Optimal prediction of time-to-failure from information revealed by damage

¹ Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622 and Université de Nice-Sophia Antipolis - 06108 Nice Cedex 2, France
² Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, University of California - Los Angeles, CA 90095, USA
³ UFR de Sciences Economiques, Gestion, Mathématiques et Informatique CNRS UMR 7536 and Université Paris X-Nanterre - 92001 Nanterre Cedex, France

Corresponding authors: dsornette@ethz.ch vitting@unice.fr

Received: 22 January 2006
Accepted: 5 April 2006

Abstract

We present a general prediction scheme of failure times based on updating continuously with time the probability for failure of the global system, conditioned on the information revealed on the pre-existing idiosyncratic realization of the system by the damage that has occurred until the present time. Its implementation on a simple prototype system of interacting elements with unknown random lifetimes undergoing irreversible damage until a global rupture occurs shows that the most probable predicted failure time (mode) may evolve non-monotonically with time as information is incorporated in the prediction scheme. In addition, both the mode, its standard deviation and, in fact, the full distribution of predicted failure times exhibit sensitive dependence on the realization of the system, similarly to “chaos” in spinglasses, providing a multi-dimensional dynamical explanation for the broad distribution of failure times observed in many empirical situations.