Reliability analysis of coherent systems subject to internal failures and external shocks

In reality, a system and its components, apart from internal failures, are often exposed to external shocks as well. Since external shocks have significant effects on the performance of the system, neglecting their effects during reliability analysis of the system leads to large prediction errors and even misleading conclusions. In this paper, we present a new method for reliability analysis of coherent systems subject to internal failures and random external shocks. The cumulative probability of failure (CPF) is used as an index to quantify the effects of random external shocks on the reliability of the components and a three-moment saddlepoint approximation approach is proposed to predict the CPF. In addition, the theory of survival signature is applied to assess the associations of the components of the system to calculate the reliability of the system efficiently. Finally, two numerical examples are utilized to demonstrate the validity and effectiveness of the proposed method.