Reliability calculation method based on the Copula function for mechanical systems with dependent failure

In order to accurately calculate the reliability of mechanical components and systems with multiple correlated failure modes and to reduce the computational complexity of these calculations, the Copula function is used to represent related structures among failure modes. Based on a correlation analysis of the failure modes of parts of a system, a life distribution model of components is constructed using the Copula function. The type of Copula model was initially selected using a binary frequency histogram of the life empirical distribution between the two components. The unknown parameters in the Copula model were estimated using the maximum likelihood estimation method and the most suitable Copula model was determined by calculating the square Euclidean distance. The reliability of series, parallel, and series–parallel systems was analyzed based on the Copula function, where life was used as a variable to measure the correlation between components. Thus, a reliability model of a system with life correlations was established. Reliability calculation of a particular diesel crank and connecting rod mechanism was taken as a practical example to illustrate the feasibility of the proposed method.