Classical and Bayesian Estimation of Reliability in Multicomponent Stress-Strength Model Based on Weibull Distribution

<p>In this study, we consider a multicomponent system which has k independent and identical strength components X1,...,Xk and each component is exposed to a common random stress Y when the underlying distributions are Weibull. The system is regarded as operating only if at least s out of k (1 ≤ s ≤ k) strength variables exceeds the random stress. We estimate the reliability of the system by using frequentist and Bayesian approaches. The Bayes estimate of the reliability has been developed by using Lindley's approximation and the Markov Chain Monte Carlo methods due to the lack of explicit forms. The asymptotic confidence interval and the highest probability density credible interval are constructed for the reliability. The comparison of the reliability estimators is made in terms of the estimated risks by the Monte Carlo simulations.</p>

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Bayesian Approaches to the Design of Markov Chain Monte Carlo Samplers

Monte Carlo and Quasi-Monte Carlo Methods 2012 - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-642-41095-6_22 ◽

2013 ◽

pp. 455-466

Author(s):

Jonathan M. Keith ◽

Christian M. Davey

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Bayesian Approaches

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The Rise of Markov Chain Monte Carlo Estimation for Psychometric Modeling

Journal of Probability and Statistics ◽

10.1155/2009/537139 ◽

2009 ◽

Vol 2009 ◽

pp. 1-18 ◽

Cited By ~ 15

Author(s):

Roy Levy

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Bayesian Approaches ◽

Mcmc Estimation ◽

Powerful Approach ◽

Psychometric Modeling ◽

Psychometric Models ◽

Monte Carlo Estimation

Markov chain Monte Carlo (MCMC) estimation strategies represent a powerful approach to estimation in psychometric models. Popular MCMC samplers and their alignment with Bayesian approaches to modeling are discussed. Key historical and current developments of MCMC are surveyed, emphasizing how MCMC allows the researcher to overcome the limitations of other estimation paradigms, facilitates the estimation of models that might otherwise be intractable, and frees the researcher from certain possible misconceptions about the models.

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Hybrid Censoring Schemes with Mixture Gamma Failure Distribution

Journal of Mathematics ◽

10.1155/2021/6641078 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Hassan M. Aljohani ◽

Nada M. Alfaer

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Gamma Distribution ◽

Type I ◽

Type Ii ◽

Posterior Density ◽

Bayesian Approaches ◽

Hybrid Censoring ◽

Highest Posterior Density

Censoring schemes have received much attention over the past decades. Hybrid censoring schemes are censoring schemes mixed of type-I (T-1) and type-II (T-2) censoring schemes, a most popular area of study in life-testing or reliability experiments. More precisely, hybrid censoring can be described as a mixture of T-I and T-2 schemes. Gamma distribution is widely used, and its connection has more distributions. Mixture and single gamma distribution will be studied to estimate parameters, based on type-II hybrid censoring schemes (T-2HCS). We will apply algorithms to compute the maximum likelihood (ML) estimators and Bayesian approaches, using statistics, such as Markov chain Monte Carlo methods. Bayes estimators and corresponding highest posterior density confidence intervals will be tabled. Also, Markov chain Monte Carlo simulation is implemented to compare the performances of the different methods and the real dataset is analyzed for illustrative purposes.

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