Capability Analysis for Profiles

Abstract. There are practical situations in which the quality of a process or product can be better characterized by a functional relationship between a response variable and one or more explanatory variables, this is called profile. Such profiles usually can be represented adequately using linear o...

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Autores:
Guevara González, Rubén Darío
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2014
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/51332
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/51332
http://bdigital.unal.edu.co/45422/
Palabra clave:
51 Matemáticas / Mathematics
Functional Data
Functional Depth
Multivariate Functional Data
Multivariate
Functional Principal Component Analysis
Nonlinear Profiles
Process Capability Analysis
Process Capability Indices
Datos Funcionales
Profundidad Funcional
Datos Funcionales Multivariados
Análisis de Componentes Principales para Funcionales Multivariados
Perfiles no Lineales
Análisis de Capacidad de Proceso
Índices de Capacidad de Proceso
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_a4649cc28cd529e4c9b12533a31a2795
oai_identifier_str oai:repositorio.unal.edu.co:unal/51332
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Capability Analysis for Profiles
title Capability Analysis for Profiles
spellingShingle Capability Analysis for Profiles
51 Matemáticas / Mathematics
Functional Data
Functional Depth
Multivariate Functional Data
Multivariate
Functional Principal Component Analysis
Nonlinear Profiles
Process Capability Analysis
Process Capability Indices
Datos Funcionales
Profundidad Funcional
Datos Funcionales Multivariados
Análisis de Componentes Principales para Funcionales Multivariados
Perfiles no Lineales
Análisis de Capacidad de Proceso
Índices de Capacidad de Proceso
title_short Capability Analysis for Profiles
title_full Capability Analysis for Profiles
title_fullStr Capability Analysis for Profiles
title_full_unstemmed Capability Analysis for Profiles
title_sort Capability Analysis for Profiles
dc.creator.fl_str_mv Guevara González, Rubén Darío
dc.contributor.author.spa.fl_str_mv Guevara González, Rubén Darío
dc.contributor.spa.fl_str_mv Vargas Navas, José Alberto
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Functional Data
Functional Depth
Multivariate Functional Data
Multivariate
Functional Principal Component Analysis
Nonlinear Profiles
Process Capability Analysis
Process Capability Indices
Datos Funcionales
Profundidad Funcional
Datos Funcionales Multivariados
Análisis de Componentes Principales para Funcionales Multivariados
Perfiles no Lineales
Análisis de Capacidad de Proceso
Índices de Capacidad de Proceso
dc.subject.proposal.spa.fl_str_mv Functional Data
Functional Depth
Multivariate Functional Data
Multivariate
Functional Principal Component Analysis
Nonlinear Profiles
Process Capability Analysis
Process Capability Indices
Datos Funcionales
Profundidad Funcional
Datos Funcionales Multivariados
Análisis de Componentes Principales para Funcionales Multivariados
Perfiles no Lineales
Análisis de Capacidad de Proceso
Índices de Capacidad de Proceso
description Abstract. There are practical situations in which the quality of a process or product can be better characterized by a functional relationship between a response variable and one or more explanatory variables, this is called profile. Such profiles usually can be represented adequately using linear or nonlinear models. While there are several studies monitoring profiles, there are few studies to evaluate the capability of a process with profile quality characteristic, particularly if the process is characterized by a nonlinear functional relationship. This dissertation introduces methods to evaluate the capability of processes characterized by nonlinear profiles (univariate or multivariate), without distributional assumptions. We propose two methods to measure the capability of processes characterized by univariate nonlinear profiles based on the concept of functional depth. These methods extend to functional data, the Process Capability Indexes proposed by Clements for measuring the capability of a process characterized by a random variable. To evaluate the capability of processes characterized by multivariate nonlinear profiles, we consider each observation as a finite dimension vector whose elements are functions. Initially, we transform the original functional data into uncorrelated functions using a dimension reduction technique for multivariate functional data. Next, the capability for each functional component is evaluated. Two sets of process capability indices to measure the capability of these functional components are proposed, having into account if the random errors follow (or not) a multivariate normal distribution. Within case where the random errors do not follow a multivariate normal distribution, we use a method based on the concept of functional depth and apply the methods proposed for the case of univariate nonlinear profiles. Performance of the methods proposed is evaluated through simulation studies. Examples illustrate the applicability of these methods. We offer conclusions and advice for future research at the end.
publishDate 2014
dc.date.issued.spa.fl_str_mv 2014-02
dc.date.accessioned.spa.fl_str_mv 2019-06-29T11:46:57Z
dc.date.available.spa.fl_str_mv 2019-06-29T11:46:57Z
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
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dc.type.content.spa.fl_str_mv Text
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format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/51332
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/45422/
url https://repositorio.unal.edu.co/handle/unal/51332
http://bdigital.unal.edu.co/45422/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Estadística
Departamento de Estadística
dc.relation.references.spa.fl_str_mv Guevara González, Rubén Darío (2014) Capability Analysis for Profiles. Doctorado thesis, National University of Colombia.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/51332/1/79386588.2014.pdf
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Vargas Navas, José AlbertoGuevara González, Rubén Darío36043287-9612-4f3c-930b-75eaf92d60d83002019-06-29T11:46:57Z2019-06-29T11:46:57Z2014-02https://repositorio.unal.edu.co/handle/unal/51332http://bdigital.unal.edu.co/45422/Abstract. There are practical situations in which the quality of a process or product can be better characterized by a functional relationship between a response variable and one or more explanatory variables, this is called profile. Such profiles usually can be represented adequately using linear or nonlinear models. While there are several studies monitoring profiles, there are few studies to evaluate the capability of a process with profile quality characteristic, particularly if the process is characterized by a nonlinear functional relationship. This dissertation introduces methods to evaluate the capability of processes characterized by nonlinear profiles (univariate or multivariate), without distributional assumptions. We propose two methods to measure the capability of processes characterized by univariate nonlinear profiles based on the concept of functional depth. These methods extend to functional data, the Process Capability Indexes proposed by Clements for measuring the capability of a process characterized by a random variable. To evaluate the capability of processes characterized by multivariate nonlinear profiles, we consider each observation as a finite dimension vector whose elements are functions. Initially, we transform the original functional data into uncorrelated functions using a dimension reduction technique for multivariate functional data. Next, the capability for each functional component is evaluated. Two sets of process capability indices to measure the capability of these functional components are proposed, having into account if the random errors follow (or not) a multivariate normal distribution. Within case where the random errors do not follow a multivariate normal distribution, we use a method based on the concept of functional depth and apply the methods proposed for the case of univariate nonlinear profiles. Performance of the methods proposed is evaluated through simulation studies. Examples illustrate the applicability of these methods. We offer conclusions and advice for future research at the end.Hay situaciones prácticas donde la calidad de un proceso o producto está mejor caracterizada por una relación funcional entre una variable de respuesta y una o más variables explicatorias, la cual es llamada perfil. Tales perfiles pueden ser representados usando modelos lineales o no lineales. Mientras que existen diferentes estudios en monitoreo de perfiles, hay pocos estudios para evaluar la capacidad de un proceso cuya característica de calidad es un perfil, particularmente de tipo no lineal. Esta disertación presenta métodos para evaluar la capacidad de estos procesos (univariados o multivariados), los cuales no emplean supuestos distribucionales. Basados en el concepto de profundidad funcional, dos métodos para medir la capacidad de procesos caracterizados por perfiles nolineales univariados son propuestos. Estos métodos extienden al campo de los datos funcionales los índices propuestos por Clements para medir la capacidad de procesos caracterizados por una variable aleatoria. Para evaluar la capacidad de procesos caracterizados por perfiles no lineales multivariados, cada observación es considerada como un vector de dimensión finita cuyos elementos son funciones. Inicialmente, los datos funcionales originales son transformados en funciones no correlactionadas usando una técnica de reducción para datos funcionales multivariados. A continuación, la capacidad para cada componente funcional es evaluada. Dos conjuntos de índices para medir la capacidad de estos componentes funcionales son propuestos, dependiendo si los errores aleatorios siguen o no una distribución normal multivariada. Para el caso donde los errores aleatorios siguen una distribución multivariada no normal, un método basado en el concepto de profundidad funcional es propuesto. El desempeño de los métodos propuestos es evaluado a través de estudios de simulación y su aplicabilidad es ilustrada en algunos ejemplos. Conclusiones y recomendaciones para futuras investigaciones son presentadas al final del documento.Doctoradoapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de EstadísticaDepartamento de EstadísticaGuevara González, Rubén Darío (2014) Capability Analysis for Profiles. Doctorado thesis, National University of Colombia.51 Matemáticas / MathematicsFunctional DataFunctional DepthMultivariate Functional DataMultivariateFunctional Principal Component AnalysisNonlinear ProfilesProcess Capability AnalysisProcess Capability IndicesDatos FuncionalesProfundidad FuncionalDatos Funcionales MultivariadosAnálisis de Componentes Principales para Funcionales MultivariadosPerfiles no LinealesAnálisis de Capacidad de ProcesoÍndices de Capacidad de ProcesoCapability Analysis for ProfilesTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDORIGINAL79386588.2014.pdfapplication/pdf3400651https://repositorio.unal.edu.co/bitstream/unal/51332/1/79386588.2014.pdf29986a7bbe49f8e912dbd4d5a405ce13MD51THUMBNAIL79386588.2014.pdf.jpg79386588.2014.pdf.jpgGenerated Thumbnailimage/jpeg3719https://repositorio.unal.edu.co/bitstream/unal/51332/2/79386588.2014.pdf.jpg85dec3982a86edd1f7be4e06c64b14fcMD52unal/51332oai:repositorio.unal.edu.co:unal/513322023-02-20 23:03:31.289Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co