Parallel systems using the Weibull model

A 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 a parallel system where its components follows 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 component reliabilities. The reason for using FBST is the fact that we are testing precise hypotheses. An example illustrates the methodology.