An Estimator of Propagation of Cascading Failure

We suggest a statistical estimator to measure the extent to which failures propagate in cascading failures such as large blackouts. The estimator is tested on a saturating branching process model of cascading failure and on failure data generated by the OPA simulation of cascading blackouts. The estimator is a standard estimator for the branching process parameter modified so as to avoid saturation effects. We discuss the statistical effectiveness of the estimator and show how estimating the failure propagation and the initial failures leads to estimates of the distribution of the numbers of cascading failures. The estimator is derived from a simple and high-level branching process model of cascading failure. We discuss how branching process approximations and in particular the propagation parameter may arise in several different models, including models of interacting infrastructures.