Reliability model for load-sharing k-out-of-n system and its numerical algorithms

Dependent failure is a difficult problem, which is not easily solved by traditional reliability models. With an increase in system complexity, dependent failure becomes more and more common. So a special reliability model is needed to describe this kind of problem. A load-sharing system is a typical dependent system. The merits of reliability block diagrams (RBD) include simplicity, intuition and ease of use. This paper builds an extendable RBD model to describe k-out-of-n load-sharing systems. A mathematical reliability model is also set up. A mathematical model with exponential and other distributions is discussed. Then the general mathematic description of the model is provided. On this basis, numerical algorithms for the model are studied. The improved GAUSS quadrature method is then adopted to solve the problem of multiple indefinite integral calculations, solving the general model. Finally, a typical case is used for verifying the correctness and veracity of the model and its algorithms.