With the growing popularity of cloud computing, the reliability of cloud services has become a key concern of cloud service providers and users. Several researchers have studied the problem of cloud service reliability assurance. However, the complexity of the cloud service provisioning system and the deep dependency stack of its layered architecture make it challenging to evaluate the reliability of cloud services. In this paper, we propose a novel analytical model of cloud service provisioning systems reliability. Further, we provide a detailed methodology for evaluating cloud service reliability using reliability block diagrams and probabilistic methods. The proposed model can be used by cloud providers to assure the reliability of their cloud services. The results of a case study using simulated cloud computing infrastructure verify the effectiveness of the proposed model.