Calculation of system failure probability with dependent failure elements

In order to calculate the failure probability of an engineering system with dependent failure elements in real world, the definition of high-order dependence is developed. Based on this definition and the interval probability theory, the traditional failure probability formula of inclusive or exclusive principles is reveised. High-order dependence in complex sysems can be determinded by hierarchical analysis and FMEA methods. In the system with dependent failure elements, the degrees of dependence can not only make it easy to calculate the failure probability, but also reduce the uncertainty of failure probability. The correctness of this method is proved by a few simple examples.