Reliability analysis of k/n(G) degradation system under dependent competing failures

Abstract

This paper examines the reliability of $k/n\left(G\right)$ systems composed of components with multiple performances that degrade over time, resulting in competing failures between soft and hard failures. The flexible Tweedie Exponential Diffusion process is employed to model the performance degradation, while the dependence between multiple performances degradation processes is established by the Copula functions. Additionally, we utilize the Weibull distribution to characterize the failure times of hard failures and construct a proportional hazards model to relate the hard failure rate to performance degradation. To estimate the model parameters and reliability function, we apply a two-stage Bayesian approach, employing the efficient Hamiltonian Monte Carlo algorithm for parameter estimation. Through simulation studies, the proposed model and method have good statistical inference performance. Finally, the constructed model and method are implemented in real data to showcase its practical applicability.