E-Bayesian estimation for system reliability and availability analysis based on exponential distribution

González‐López, V. A.; Gholizadeh, Ramin; Galarza, Christian E.

doi:10.1080/03610918.2016.1202269

Cited by 19 publications

(7 citation statements)

References 2 publications

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“…where 𝐷 is the domain of 𝜃 𝑖1 and 𝜃 𝑖2 . According to Han 8 and Veronica et al, 12 the prior parameters 𝜃 𝑖1 and 𝜃 𝑖2 should be selected to guarantee that 𝑓(𝑟 𝑖 ) is a decreasing function of 𝑟 𝑖 . The derivative of 𝑓(𝑟 𝑖 ) with respect to 𝑟 𝑖 is…”

Section: Hierarchical Bayesian Estimationmentioning

confidence: 99%

“…If the prior density function of hyper parameter

\theta _{i1}

and

\theta _{i2}

are

\pi (\theta _{i1},\theta _{i2})

, then, the corresponding hierarchical prior density function of

r_i

\begin{equation} \pi ^{\ast }(r_{i})=\int \int _{D}\pi (r_i|\theta _{i1},\theta _{i2})\pi (\theta _{i1}, \theta _{i2})d\theta _{i1} d\theta _{i2} \end{equation}

where D is the domain of

\theta _{i1}

and

\theta _{i2}

. According to Han 8 and Veronica et al., 12 the prior parameters

\theta _{i1}

and

\theta _{i2}

should be selected to guarantee that

f(r_i)

is a decreasing function of

r_i

. The derivative of

f false(r_{i} fal...

…”

Section: Hierarchical Bayesian Estimationmentioning

confidence: 99%

“…Martz and Waller 11 gave a good monograph on this topic. Recently, E-Bayesian method have been applied to reliability and availability systems by Veronica et al 12 They applied three different distributions for the parameters in prior distribution to investigate the influence of the different prior distributions on the E-Bayesian estimation. Actually when we have a system with different components, for estimation reliability or for simulation, we have to provide some parameters.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of waste‐to‐energy system reliability under hierarchical Bayesian

Gholizadeh

Londoño

Fazlollahtabar

2022

Quality & Reliability Eng

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In this paper, we discuss about the hierarchical Bayesian (HB) estimation concerning system reliability for a waste-to-energy (WTE) process. The main goal of this approach is to obtain this estimation WTE process reliability under different loss functions related series, parallel, and 𝑘-out-of-𝑚 systems. In this case, we can drive system outcome by estimating each individual component. It is assumed that components are independent and identically distributed exponential random variables. Properties of the HB estimations under different loss functions are also provided, and comparisons are made between Bayesian and HB estimators via Monte Carlo simulation. The implementation of the proposed procedure was illustrated in detail by employing numerical practical examples extracted from a WTE process at the final part of this paper.

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Section: Hierarchical Bayesian Estimationmentioning

confidence: 99%

“…If the prior density function of hyper parameter

\theta _{i1}

and

\theta _{i2}

are

\pi (\theta _{i1},\theta _{i2})

, then, the corresponding hierarchical prior density function of

r_i

\begin{equation} \pi ^{\ast }(r_{i})=\int \int _{D}\pi (r_i|\theta _{i1},\theta _{i2})\pi (\theta _{i1}, \theta _{i2})d\theta _{i1} d\theta _{i2} \end{equation}

where D is the domain of

\theta _{i1}

and

\theta _{i2}

. According to Han 8 and Veronica et al., 12 the prior parameters

\theta _{i1}

and

\theta _{i2}

should be selected to guarantee that

f(r_i)

is a decreasing function of

r_i

. The derivative of

f false(r_{i} fal...

…”

Section: Hierarchical Bayesian Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of waste‐to‐energy system reliability under hierarchical Bayesian

Gholizadeh

Londoño

Fazlollahtabar

2022

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…Originally the Kumaraswamy probability distribution was proposed by Poondi Kumaraswamy in 1980. The Kumaraswamy double bounded distribution is denoted by KUD (θ,λ) on the interval (0, 1), The Kumaraswamy is similar to the beta distribution but has the key advantage of closed from cumulative distribution function (CDF), has its probability density function (pdf) for Kumaraswamy with two parameters θ> 0 and λ> 0 is [1], [2].…”

Section: Introductionmentioning

confidence: 99%

The Kumaraswamy Distribution: Statistical Properties and Application

Badra¹,

Mohammed²

2022

Int. J. Adv. Sci. Eng. Inf. Technol.

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Modeling and analyzing lifetime data is an important aspect of statistical work in various scientific and technological fields such as medicine, engineering, insurance, and finance. The modeling and analysis of lifetimes is an important aspect of statistical work in various scientific and technological fields. In recent years, inverted Kumaraswamy distribution has been used quite effectively to model many lifetime data. The most broadly applied statistical distribution is Kumaraswamy distribution in hydrological problems and many natural phenomena. The Kumaraswamy distribution (KD) is widely applied for modeling data in practical domains, such as medicine, engineering, economics, and physics. The present work proposes the Bayesian estimators of KD parameters through the use of type-II censoring data in this research the problem to estimate the unknown parameters of Kumaraswamy distribution with two parameters and λ, these estimates are a maximum likelihood of ordered observation and the Bayesian for the parameter of the Kumaraswamy distribution (KUD) depended on ranked set sampling (RSS) techniques. Both the simulated are inserted into real-life data sets and are considered to make a comparison between the estimation based on Maximum Likelihood estimators and Bayesian Estimation methods based on (RSS) techniques. For comparison purposes, we employed (100) mean square error and the criteria like AICC (Akaike information corrected criterion). Finally, the importance and flexibility of the new model of real data set are proved empirically.

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“…The E-Bayesian method can be used to estimate statistical distribution parameters. Gonzalez-Lopez et al used E-Bayesian to gain flexibility in the reliability-availability system estimation based on exponential distribution under the squared error loss function [16]. Han estimated the system failure probability with the E-Bayesian method, and the relationship of E-Bayesian estimators with three different prior distributions of hyperparameters was revealed [17].…”

Section: Introductionmentioning

confidence: 99%

E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples

Okasha

Wang

2020

Advances in Mathematical Physics

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Type-II censored data is an important scheme of data in lifetime studies. The purpose of this paper is to obtain E-Bayesian predictive functions which are based on observed order statistics with two samples from two parameter Burr XII model. Predictive functions are developed to derive both point prediction and interval prediction based on type-II censored data, where the median Bayesian estimation is a novel formulation to get Bayesian sample prediction, as the integral for calculating the Bayesian prediction directly does not exist. All kinds of predictions are obtained with symmetric and asymmetric loss functions. Two sample techniques are considered, and gamma conjugate prior density is assumed. Illustrative examples are provided for all the scenarios considered in this article. Both illustrative examples with real data and the Monte Carlo simulation are carried out to show the new method is acceptable. The results show that Bayesian and E-Bayesian predictions with the two kinds of loss functions have little difference for the point prediction, and E-Bayesian confidence interval (CI) with the two kinds of loss functions are almost similar and they are more accurate for the interval prediction.

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E-Bayesian estimation for system reliability and availability analysis based on exponential distribution

Cited by 19 publications

References 2 publications

Estimation of waste‐to‐energy system reliability under hierarchical Bayesian

Estimation of waste‐to‐energy system reliability under hierarchical Bayesian

The Kumaraswamy Distribution: Statistical Properties and Application

E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples

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