# Análise de Sobrevivência e Confiabilidade

## Modelo de Regressão Exponencial com Longa-duração: Uma Aplicação

Autor(es) e Instituição:
Douglas Augusto Matheus - Universidade Estadual de Maringá
Daniele Cristina Tita Granzotto - Universidade Estadual de Maringá
Douglas Augusto Matheus

população, através de um parâmetro de longa-duração. Além disso, utilizamos do modelo exponencial com regressão no parâmetro de escala para incorporar, além da longa-duração, as covariáveis em estudo.

Palavras-chave: Análise de Sobrevivência, longa-duração, regressão, exponencial.

Resumo estendido:

## Um Estudo do Modelo de Risco Logístico Generalizado Dependente do Tempo com Fragilidade

Autor(es) e Instituição:
Eder Angelo Milani - UFSCar
Vera Lúcia Damasceno Tomazella - UFSCar
Teresa Cristina Martins Dias - UFSCar
Eder Angelo Milani

Neste trabalho apresentamos o modelo de risco logístico generalizado dependente do tempo (GTDL) com fragilidade. Utilizando dados gerados calculamos a probabilidade de cobertura para diferentes porcentagem de observações censuradas e tamanho de amostra. Também calculamos a inflação da variância para os parâmetros que medem o efeito do tempo e da covariável quando estimamos o parâmetro da fragilidade dos dados.

Resumo estendido:

## The Kumaraswamy-Generalized Gamma Distribution with Application in Survival Analysis

Autor(es) e Instituição:
Marcelino Alves Rosa de Pascoa / ESALQ - USP
Edwin Moisés Marcos Ortega / ESALQ - USP
Gauss Moutinho Cordeiro / DEINFO - UFRPE
Patrícia Ferreira Paranaíba / ESALQ - USP
Marcelino Alves Rosa de Pascoa

Based on the Kumaraswamy distribution (Jones, 2009), we study the so-called Kum-generalized gamma distribution that is capable of modeling bathtub-shaped hazard rate functions. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models such as the exponentiated generalized gamma, exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma, generalized Rayleigh, among several others. Some mathematical properties of the Kum-generalized gamma distribution are studied. We obtain two infinite sum representations for the moments and for the moment generating function. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. Two real data sets are analyzed with this distribution.

Trabalho completo:

## The Beta Burr XII Distribution with Applications to Lifetime Data

Autor(es) e Instituição:
Patrícia Ferreira Paranaiba / ESALQ- USP
Edwin Moisés Marcos Ortega / ESALQ- USP
Gauss Moutinho Cordeiro / DEINFO - UFRPE
Rodrigo Rossetto Pescim / ESALQ-USP
Marcelino Alves Rosa de Pascoa / ESALQ-USP
Patrícia Ferreira Paranaiba

For the first time, a five-parameter distribution, so-called the beta Burr XII distribution, is defined and investigated. The new distribution contains as special sub-models some well-known distributions discussed in the literature, such as the logistic, Weibull and Burr XII distributions, among several others. We derive its moment generating function. As a special case, we obtain the moment generating function of the Burr XII distribution, which seems to be a new result. Moments, mean deviations, Bonferroni and Lorenz curves and reliability are provided. We derive two representations for the moments of the order statistics. The method of maximum likelihood is proposed for estimating the model parameters. We obtain the observed information matrix. An application to a real data set demonstrates that the new distribution can provide a better fit than other classical models. We hope that this generalization may attract wider applications in reliability, biology and lifetime data analysis.

Trabalho completo:

## A Bayesian Analysis for the Block & Basu Bivariate Exponential Distribution: An Example of Application.

Autor(es) e Instituição:
Carlos Aparecido dos Santos - DES / UEM
Jorge Alberto Achcar - ICMC / USP
Carlos Aparecido dos Santos

In this work, we introduce a Bayesian Analysis for the Block &
Basu bivariate exponential distribution using Markov Chain Monte
Carlo (MCMC) methods and considering lifetimes in presence of
covariates and censored data. Posterior summaries of interest are
obtained using the popular WinBUGS software. An numerical illustration
is introduced considering a medical data set related to the
recurrence times of infection for kidney patients.

Resumo estendido:

## The Complementary Exponential Power Lifetime Model

Autor(es) e Instituição:
Gladys Dorotea Cacsire Barriga
Vicente Garibay Cancho
Gladys Dorotea Cacsire Barriga

In this paper we propose a new lifetime distribution which can handle bathtub-shaped, unimodal, increasing and decreasing hazard rate functions. The model has three parameters and generalizes the exponential power distribution proposed by Smith & Bain (1975) by inclusion of an additional shape parameter. Maximum likelihood estimation procedure is discussed. A small-scale simulation study examine the performance of the likelihood ratio statistics under small and moderate sized samples. Three real data sets illustrate the methodology.

## Modelo beta Weibull modificada em Análise de Sobrevivência

Autor(es) e Instituição:
Valdemiro Piedade Vigas (Universidade Federal da Bahia)
Giovana Oliveira Silva (Universidade Federal da Bahia)

Resumo estendido:

## Modeling Bivariate Survival Data Based on Copulas

Autor(es) e Instituição:
Adriano Kamimura Suzuki - Universidade Federal de São Carlos
Francisco Louzada Neto - Universidade Federal de São Carlos
Vicente Garibay Cancho - Universidade de São Paulo

We propose the use of long-term models as marginal distributions of bivariate survival times with dependence function modeled by copulas, obtaining a straightforwardly extension of the model proposed by Romeo et al (2006) and a more appropriate model for The Diabetic Retinopathy Study Research Group (1976) data.

## Predição em Modelos de Tempo de Falha com Efeito Aleatório para Avaliação de Riscos de Falhas em Poços Petrolíferos

Autor(es) e Instituição:
João Batista Carvalho (UFRN)
Dione Maria Valença (UFRN)
Julio da Motta Singer (IME-USP)
João Batista Carvalho

Resumo estendido:

## Bayesian Inference for Power Law Processes with Applications in Repairable Systems

Autor(es) e Instituição:
Maristela Dias de Oliveira - UFMG/UFBA
Enrico A. Colosimo - UFMG
Gustavo L. Gilardoni - UNB
Maristela Dias de Oliveira

Statistical models for recurrent events are of great interest in repairable systems reliability and maintenance. The adopted model under minimal repair maintenance is frequently a Nonhomogeneous Poisson Process with the Power Law Process (PLP) intensity function. Although inference for the PLP is generally based on maximum likelihood theory, some advantages of the Bayesian approach have been reported in the literature. In this paper it is proposed that the PLP intensity be reparametrized in terms of ($\beta;\eta$), where $\beta$ is the elasticity of the mean number of events with respect to time and $\eta$ is the mean number of events for the period in which the sistem was actually observed.
It is shown that $\beta$ and $\eta$ are orthogonal and that the likelihood becomes proportional
to a product of Gamma densities. Therefore, the family of natural conjugate priors is
also a product of Gammas. The idea is extended to the case that several realizations of
the same PLP are observed along overlapping periods of time. The results are applied
to a real problem concerning the determination of the optimal periodicity of preventive
maintenance for a set of power transformers. Some Monte Carlo simulations are provided
to study the frequentist behavior of the Bayesian estimates and to compare them with
the maximum likelihood estimates.

Resumo estendido: