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 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.

• 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