Stochastic Random Walk Algorithm for Predicting Fatal Events in Multi-component Systems

This paper proposes a stochastic algorithm for simulating the wear-out dynamics of a multi-component system (machine, apparatus, equipment) based on random walk with negative drift. The negative drift represents a deterministic tendency towards decreasing the level of proper functioning of the components of the system. In addition to the deterministic drift, white noise fluctuations are assumed to interfere with the gradual deterministic wearing out of the components. The algorithm allows, given a past behavior of the system, to determine, via multiple simulations, the probability of a fatal event in the consequent (future) moments. The goal is to establish the best time to stop the functioning of the system and undertake a repair, e.g. replacing components that are too worn-out, etc. The main idea is that a system should be running without interruption as long as possible, without this endangering the good working order of the system. The working of the system should be interrupted for repair activities if the probability of a fatal event has reached a certain value, but not before that. In this way, we can minimize the number of repairs without allowing the risk of a fatal incident to go above certain pre-specified level.