A DNN-based reliability evaluation method for multi-state series-parallel systems considering semi-Markov process

In order to evaluate the reliability of the multi-state series-parallel system considering semi-Markov process (MSSPS-SMP), the integral equations have been utilized to calculate the state probability distributions. Nevertheless, to solve the formulated integral equations, it is impossible to avoid time-consuming convolution operations for any numerical method, which can result in significant reliability evaluation complexity. To address the above problems, a deep neural network (DNN)-based method is proposed for the reliability evaluation of the MSSPS-SMP. For a multi-state component, the reliability parameters representing the arbitrary distributions of the SMP are firstly extracted as the input feature to DNN, while the corresponding state probability distributions serve as the output of DNN naturally. On this basis, the DNN is deployed to establish a direct mapping relationship between the reliability parameters and state probability distributions. Instead of repeating complicated calculations of SMP-related convolution operation, the well-trained DNN model can effectively determine the performance distributions of multi-state components given the varying reliability parameters. On this basis, the Lz-transform technique is utilized to develop the unified representations of dynamic reliability models of various multi-state components considering SMP. Combined with the Lz-transform, the time-varying performance distribution of the MSSPS-SMP with complicated structures of several components can be determined.