Browsing by Author "Tomazella, Vera L. D."

Now showing 1 - 7 of 7
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    A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data
    (2023) Mota, Alex; Milani, Eder A.; Leao, Jeremias; Ramos, Pedro L.; Ferreira, Paulo H.; Junior, Oilson G.; Tomazella, Vera L. D.; Louzada, Francisco
    In this paper, we propose a new cure rate frailty regression model based on a two-parameter weighted Lindley distribution. The weighted Lindley distribution has attractive properties such as flexibility on its probability density function, Laplace transform function on closed-form, among others. An advantage of proposed model is the possibility to jointly model the heterogeneity among patients by their frailties and the presence of a cured fraction of them. To make the model parameters identifiable, we consider a reparameterized version of the weighted Lindley distribution with unit mean as frailty distribution. The proposed model is very flexible in sense that has some traditional cure rate models as special cases. The statistical inference for the model's parameters is discussed in detail using the maximum likelihood estimation under random right-censoring. Further, we present a Monte Carlo simulation study to verify the maximum likelihood estimators' behavior assuming different sample sizes and censoring proportions. Finally, the new model describes the lifetime of 22,148 patients with stomach cancer, obtained from the Fundacao Oncocentro de Sao Paulo, Brazil.
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    Frailty model for multiple repairable systems hierarchically represented subject to competing risks
    (2024) Gonzatto Junior, Oilson A.; Fernandes, Willian R.; Ramos, Pedro L.; Tomazella, Vera L. D.; Louzada, Francisco
    In this paper, we propose a statistical model to describe the behaviour of failure times associated with groups of repairable systems hierarchically represented, under a competing risks framework, considering the existence of unobserved heterogeneity that acts individually on systems of each group, as well as the possibility of imperfect repairs whose initial failure rate is in the form of the power law. In this context for the unobserved heterogeneity in the groups, we consider the multiplicative frailty. To illustrate the use of the proposed model, we consider a database with the failures of 38 agricultural machines categorized into five different groups. We understand that the tractor fleet corresponds to the farm's agricultural system, therefore the need for intervention in this system occurs with the failure of any unit, individually, in a serial structure, of competing risks.e On the other hand, the understanding of the time in which all the machinery that makes up the fleet will have required some intervention is obtained by analysing the results under a parallel structure.
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    Improved objective Bayesian estimator for a PLP model hierarchically represented subject to competing risks under minimal repair regime
    (2021) Louzada, Francisco; Cuminato, Jose A.; Rodriguez, Oscar M. H.; Tomazella, Vera L. D.; Ferreira, Paulo H.; Ramos, Pedro L.; Milani, Eder A.; Bochio, Gustavo; Perissini, Ivan C.; Gonzatto Junior, Oilson A.; Mota, Alex L.; Alegria, Luis F. A.; Colombo, Danilo; Perondi, Eduardo A.; Wentz, Andre V.; Junior, Anselmo L. Silva; Barone, Dante A. C.; Santos, Hugo F. L.; Magalhaes, Marcus V. C.
    In this paper, we propose a hierarchical statistical model for a single repairable system subject to several failure modes (competing risks). The paper describes how complex engineered systems may be modelled hierarchically by use of Bayesian methods. It is also assumed that repairs are minimal and each failure mode has a power-law intensity. Our proposed model generalizes another one already presented in the literature and continues the study initiated by us in another published paper. Some properties of the new model are discussed. We conduct statistical inference under an objective Bayesian framework. A simulation study is carried out to investigate the efficiency of the proposed methods. Finally, our methodology is illustrated by two practical situations currently addressed in a project under development arising from a partnership between Petrobras and six research institutes.
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    Objective bayesian analysis for multiple repairable systems
    (2021) D'Andrea, Amanda M. E.; Tomazella, Vera L. D.; Aljohani, Hassan M.; Ramos, Pedro L.; Almeida, Marco P.; Louzada, Francisco; Verssani, Bruna A. W.; Gazon, Amanda B.; Afify, Ahmed Z.
    This article focus on the analysis of the reliability of multiple identical systems that can have multiple failures over time. A repairable system is defined as a system that can be restored to operating state in the event of a failure. This work under minimal repair, it is assumed that the failure has a power law intensity and the Bayesian approach is used to estimate the unknown parameters. The Bayesian estimators are obtained using two objective priors know as Jeffreys and reference priors. We proved that obtained reference prior is also a matching prior for both parameters, i.e., the credibility intervals have accurate frequentist coverage, while the Jeffreys prior returns unbiased estimates for the parameters. To illustrate the applicability of our Bayesian estimators, a new data set related to the failures of Brazilian sugar cane harvesters is considered.
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    Reliability assessment of repairable systems with series-parallel structure subjected to hierarchical competing risks under minimal repair regime
    (2022) Louzada, Francisco; Tomazella, Vera L. D.; Gonzatto, Oilson A.; Bochio, Gustavo; Milani, Eder A.; Ferreira, Paulo H.; Ramos, Pedro L.
    In this paper, we seek to propose a model that allows us to evaluate the failure times of a single repairable system represented hierarchically, exposed to competing risks and under a minimal repair framework. Our study can be regarded as an extension of the research presented in Louzada et al. (2019), which comprises the representation of complex systems through a hierarchical structure in series and/or in parallel. For this, we deduce the general form of the model, as well as the likelihood function associated with it, to obtain reliable estimates for the parameters that index the model. In addition, we display the mechanism for generating random numbers based on the presented structure, which enables obtaining point and interval estimates (via parametric bootstrap) in a more convenient way for reliability curves at any level of the system hierarchy. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed maximum likelihood estimators and confidence intervals for the model parameters. Finally, we illustrate the applicability of our model and methods with applications that deal with the reliability modeling of a robotic unit still under development, resulting from a project carried out in partnership between Petrobras and other Brazilian research centers.
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    Statistical Inference for Generalized Power-Law Process in repairable systems
    (2024) Lopes, Tito; Tomazella, Vera L. D.; Leao, Jeremias; Ramos, Pedro L.; Louzada, Francisco
    Repairable systems are often used to model the reliability of restored components after a failure is observed. Among various reliability growth models, the power law process (PLP) or Weibull process has been widely used in industrial problems and applications. In this article, we propose a new class of model called the generalized PLP (GPLP), based on change points. These can be treated as known or unknown parameters, or interpreted as failure times. Herein, we consider the impact of all or some fixes on the failure intensity function. In this context, unlike the usual PLP, the GPLP is not restricted to the assumption of minimal repair (MR). Other situations, such as perfect, efficient, and harmful repair, can be considered. We present some special cases of the GPLP, such as the main models used to analyze repairable systems under the assumption of imperfect repair. The estimators of the proposed model parameters were obtained using the maximum likelihood method. We evaluated the performance of the parameter estimators through Monte Carlo (MC) simulations. The proposed approach is fully illustrated using two real failure time datasets.
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    Weighted Lindley frailty model: estimation and application to lung cancer data
    (2021) Mota, Alex; Milani, Eder A.; Calsavara, Vinicius F.; Tomazella, Vera L. D.; Leao, Jeremias; Ramos, Pedro L.; Ferreira, Paulo H.; Louzada, Francisco
    In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of Sao Paulo, Brazil.