Importance measure for K-out-of-n: G systems under dynamic random load considering strength degradation

Highlights: • Proposed conditional system strength extends SSI model to importance analysis. • Dynamic importance measure for k-out-of-n: G system with strength degradation is given. • Monte Carlo method is developed and corroborates the analytical solutions. • Importance analysis for identifying the time-varying weakness of compressor is modeled. Taking the importance analysis of the compressor rotor system as an opportunity and combining the structural characteristics of the blade, this paper proposes a dynamic importance measure considering component strength degradation for the k-out-of-n: G system under dynamic random load. The k-out-of-n: G system consists of n components, and it works if and only if at least k components are functioning. As an effective analytical tool in the reliability field, the application of importance measures in critical equipment and complex systems is a problem worthy of study. Based on the stress-strength interference (SSI) model, the two most common degradation patterns are incorporated into the modeling of importance measure, i.e., the component strength degrades with the times of load action or degrades with time. The dynamic importance measure not only provides a continuous and dynamic analysis method for the computation of the component importance but also effectively reflects the effects of strength degradation, which will help to identify the weaknesses of systems comprehensively and accurately. A numerical case is presented to illustrate the application of the importance measure and shows some unique properties. Meanwhile, a Monte Carlo (MC) simulation method is developed to validate the results of the proposed importance measure.