Wireless sensor networks (WSNs) have widely been applied in various industries and business fields covering large geographical regions. It is therefore important to be able to model, assess and predict the reliability of WSNs since the failures can have a great effect on the monitoring or control systems that are normally depending on the WSNs. In this paper, the general WSN reliability models are developed by deleting the independent assumption of component or subsystem failures and are consequently more reasonable to characterise the failure process of WSNs. The methodology in the proposed WSN reliability models is to consider that the failure times of subsystems are dependent variables and their joint distribution is obtained by binding their marginal failure distributions together through a copula function. For specific Frank copula functions, the Star-based WSN reliability models are derived and their properties are also discussed in this paper.