Quantifying Uncertainty for System Failure Prognostics: Enhanced Approach Based on Interval-Valued Probabilities

Abstract

Failure prognostics being performed for any complex industrial system typically meets serious obstacles caused by uncertainty. This uncertainty actually has a hierarchical structure due to the peculiarities of its influence to the prognostics results. Namely, to quantify the chances of a system failure we normally have to apply probabilistic (non-deterministic) model. Such a model reflects the randomness and the diversity of the factors initiating a failure (the ‘first order uncertainty’). However the estimated probability of the failure may differ from its real value by the so-called ‘bias’. So the imperfectness of the probabilistic models becomes the source of the ‘second order uncertainty’. This means that the interval-valued probabilities can often describe the reality more adequately than single valued ones.
The paper presents the novel approach to system life prognostics based on the usage of the interval-valued statistical characteristics. The problem statement remarkably has many features similar to those considered in the classical publications on the theory of imprecise probabilities. Nevertheless the methodology used to find the prognostics result is very different and involves the technique from the optimal control theory. It relies on the state space representation of the system life cycle and Pontryagin’s principle of maximum modified to optimization problems with the integral and non-integral types of constraints. This novelty allows generalizing the ways to process additional information on the system reliability efficiently and makes the resulted intervals for the probability values tighter. In turn the decrease of the corresponding imprecision provides favorable conditions for justified decisions on the failure prevention, e.g. maintenance planning.