TITLE:
Reliability Estimators for the Components of Series and Parallel Systems: The Weibull Model
AUTHORS:
Felipe L. Bhering, Carlos A. de B. Pereira, Adriano Polpo
KEYWORDS:
Bayesian Analysis, Hierarchical Model, Left Censored Data, Right Censored Data
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.11,
June
20,
2014
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.