John Wiley & Sons.Montgomery, D. C. & Mastrangelo, C. M. (1991), “Some Statistical Process Control Methods for Autocorrelated Data”, Journal of Quality Technology 23(3), 179-193.Noorossana, R., Amiri, A. & Soleimani, P. (2008), “On the Monitoring of Autocorrelated Linear Profiles”, Communications in Statistics|Theory and Methods 37(3), 425-442.Noorossana, R., Saghaei, A. & Amiri, A. (2011), Statistical Analysis of Profile Monitoring, Wiley Series in Probability and Statistics, Jhon Wiley & Sons, Inc.Noorossana, R. & Vaghe_, S. (2006), “E_ect of autocorrelation on performance of the MCUSUM control chart”, Quality Reliability Engeenering International 22, 191-197.Osei-Aning, R., Abbasi, S. A. & Riaz, M. (2017a), “Mixed EWMA-CUSUM and mixed CUSUM-EWMA modified control charts for monitoring first order autoregressive processes”, Quality Technology and Quantitative Management 14(4), 429-453. URL: http://dx.doi.org/10.1080/16843703.2017.1304038Osei-Aning, R., Abbasi, S. A. & Riaz, M. (2017b), “Monitoring of serially correlated processes using residual control charts”, Scientia Iranica 24(3), 1603-1614.Pan, J.-N. & Chen, S.-T. (2008), “Monitoring long-memory air quality data using ARFIMA model”, Environmetrics 19(2), 209-219.Pan, X. & Jarret, J. (2007), “Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation”, International journal of production economics 106, 204-216.Paynabar, K. & Jin, J. (2011), “Characterization of non-linear profiles variations using mixed-effect models and wavelets”, IIE Transactions (Institute of Industrial Engineers) 43(4), 275-290.Pilavakis, D., Paparoditis, E. & Sapatinas, T. (2019), “Moving block and tapered block bootstrap for functional time series with an application to the Ksample mean problem”, Bernoulli 25(4B), 3496-3526. URL: https://doi.org/10.3150/18-BEJ1099Psarakis, S. & Papaleonida, G. E. A. (2007), “SPC Procedures for Monitoring Autocorrelated Processes”, Quality Technology & Quantitative Management 4(4), 501-540.Qiu, P. (2013), Introduction to statistical process control, CRC Press.Qiu, P., Zou, C. & Wang, Z. (2010), “Nonparametric profile monitoring by mixed effects modeling”, Technometrics 52(3), 265-277.Ramsay, J. & Silverman, B. W. (2005), Functional Data Analysis, Springer Series in Statistics, Springer.Reynolds, M. R., Arnold, J. C. & Baik, J. W. (1996), “Variable sampling interval X charts in the presence of correlation”, Journal of Quality Technology 28(1), 12-30. URL: https://doi.org/10.1080/00224065.1996.11979633Roberts, S. W. (1959), “Control chart tests based on geometric moving averages”, Techno- metrics 1(3), 239-250. URL: https://www.tandfonline.com/doi/abs/10.1080/00401706.1959.10489860Ryan, T. P. (2011), Statistical Methods for Quality Improvement: Third Edition, 3 edn, John Wiley & Sons.Sheu, S. H., Ouyoung, C. W. & Hsu, T. S. (2013), “Phase II statistical process control for functional data”, Journal of Statistical Computation and Simulation 83(11), 2144-2159.Shiau, J.-J. H. & Ya-Chen, H. (2005), “Robustness of the EWMA Control Chart to Nonnormality for Autocorrelated Processes”, Quality Technology & Quantitative Management 2(2), 125-146. URL: https://doi.org/10.1080/16843703.2005.11673089Shongwe, S. & Malela-Majika, J. (2019), “Shewhart-type monitoring schemes with suplementary w-of-w run-rules to monitor the mean of autocorrelated samples”, Communications in Statistics - Simulation and Computation pp. 1-30.Siddiqui, Z. & Abdel-Salam, A. S. G. (2019), “A semiparametric profile monitoring via residuals”, Quality and Reliability Engineering International 35(4), 959-977.Steiner, S., Jensen, W. A., Grimshaw, S. D. & Espen, B. (2016), “Nonlinear profile monitoring for oven-temperature data”, Journal of Quality Technology 48(1), 84-97.Tang, L. C. & Cheong, W. T. (2006), “A control scheme for high-yield correlated production under group inspection”, Journal of Quality Technology 38(1), 45-55. URL: https://doi.org/10.1080/00224065.2006.11918583Vanbrackle, L. N. & Reynolds, M. R. J. (1997), “EWMA and CUSUM control charts in the presence of correlation”, Communications in Statistics - Simulation and Computation 26(3), 979-1008. URL: https://doi.org/10.1080/03610919708813421Walker, E. & Wright, S. P. (2002), “Comparing curves using additive models”, Journal of Quality Technology 34(1), 118-129.Wang, H., Kim, S. H., Huo, X., Hur, Y. & Wilson, J. R. (2015), “Monitoring nonlinear profiles adaptively with a wavelet-based distribution-free CUSUM chart”, International Journal of Production Research 53(15), 4648-4667. URL: http://dx.doi.org/10.1080/00207543.2015.1029085Wardell, D., Moskowitz, H. & Plante, R. (1994), “Control charts in the presence of data autocorrelation”, Management Science 38(8), 1084-1105.Williams, J. D. (2011), Parametric Nonlinear Profiles, in R. Noorossana, A. Saghaei & A. Amiri, eds, “Statistical Analysis of Profile Monitoring”, Wiley Series in Probability and Statistics, Jhon Wiley & Sons, Inc, chapter 5, pp. 129-156.Woodall, W. (2017), “Bridging the gap between theory and practice in basic statistical process monitoring”, Quality Engineering 29(1), 2-15.Woodall, W. H. (2007), “Current research on profile monitoring”, Producao 17(3), 420-425.Woodall, W. H. & Montgomery, D. C. (1999), “Research Issues and Ideas in Statistical Process Control”, Journal of Quality Technology 31(4), 376-386. URL: https://doi.org/10.1080/00224065.1999.11979944Zhang, J., Ren, H., Yao, R., Zou, C. & Wang, Z. (2015), “Phase I analysis of multivariate profiles based on regression adjustment”, Computers and Industrial Engineering 85, 132- 144. URL: http://www.sciencedirect.com/science/article/pii/S0360835215001047Zhang, N. (1998), “A statistical control chart for stationary process data”, Technometrics 40(1), 24-39.Público generalLICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/80213/1/license.txtcccfe52f796b7c63423298c2d3365fc6MD51ORIGINAL1032470253.2020.pdf1032470253.2020.pdfTesis de Maestría en Ciencias Estadísticaapplication/pdf1250121https://repositorio.unal.edu.co/bitstream/unal/80213/2/1032470253.2020.pdf270cee843a6015e70086d9598768793eMD52THUMBNAIL1032470253.2020.pdf.jpg1032470253.2020.pdf.jpgGenerated Thumbnailimage/jpeg3571https://repositorio.unal.edu.co/bitstream/unal/80213/3/1032470253.2020.pdf.jpg9fc9097c937d493bb87556029223db23MD53unal/80213oai:repositorio.unal.edu.co:unal/802132024-07-29 00:02:52.915Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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 |