Banca de DEFESA: CAMILA RIBEIRO DA SILVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : CAMILA RIBEIRO DA SILVA
DATE: 25/08/2023
TIME: 14:00
LOCAL: https://meet.google.com/bby-bmrd-mnf
TITLE:

Shewhart Control Chart considering the Inflated Unit Gamma Distribution

KEY WORDS:

Control charts; inflated data; inflated unit gamma distribution; rates and proportions.

PAGES: 73
BIG AREA: Ciências Agrárias
AREA: Agronomia
SUMMARY:

Statistical process control (SPC) is one of the axes that contemplate the area of quality control. Control charts, one of the tools of SPC, were originally developed to monitor industrial processes. However, in recent years, its application has been shown to be of great relevance in monitoring variables in different contexts. Regarding the monitoring of variables, in some cases, the objective is to monitor the behavior of variables that assume values in the intervals [0,1) or (0,1], that is, variables with inflation of zeros or ones. In view of the limitation of appropriate control charts to monitor variables in the intervals (0,1] and [0,1), the respective thesis work aims to propose control charts based on the inflated unit gamma distribution. Thus, we initially propose the unitary gamma distribution inflated at zero and one and derive its main properties.  Additionally, we derive expressions to obtain the maximum likelihood estimators of the parameters of the distribution and conduct simulations to evaluate the performance of confidence intervals and hypothesis tests in finite sample sizes. In the formulation of the model, we start from a parameterization in which the proposed distribution is expressed in terms of the mean of the inflated distribution. This parameterization becomes more attractive, considering that in control charts, when the subgroup size is greater than 1, it is common to be interested in monitoring the process mean. In addition, two applications to real data are presented to illustrate the applicability of the proposed distribution. Next, we propose the inflated unit gamma control chart, for monitoring variables that take the values zero or one. In constructing the proposed chart, we assume that the monitored variable follows inflated unit gamma distribution. An extensive Monte Carlo simulation study was conducted to evaluate the performance of the control charts in terms of run length.  We perform a comparison between the inflated unit gamma control chart and the inflated beta control chart, considering two approaches. In the first, considering individual observations and in the second, sample subgroups of size m = 8, 15, 30 and 50. Numerical results show that the proposed chart performed well in the two approaches considered. Additionally, an application to real data sets illustrates the applicability of the proposed control chart.

COMMITTEE MEMBERS:
Externo à Instituição - FÁBIO MARIANO BAYER - UFSM
Interno - JOSIMAR MENDES DE VASCONCELOS
Interno - LUCIAN BOGDAN BEJAN
Presidente - PAULO JOSE DUARTE NETO
Externo à Instituição - TATIENE CORREIRA DE SOUZA - UFPB