Modeling and reliability analysis of k -out-of-2 n : F balanced systems with common-mode degradation

Motivated by the degradation characteristics and the operation and maintenance requirements of railway rail grids in small radius curved sections, a novel k-out-of-2n: F balanced system model with common-mode degradation is proposed. The dependency structure among components is characterized by hierarchical copula functions. The state distances of components located at symmetrical positions are the quantitative indicators of the system balance. The system fails as long as at least k components fail due to threshold failures or imbalanced failures. The cumulative distribution function of the system lifetime is given by using the probability analysis method. Under single monitoring information that the system is working and the failed components have been identified, the residual lifetime distribution of the system is also discussed. Numerical examples are given to illustrate the effectiveness of the model.