Banca de DEFESA: ANA CLAUDIA DA SILVA BATISTA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE : ANA CLAUDIA DA SILVA BATISTA
DATA : 23/05/2019
HORA: 14:00
LOCAL: Sala 12 do IME-UFBA
TÍTULO:

Multivariate Statistical Process Control Based on Copula Functions

PALAVRAS-CHAVES:

Multivariate SPC. Average Run Length. Density Level Set Estimation. Copula. Tolerance Region.

PÁGINAS: 60
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Probabilidade e Estatística
SUBÁREA: Estatística
ESPECIALIDADE: Análise Multivariada
RESUMO:

Statistical Process Control (SPC) is a powerful set of tools used to solve problems in order to reduce variability and obtain stability of services or production processes (Montgomery, 2016). The Control Chart is a widely used process monitoring technique, whose main goal is to detect the occurrence of special causes that lead to the change of process as soon as it occurs. A major challenge in statistical quality control is the monitoring and detection of changes in quality characteristics evaluated simultaneously. The multivariate process control chart based on the Hotelling's T2 statistic is the most popular for monitoring the mean vector. However, it assumes that the data follow a multivariate normal distribution (which in practice rarely occurs) and are uncorrelated. Baíllo and Cuevas (2006) proposed the use of tolerance regions obtained from density level set estimates as a detection tool. On the other hand, Verdier (2013) suggested the use of copula-based models, which are simple and flexible tools for multivariate modeling, for obtaining such estimates. In this work, we present an extension of the non-normal approach based on copula functions introduced by Verdier (2013), that is, we explore the trivariate copulas case in addition to the bivariate one. For both situations, we consider the parametric and semi-parametric approaches (the latter one, with the use of kernel margins, as in Verdier, 2013), and we also present a totally non-parametric approach. Thus, we first compared the tolerance region derived from the copula modeling with the usual one based on the Hotelling’s T2 statistic, both constructed under the approach of density level set estimation. The simulations performed here allowed the variation of: (i) the original data distribution, where we considered the parametric (parametric copula and marginal distributions), semi-parametric (parametric copula and kernel margins) and non-parametric (nonparametric copula) cases; (ii) the association degree of association among the variables (weak, moderate and strong); (iii) and the magnitude of changes in the mean vector. Finally, we applied the proposed methodology to a bivariate data set on measurements of the deflection and curvature from brass and steel bimetal thermostats, as well as a trivariate data set related to water quality measured by pH, nitrates and phosphates. Both data sets are available in the MSQC package (Santos-Fernández, 2016) of the R software.

MEMBROS DA BANCA:
Presidente - 1961783 - PAULO HENRIQUE FERREIRA DA SILVA
Interno - 1175242 - GIOVANA OLIVEIRA SILVA
Externo à Instituição - ROBERTO DA COSTA QUININO - UFMG