DSpace Angular :: Browsing by Author "Louzada, Francisco"

Browsing by Author "Louzada, Francisco"

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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.
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.
New statistical process control charts for overdispersed count data based on the Bell distribution
(2023) Boaventura, Laion L.; Ferreira, Paulo H.; Fiaccone, Rosemeire L.; Ramos, Pedro L.; Louzada, Francisco
Poisson distribution is a popular discrete model used to describe counting information, from which traditional control charts involving count data, such as the c and u charts, have been established in the literature. However, several studies recognize the need for alternative control charts that allow for data overdispersion, which can be encountered in many fields, including ecology, healthcare, industry, and others. The Bell distribution, recently proposed by Castellares et al. (2018), is a particular solution of a multiple Poisson process able to accommodate overdispersed data. It can be used as an alternative to the usual Poisson (which, although not nested in the Bell family, is approached for small values of the Bell distribution) Poisson, negative binomial, and COM-Poisson distributions for modeling count data in several areas. In this paper, we consider the Bell distribution to introduce two new exciting, and useful statistical control charts for counting processes, which are capable of monitoring count data with overdispersion. The performance of the so-called Bell charts, namely Bell-c and Bell-u charts, is evaluated by the average run length in numerical simulation. Some artificial and real data sets are used to illustrate the applicability of the proposed control charts.
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.
Objective Bayesian analysis for the differential entropy of the Gamma distribution
(2024) Ramos, Eduardo; Egbon, Osafu A.; Ramos, Pedro L.; Rodrigues, Francisco A.; Louzada, Francisco
The paper introduces a fully objective Bayesian analysis to obtain the posterior distribution of an entropy measure. Notably, we consider the gamma distribution, which describes many natural phenomena in physics, engineering, and biology. We reparametrize the model in terms of entropy, and different objective priors are derived, such as Jeffreys prior, reference prior, and matching priors. Since the obtained priors are improper, we prove that the obtained posterior distributions are proper and that their respective posterior means are finite. An intensive simulation study is conducted to select the prior that returns better results regarding bias, mean square error, and coverage probabilities. The proposed approach is illustrated in two datasets: the first relates to the Achaemenid dynasty reign period, and the second describes the time to failure of an electronic component in a sugarcane harvest machine.
On Posterior Properties of the Two Parameter Gamma Family of Distributions
(2021) Ramos, Pedro L.; Dey, Dipak K.; Louzada, Francisco; Ramos, Eduardo
The gamma distribution has been extensively used in many areas of applications. In this paper, considering a Bayesian analysis we provide necessary and sufficient conditions to check whether or not improper priors Lead to proper posterior distributions. Further, we also discuss sufficient conditions to verify if the obtained posterior moments are finite. An interesting aspect of our findings are that one can check if the posterior is proper or improper and also if its posterior moments are finite by looking directly in the behavior of the proposed improper prior. To illustrate our proposed methodology these results are applied in different objective priors.
POWER LAWS DISTRIBUTIONS IN OBJECTIVE PRIORS
(2023) Ramos, Pedro Luiz; Rodrigues, Francisco A.; Ramos, Eduardo; Dey, Dipak K.; Louzada, Francisco
Using objective priors in Bayesian applications has become a common way of analyzing data without using subjective information. Formal rules are usually used to obtain these prior distributions, and the data provide the dominant infor-mation in the posterior distribution. However, these priors are typically improper, and may lead to an improper posterior. Here, for a general family of distribu-tions, we show that the objective priors obtained for the parameters either follow a power law distribution, or exhibit asymptotic power law behavior. As a result, we observe that the exponents of the model are between 0.5 and 1. Understand-ing this behavior allows us to use the exponent of the power law directly to verify whether such priors lead to proper or improper posteriors. The general family of distributions we consider includes essential models such as the exponential, gamma, Weibull, Nakagami-m, half-normal, Rayleigh, Erlang, and Maxwell Boltzmann dis-tributions, among others. In summary, we show that understanding the mechanisms that describe the shape of a prior provides essential information that can be used to understand the properties of posterior distributions.
Power-law distribution in pieces: a semi-parametric approach with change point detection
(2024) Ramos, Pedro L.; Jerez-Lillo, Nixon; Segovia, Francisco A.; Egbon, Osafu A.; Louzada, Francisco
Piecewise models play a crucial role in statistical analysis as they allow the same pattern to be adjusted over different regions of the data, achieving a higher quality of fit than would be obtained by fitting them all at once. The standard piecewise linear distribution assumes that the hazard rate is constant between each change point. However, this assumption may be unrealistic in many applications. To address this issue, we introduce a piecewise distribution based on the power-law model. The proposed semi-parametric distribution boasts excellent properties and features a non-constant hazard function between change points. We discuss parameter estimates using the maximum likelihood estimators (MLEs), which yield closed-form expressions for the estimators and the Fisher information matrix for both complete and randomly censored data. Since MLEs can be biased for small samples, we derived bias-corrected MLEs that are unbiased up to the second order and also have closed-form expressions. We consider a profiled MLE approach to estimate change points and construct a hypothesis test to determine the number of change points. We apply our proposed model to analyze the survival pattern of monarchs in the Pharaoh dynasties. Our results indicate that the piecewise power-law distribution fits the data well, suggesting that the lifespans of pharaonic monarchs exhibit varied survival patterns.
Reducing delivery insurance costs through risk score model for food delivery company
(2024) Panham, Diogo Silva; Louzada, Francisco; Ramos, Pedro L.
In this paper, we propose a novel pricing model for delivery insurance in a food delivery company in Latin America, with the aim of reducing the high costs associated with the premium paid to the insurer. To achieve this goal, a thorough analysis was conducted to estimate the probability of losses based on delivery routes, transportation modes, and delivery drivers' profiles. A large amount of data was collected and used as a database, and various statistical models and machine learning techniques were employed to construct a comprehensive risk profile and perform risk classification. Based on the risk classification and the estimated probability associated with it, a new pricing model for delivery insurance was developed using advanced mathematical algorithms and machine learning techniques. This new pricing model took into account the pattern of loss occurrence and high and low-risk behaviors, resulting in a significant reduction of insurance costs for both the contracting company and the insurer. The proposed pricing model also allowed for greater flexibility in insurance contracting, making it more accessible and appealing to delivery drivers. The use of estimated loss probabilities and a risk score for the pricing of delivery insurance proved to be a highly effective and efficient alternative for reducing the high costs associated with insurance, while also improving the profitability and competitiveness of the food delivery company in Latin America.
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.
Sampling with censored data: a practical guide
(2024) Ramos, Pedro L.; Guzman, Daniel C. F.; Mota, Alex L.; Saavedra, Daniel A.; Rodrigues, Francisco A.; Louzada, Francisco
In this review, we present a simple guide for researchers to obtain pseudo-random samples with censored data. We focus our attention on the most common types of censored data, such as type I, type II, and random censoring. We discussed the necessary steps to sample pseudo-random values from long-term survival models where an additional cure fraction is informed. For illustrative purposes, these techniques are applied in the Weibull distribution. The algorithms and codes in R are presented, enabling the reproducibility of our study. Finally, we developed an R package that encapsulates these methodologies, providing researchers with practical tools for implementation.
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.
Statistical process control of overdispersed count data based on one-parameter Poisson mixture models
(2022) Jesus, Bruno D.; Ferreira, Paulo H.; Boaventura, Laion L.; Fiaccone, Rosemeire L.; Bertoli, Wesley; Ramos, Pedro L.; Louzada, Francisco
The Poisson distribution is a discrete model widely used to analyze count data. Statistical control charts based on this distribution, such as the c$c$ and u$u$ charts, are relatively well-established in the literature. Nevertheless, many studies suggest the need for alternative approaches that allow for modeling overdispersion, a phenomenon that can be observed in several fields, including biology, ecology, healthcare, marketing, economics, and industry. The one-parameter Poisson mixture distributions, whose literature is extensive and essential, can model extra-Poisson variability, accommodating different overdispersion levels. The distributions belonging to this class of models, including the Poisson-Lindley (PL), Poisson-Shanker (PSh), and Poisson-Sujatha (PSu) models, can thus be used as interesting alternatives to the usual Poisson and COM-Poisson distributions for analyzing count data in several areas. In this paper, we consider the class of probabilistic models mentioned above (as well as the cited three members of such a class) to develop novel and useful statistical control charts for counting processes, monitoring count data that exhibit overdispersion. The performance of the so-called one-parameter Poisson mixture charts, namely the PLc$\text{PL}_c$-PLu$\text{PL}_u$, PShc$\text{PSh}_c$-PShu$\text{PSh}_u$, and PSuc$\text{PSu}_c$-PSuu$\text{PSu}_u$ charts, is measured by the average run length in exhaustive numerical simulations. Some data sets are used to illustrate the applicability of the proposed methodology.
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.

Browsing by Author "Louzada, Francisco"

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