Bayesian Inference of δ = P(X &lt; Y) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples

Byrnes, Jessie Marie; Lin, Yu‐Jau; Tsai, Tzong‐Ru; Lio, Yuhlong

doi:10.3390/math7090794

Cited by 8 publications

(4 citation statements)

References 23 publications

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“…EL-Sagheer et al [15] studied Bayesian and maximum likelihood estimation methods for the three-parameter BurrXII distribution with a unified hybrid censoring scheme. Byrnes et al [16] studied the performance of using different loss functions to implement the MCMC Bayesian estimation method for estimating the parameter δ = P(X < Y), where X and Y follow two-parameter BurrXII distributions. EL-Sagheer et al [17] proposed Bayesian inference methods for the three-parameter BurrXII distribution based on randomly censoring samples.…”

Section: Historical Review and Literature Reviewmentioning

confidence: 99%

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

et al. 2020

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The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration.

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Section: Historical Review and Literature Reviewmentioning

confidence: 99%

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

et al. 2020

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“…Many authors presented a lot of papers about the estimation of R = P(X < Y) for various distributions due to the practical point of view of reliability stress-strength model. For instance, the reader can see [1][2][3][4][5]. Multlak et al [6] used Ranked-set sampling (RSS) in the case of the exponential distribution for estimating a stress-strength model.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

et al. 2022

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The current work focuses on ranked set sampling and a simple random sample as sampling approaches for determining stress–strength reliability from the inverted Topp–Leone distribution. Asymptotic confidence intervals are established, along with a maximum likelihood estimator of the parameters and stress–strength reliability. The reliability of such a system is assessed using the Bayesian approach under symmetric and asymmetric loss functions. The highest posterior density credible interval is constructed successively. The results are extracted using Monte Carlo simulation to compare the proposed estimators performance with different sample sizes. Finally, by looking at waiting time data and failure times of insulating fluid, the usefulness of the suggested technique is demonstrated.

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“…Akgül et al [5] presented inferences on stress-strength reliability based on ranked set sampling data in the case of Lindley distribution. Byrnes et al [6] made a Bayesian inference of R for Burr type XII distribution based on progressively first failure-censored samples. Zhang et al [7] studied the reliability of generalized Rayleigh distribution under progressive type II censoring.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

Ezmareh

Yari

2022

Advances in Mathematical Physics

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This paper develops the problem of estimating stress-strength reliability for Gompertz lifetime distribution. First, the maximum likelihood estimation (MLE) and exact and asymptotic confidence intervals for stress-strength reliability are obtained. Then, Bayes estimators under informative and noninformative prior distributions are obtained by using Lindley approximation, Monte Carlo integration, and MCMC. Bayesian credible intervals are constructed under these prior distributions. Also, simulation studies are used to illustrate these inference methods. Finally, a real dataset is analyzed to show the implementation of the proposed methodologies.

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Bayesian Inference of δ = P(X < Y) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples

Cited by 8 publications

References 23 publications

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

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