Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data

• Published in: Reliability engineering & system safety Vol. 100; pp. 48 - 57
• Main Authors: Soliman, Ahmed A., Abd-Ellah, Ahmed H., Abou-Elheggag, Naser A., Ahmed, Essam A.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.2012; Elsevier
• Subjects: Applied sciences; Asymmetry; Balanced loss; Balancing; Bayesian analysis; Bayesian estimation; Bootstrap; Estimates; Exact sciences and technology; Gibbs and Metropolis–Hasting samplers; Hybrid MCMC approach; Intervals; Mathematical models; Mathematics; Maximum likelihood estimation; Modified Weibull distribution; Monte Carlo methods; Operational research and scientific management; Operational research. Management science; Parametric inference; Probability and statistics; Progressive type-II censoring; Reliability theory. Replacement problems; Sampling theory, sample surveys; Sciences and techniques of general use; Statistics; Maximum likelihood estimation; Hybrid MCMC approach; Bayesian estimation; Progressive type-II censoring; Gibbs and Metropolis–Hasting samplers; Balanced loss; Bootstrap; Modified Weibull distribution; Parameter estimation; Interval estimation; Censored sample; Modeling; Markov chain; Parametric method; Loss function; Weibull distribution; Bayes estimation; Monte Carlo method; Durability; Markov model; Gibbs sampling; Lifetime; Asymmetry; Point estimation; Maximum likelihood; Reliability; Gibbs and Metropolis-Hasting samplers
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2011.12.013

In this paper, we investigate the problem of point and interval estimations for the modified Weibull distribution (MWD) using progressively type-II censored sample. The maximum likelihood (ML), Bayes, and parametric bootstrap methods are used for estimating the unknown parameters as well as some lifetime parameters (reliability and hazard functions). Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. Bayes estimates and the credible intervals are obtained under the assumptions of informative and noninformative priors. The results of Bayes method are obtained under both the balanced squared error loss (bSEL) and balanced linear-exponential (bLINEX) loss. We show that these loss functions are more general, which include the MLE and both symmetric and asymmetric Bayes estimates as special cases. Finally, Two real data sets have been analyzed for illustrative purposes.