Reliability analysis of uncertain random systems based on uncertain differential equation

Abstract

Typical failure modes of degradation and shock processes have been applied which are named as soft failures and hard failures, respectively. This paper discusses the reliability of uncertain random systems where randomness is regarded as objective indeterminacy with enough sample data, and uncertainty is referred to epistemic indeterminacy with insufficient sample data. Considering that the combination of internal and external factors, the degradation process is modelled by an uncertain differential equation, and external shocks are driven by an uncertain random renewal process where state variables are uncertain random variables. Chance measure is applied to define the reliability index which is distinguished from traditional reliability assessment methods that utilize probability measure. Three types of reliability models possessed with independent failures are presented, where the general reliability index formulas are provided. The analysis results of Caohai Nature Reserve show that uncertain random modelling method provides an effective approach to system reliability assessment.