Statistical analysis for weibull distributions in presence of right and left censoring

Series system reliability is based on the minimum life time of its components. Its dual, the parallel system, is based on maximum. Here, we consider the statistical analysis of both, series and parallel, systems where the components follow the Weibull parametric model. Our perspective is Bayesian. Due to the mathematical complexity, to obtain the posterior distribution we use the Metropolis-Hasting simulation method. Based on this posterior, we evaluated the evidence of the Full Bayesian Significance Test (FBST) for comparing the reliabilities of the components. The reason for using FBST is the fact that we are testing precise hypotheses. We also compute the probability of a particular component be responsible for the system failure. An example illustrates the methodology.