Optimal Prediction of Time-to-Failure from Information Revealed by Damage

TL;DR

This paper introduces a dynamic prediction method for failure times in systems, updating probabilities with damage information, revealing complex behaviors like non-monotonic failure time evolution and sensitive dependence on system realization.

Contribution

It develops a general failure prediction scheme that incorporates real-time damage information, demonstrating complex behaviors and realization-dependent variability in failure predictions.

Findings

Predicted failure time mode can evolve non-monotonically.

Failure time distribution shows sensitive dependence on system realization.

Full distribution exhibits broad variability similar to chaos phenomena.

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.