Abstract
This paper presents a hierarchical Bayesian approach to the estimation of components' reliability (survival) using a Weibull model for each of them. The proposed method can be used to estimation with general survival censored data, because the estimation of a component's reliability in a series (parallel) system is equivalent to the estimation of its survival function with right- (left-) censored data. Besides the Weibull parametric model for reliability data, independent gamma distributions are considered at the first hierarchical level for the Weibull parameters and independent uniform distributions over the real line as priors for the parameters of the gammas. In order to evaluate the model, an example and a simulation study are discussed.
Highlights
This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability using a Weibull model for each component in series and parallel systems
Rodrigues et al [4] performed a simulation study of three different methods to estimate the reliability of a series system
They compared the Kaplan-Meier estimator [1], maximum likelihood estimator (MLE) and the Bayesian plug-in estimator (BPE) for Weibull reliability systems. Their results indicated that MLE and BPE are similar in quality and that both outperformed the Kaplan-Meier estimator
Summary
This paper presents a hierarchical Bayesian approach to the estimation of components’ reliability using a Weibull model for each component in series and parallel systems. Rodrigues et al [4] performed a simulation study of three different methods to estimate the reliability of a series system They compared the Kaplan-Meier estimator [1], maximum likelihood estimator (MLE) and the Bayesian plug-in estimator (BPE) for Weibull reliability systems. To the best of our knowledge, Polpo and Pereira [5] were the first to address the nonparametric reliability estimation in parallel systems and their components, using the Bayesian paradigm. Polpo et al [7] presented the reliability estimation with Weibull models and non-informative priors, using the Bayesian paradigm. We note that an extended abstract of this work has appeared in the Brazilian Conference on Bayesian Statistics [8]
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