Reliability analysis of voting system with dependent components

Considering the degradation characteristics of railway rail grids, a common-mode degradation voting system is proposed, and the expression of the system lifetime distribution function is obtained. Each component is assumed to degradate according to Gamma process. Copula function is applied to measure the dependency strength among components. The model does not impose constraints on component lifetime distributions, symmetry, or dependence structures. The system lifetime distribution function is derived from the Copula function in conjunction with components' lifetime distribution functions and it is also represented as the linear operation of marginal Copula functions of the system. Numerical examples are given to illustrate the effectiveness of the model.