Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach

Ahmed, Essam A.

doi:10.1080/02664763.2013.847907

Cited by 69 publications

(33 citation statements)

References 23 publications

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“…Usually, it is impossible to obtain the analytically summarizing posterior distributions, which is mainly due to the complexity of the integral at the denominator and limits the practical implementation of the Bayesian approach. Markov chain Monte Carlo (MCMC) algorithm is a Monte Carlo integration method which (a) draws samples directly from the target posterior distribution, (b) generates a dependent sample in contrast to the output of "direct" simulation method (a simple, original method), and (c) estimates the target parameter values and the posterior distributions without specifying a parametric statistical distribution (Ahmed 2014). MCMC can provide a flexible and efficient way to use complicated, high-dimensional models and estimate the corresponding posterior distributions with accuracy (Gilks et al 1996).…”

Section: Bayesian Approachmentioning

confidence: 99%

A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region

Guo

et al. 2016

Environ Sci Pollut Res

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In this study, a Bayesian-based two-stage inexact optimization (BTIO) method is developed for supporting water quality management through coupling Bayesian analysis with interval two-stage stochastic programming (ITSP). The BTIO method is capable of addressing uncertainties caused by insufficient inputs in water quality model as well as uncertainties expressed as probabilistic distributions and interval numbers. The BTIO method is applied to a real case of water quality management for the Xiangxi River basin in the Three Gorges Reservoir region to seek optimal water quality management schemes under various uncertainties. Interval solutions for production patterns under a range of probabilistic water quality constraints have been generated. Results obtained demonstrate compromises between the system benefit and the system failure risk due to inherent uncertainties that exist in various system components. Moreover, information about pollutant emission is accomplished, which would help managers to adjust production patterns of regional industry and local policies considering interactions of water quality requirement, economic benefit, and industry structure.

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Section: Bayesian Approachmentioning

confidence: 99%

A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region

Guo

et al. 2016

Environ Sci Pollut Res

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“…Reference [18] used the Delta method for estimation of new Weibull-Pareto distribution based on progressive Type-II censored sample. Reference [19] also used this method for estimation of the two-parameter bathtub lifetime model. Different loss functions for Bayes estimation are considered and realized through Monte Carlo method.…”

Section: Approximate Confidence Intervals Of Entropymentioning

confidence: 99%

Entropy Estimation of Inverse Weibull Distribution under Adaptive Type-II Progressive Hybrid Censoring Schemes

Gui

2019

Symmetry

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This paper discusses entropy estimations for two-parameter inverse Weibull distributions under adaptive type-II progressive hybrid censoring schemes. Estimations of entropy derived by maximum likelihood estimation method and Bayes estimation method are both considered. Different Bayes estimators using squared loss function, Linex loss function, general entropy loss function, and balanced loss function are derived. Numerical results are derived by Lindley’s approximation method. Especially, the interval estimation of entropy is derived through maximum likelihood estimation method. To test the effectiveness of the estimations, simulation studies are conducted. These entropy estimation methods are illustrated and applied to analyze a real data set.

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“…e methods mentioned above are not appropriate for building the reliability models of the CNC system because of highly complex calculations involved. With the development of the Markov Chain Monte Carlo (MCMC) methods [7][8][9][10], the limitations of computational complexity have been overcome. Accordingly, another fusion method, Bayesian inference, has been further studied.…”

Section: Introductionmentioning

confidence: 99%

Developing a Reliability Model of CNC System under Limited Sample Data Based on Multisource Information Fusion

Peng

Cai

Liu

et al. 2020

Mathematical Problems in Engineering

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The reliability of the computer numerical control (CNC) system affects its processing performance and is a major concern in the manufacturing industry today. However, existing reliability models to assess the reliability of the CNC system often exhibit relatively large errors due to inadequate treatment of small samples. In order to get around the constraint of limited lifetime failure data and take full advantage of existing reliability parameters in traditional reliability models, a multisource information fusion-based reliability model grounded on Bayesian inference is proposed to deal with the small sample size. The prior distributions are derived by using the probability encoding method and conjugate distribution based on the idea of multisource information fusion. Then, using the Jensen–Shannon divergence (JSD) to measure the similarity between prior information and field observation data, a constrained optimization problem is established to determine the respective weight of prior information and field observation data. Finally, by conducting the reliability analysis of repairable CNC systems, the validity of the proposed model and its prior distribution derivation method are verified.

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Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach

Cited by 69 publications

References 23 publications

A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region

A Bayesian-based two-stage inexact optimization method for supporting stream water quality management in the Three Gorges Reservoir region

Entropy Estimation of Inverse Weibull Distribution under Adaptive Type-II Progressive Hybrid Censoring Schemes

Developing a Reliability Model of CNC System under Limited Sample Data Based on Multisource Information Fusion

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