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Víctor Leiva - One of the best experts on this subject based on the ideXlab platform.
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Statistical Quality Control and Reliability Analysis Using the Birnbaum-Saunders Distribution with Industrial Applications
Statistical Quality Technologies, 2019Co-Authors: Víctor Leiva, Fabrizio Ruggeri, Carolina Marchant, Helton SauloAbstract:Quality improvement has been an important aspect considered by companies since the last century. However, today it is even more relevant in business and industry, particularly for production and service companies. Statistical quality control is the quantitative tool for quality improvement. The Gaussian Distribution was the main ingredient of this quantitative tool, but nowadays new Distributions are being considered, some of them taking into account asymmetry. The Birnbaum-Saunders model is one of these Distributions and has recently received considerable attention because of its interesting properties and its relationship with the Gaussian Distribution. Since its origins and applications in material science, the Birnbaum-Saunders Distribution has found widespread uses in several areas, including quality control, with now well-developed methods that allow in-depth analyses. In this work, statistical quality control and reliability tools based on the Birnbaum-Saunders Distribution are introduced. Implementation of those tools is presented using the R software. For the internal quality of companies, control charts for attributes and variables, as well as their multivariate versions and capability indices, are presented, discussed and illustrated with real data. For external quality, acceptance sampling plans are also presented and discussed. The main aspects of reliability, sometimes defined as ‘quality over time”, is discussed using the Birnbaum-Saunders Distribution, illustrating them with data on nanotechnologies.
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A methodology based on the Birnbaum–Saunders Distribution for reliability analysis applied to nano-materials
Reliability Engineering & System Safety, 2017Co-Authors: Víctor Leiva, Fabrizio Ruggeri, Helton Saulo, Juan VivancoAbstract:Abstract The Birnbaum–Saunders Distribution has been widely studied and applied to reliability studies. This paper proposes a novel use of this Distribution to analyze the effect on hardness, a material mechanical property, when incorporating nano-particles inside a polymeric bone cement. A plain variety and two modified types of mesoporous silica nano-particles are considered. In biomaterials, one can study the effect of nano-particles on mechanical response reliability. Experimental data collected by the authors from a micro-indentation test about hardness of a commercially available polymeric bone cement are analyzed. Hardness is modeled with the Birnbaum–Saunders Distribution and Bayesian inference is performed to derive a methodology, which allows us to evaluate the effect of using nano-particles at different loadings by the R software.
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a methodology based on the birnbaum Saunders Distribution for reliability analysis applied to nano materials
Reliability Engineering & System Safety, 2017Co-Authors: Víctor Leiva, Fabrizio Ruggeri, Helton Saulo, Juan VivancoAbstract:Abstract The Birnbaum–Saunders Distribution has been widely studied and applied to reliability studies. This paper proposes a novel use of this Distribution to analyze the effect on hardness, a material mechanical property, when incorporating nano-particles inside a polymeric bone cement. A plain variety and two modified types of mesoporous silica nano-particles are considered. In biomaterials, one can study the effect of nano-particles on mechanical response reliability. Experimental data collected by the authors from a micro-indentation test about hardness of a commercially available polymeric bone cement are analyzed. Hardness is modeled with the Birnbaum–Saunders Distribution and Bayesian inference is performed to derive a methodology, which allows us to evaluate the effect of using nano-particles at different loadings by the R software.
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Genesis of the Birnbaum–Saunders Distribution
The Birnbaum-Saunders Distribution, 2016Co-Authors: Víctor LeivaAbstract:In this chapter, a background and the history of life Distributions, as well as some of its indicators, such as the failure rate and reliability function, are provided. In addition, we detail how the fatigue processes are developed and the genesis and mathematical derivation of the Birnbaum–Saunders Distribution. Furthermore, a connection between this Distribution and the law of proportionate effects is discussed. Moreover, several real-world applications of the Birnbaum–Saunders Distribution are mentioned.
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genesis of the birnbaum Saunders Distribution
The Birnbaum-Saunders Distribution, 2016Co-Authors: Víctor LeivaAbstract:In this chapter, a background and the history of life Distributions, as well as some of its indicators, such as the failure rate and reliability function, are provided. In addition, we detail how the fatigue processes are developed and the genesis and mathematical derivation of the Birnbaum–Saunders Distribution. Furthermore, a connection between this Distribution and the law of proportionate effects is discussed. Moreover, several real-world applications of the Birnbaum–Saunders Distribution are mentioned.
Artur J Lemonte - One of the best experts on this subject based on the ideXlab platform.
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A note on the Fisher information matrix of the Birnbaum–Saunders Distribution
Journal of Statistical Theory and Applications, 2016Co-Authors: Artur J LemonteAbstract:We show that the Fisher information matrix of the Birnbaum–Saunders Distribution can present numerical problems for some values of the shape parameter. To overcome this problem, we provide a simple analytical approximation which works very well.
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The exponentiated generalized Birnbaum-Saunders Distribution
Applied Mathematics and Computation, 2014Co-Authors: Gauss M. Cordeiro, Artur J LemonteAbstract:A new Distribution called the exponentiated generalized Birnbaum-Saunders Distribution is proposed and studied. The new Distribution is quite flexible to model survival data, reliability problems, fatigue life studies and hydrological data. It can have decreasing, increasing, upside-down bathtub, bathtub-shaped, increasing-decreasing-increasing and decreasing-increasing-decreasing hazard rate functions. We provide a comprehensive account of the mathematical properties of the new Distribution and various structural quantities are derived. We discuss maximum likelihood estimation of the model parameters for uncensored and censored data. Two empirical applications of the new model to real data are presented for illustrative purposes.
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a new extension of the birnbaum Saunders Distribution
Brazilian Journal of Probability and Statistics, 2013Co-Authors: Artur J LemonteAbstract:In this paper, a new extension for the Birnbaum–Saunders Distribution, which has been applied to the modeling of fatigue failure times and reliability studies, is introduced. The proposed model, called the Marshall–Olkin extended Birnbaum–Saunders Distribution, arises based on the scheme introduced by Marshall and Olkin [Biometrika84 (1997) 641–652]. The maximum likelihood estimators and statistical inference for the new Distribution parameters and influence diagnostic for the new Distribution are presented. Finally, the proposed new Distribution is applied to model three real data sets.
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A log-linear regression model for the β-Birnbaum-Saunders Distribution with censored data
Computational Statistics & Data Analysis, 2012Co-Authors: Edwin M. M. Ortega, Gauss M. Cordeiro, Artur J LemonteAbstract:The @b-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) Distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-@b-Birnbaum-Saunders Distribution by the logarithm of the @b-Birnbaum-Saunders Distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-@b-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets.
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Testing hypotheses in the Birnbaum-Saunders Distribution under type-II censored samples
Computational Statistics & Data Analysis, 2011Co-Authors: Artur J Lemonte, Silvia L P FerrariAbstract:The two-parameter Birnbaum-Saunders Distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this Distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders Distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders Distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented.
N. Balakrishnan - One of the best experts on this subject based on the ideXlab platform.
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maximum likelihood estimation of the parameters of student s t birnbaum Saunders Distribution a comparative study
Communications in Statistics - Simulation and Computation, 2019Co-Authors: N. Balakrishnan, Farouq Mohammad A. AlamAbstract:AbstractIn the last decade, Diaz-Garcia and Leiva-Sanchez (2005, 2007) proposed a generalized Birnbaum-Saunders Distribution based on elliptically contoured Distributions. A special case of this ge...
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a robust multivariate birnbaum Saunders Distribution em estimation
Statistics, 2018Co-Authors: Renata G. Romeiro, Filidor Vilca, N. BalakrishnanAbstract:We propose here a robust multivariate extension of the bivariate Birnbaum–Saunders (BS) Distribution derived by Kundu et al. [Bivariate Birnbaum–Saunders Distribution and associated inference. J Mu...
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birnbaum Saunders Distribution based on laplace kernel and some properties and inferential issues
Statistics & Probability Letters, 2015Co-Authors: Xiaojun Zhu, N. BalakrishnanAbstract:Abstract For the Birnbaum–Saunders Distribution based on Laplace kernel, we discuss the shape characteristics of density and hazard functions. We show the existence and uniqueness of maximum likelihood estimates. Simple modified moment estimators are proposed and compared with maximum likelihood estimates.
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a robust extension of the bivariate birnbaum Saunders Distribution and associated inference
Journal of Multivariate Analysis, 2014Co-Authors: Filidor Vilca, N. Balakrishnan, Camila Borelli ZellerAbstract:We propose here a robust extension of the bivariate Birnbaum-Saunders (BS) Distribution derived recently by Kundu et al. (2010). This extension is based on scale mixtures of normal (SMN) Distributions that are used for modeling symmetric data. This type of bivariate Birnbaum-Saunders Distribution based on SMN models is an absolutely continuous Distribution whose marginals are of univariate Birnbaum-Saunders type. We then develop the EM-algorithm for the maximum likelihood (ML) estimation of the model parameters, and illustrate the obtained results with a real data and display the robustness feature of the estimation procedure developed here.
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bivariate birnbaum Saunders Distribution and associated inference
Journal of Multivariate Analysis, 2010Co-Authors: Debasis Kundu, N. Balakrishnan, Ahad JamalizadehAbstract:Univariate Birnbaum-Saunders Distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum-Saunders Distribution which is an absolutely continuous Distribution whose marginals are univariate Birnbaum-Saunders Distributions. Different properties of this bivariate Birnbaum-Saunders Distribution are then discussed. This new family has five unknown parameters and it is shown that the maximum likelihood estimators can be obtained by solving two non-linear equations. We also propose simple modified moment estimators for the unknown parameters which are explicit and can therefore be used effectively as an initial guess for the computation of the maximum likelihood estimators. We then present the asymptotic Distributions of the maximum likelihood estimators and use them to construct confidence intervals for the parameters. We also discuss likelihood ratio tests for some hypotheses of interest. Monte Carlo simulations are then carried out to examine the performance of the proposed estimators. Finally, a numerical data analysis is performed in order to illustrate all the methods of inference discussed here.
Sandile Charles Shongwe - One of the best experts on this subject based on the ideXlab platform.
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Multiple Dependent State Repetitive Sampling-Based Control Chart for Birnbaum–Saunders Distribution
Journal of Mathematics, 2020Co-Authors: Muhammad Aslam, Ambreen Shafqat, G. Srinivasa Rao, Jean-claude Malela-majika, Sandile Charles ShongweAbstract:This paper proposes a new control chart for the Birnbaum–Saunders Distribution based on multiple dependent state repetitive sampling (MDSRS). The proposed control chart is a generalization of the control charts based on single sampling, repetitive sampling, and multiple dependent state sampling. Its sensitivity is evaluated in terms of the average run length (ARL) using both exact formulae and simulations. A comprehensive comparison between the Birnbaum–Saunders Distribution control chart based on the MDSRS method and other existing competing methods is provided using a simulation study as well as a real-life illustration. The results reveal that the proposed chart outperforms the existing charts considered in this study by having better shift detection ability.
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multiple dependent state repetitive sampling based control chart for birnbaum Saunders Distribution
Journal of Mathematics, 2020Co-Authors: Muhammad Aslam, Ambreen Shafqat, Srinivasa G Rao, Jeanclaude Malelamajika, Sandile Charles ShongweAbstract:This paper proposes a new control chart for the Birnbaum–Saunders Distribution based on multiple dependent state repetitive sampling (MDSRS). The proposed control chart is a generalization of the control charts based on single sampling, repetitive sampling, and multiple dependent state sampling. Its sensitivity is evaluated in terms of the average run length (ARL) using both exact formulae and simulations. A comprehensive comparison between the Birnbaum–Saunders Distribution control chart based on the MDSRS method and other existing competing methods is provided using a simulation study as well as a real-life illustration. The results reveal that the proposed chart outperforms the existing charts considered in this study by having better shift detection ability.
Yimin Shi - One of the best experts on this subject based on the ideXlab platform.
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estimation for birnbaum Saunders Distribution in simple step stress accelerated life test with type ii censoring
Communications in Statistics - Simulation and Computation, 2016Co-Authors: Tianyu Sun, Yimin ShiAbstract:This paper develops the Bayesian estimation for the Birnbaum–Saunders Distribution based on Type-II censoring in the simple step stress–accelerated life test with power law accelerated form. Maximum likelihood estimates are obtained and Gibbs sampling procedure is used to get the Bayesian estimates for shape parameter of Birnbaum–Saunders Distribution and parameters of power law–accelerated model. Asymptotic normality method and Markov Chain Monte Carlo method are employed to construct the corresponding confidence interval and highest posterior density interval at different confidence level, respectively. At last, the results are compared by using Monte Carlo simulations, and a numerical example is analyzed for illustration.
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Estimation for Birnbaum–Saunders Distribution in Simple Step Stress–accelerated Life Test with Type-II Censoring
Communications in Statistics - Simulation and Computation, 2015Co-Authors: Tianyu Sun, Yimin ShiAbstract:This paper develops the Bayesian estimation for the Birnbaum–Saunders Distribution based on Type-II censoring in the simple step stress–accelerated life test with power law accelerated form. Maximum likelihood estimates are obtained and Gibbs sampling procedure is used to get the Bayesian estimates for shape parameter of Birnbaum–Saunders Distribution and parameters of power law–accelerated model. Asymptotic normality method and Markov Chain Monte Carlo method are employed to construct the corresponding confidence interval and highest posterior density interval at different confidence level, respectively. At last, the results are compared by using Monte Carlo simulations, and a numerical example is analyzed for illustration.
