A Bayesian Hierarchical Power Law Process Model for Multiple Repairable Systems with an Application to Supercomputer Reliability

Los Alamos National Laboratory was home to the Blue Mountain supercomputer, which at one point was the world's fastest computer. This paper presents and analyzes hardware failure data from Blue Mountain. Nonhomogeneous Poisson process models are fit to the data within a hierarchical Bayesian framework using Markov chain Monte Carlo methods. The implementation of these methods is convenient and flexible. Simulations are used to demonstrate strong frequentist properties and provide comparisons between time-truncated and failure-count designs and demonstrate the benefits of hierarchical modeling of multiple repairable systems over the modeling of such systems separately.