Cloud computing is a paradigm that provides services through the Internet. The paradigm has been influenced by previously available technologies (for example cluster, peer-to-peer, and grid computing) and has now been adopted by almost all large organizations. Companies such as Google, Amazon, Microsoft and Facebook have made significant investments in cloud computing, and now provide services with high levels of dependability. The efficient and accurate assessment of cloud-based infrastructure is fundamental in guaranteeing both business continuity and uninterrupted public services, as much as is possible. This paper presents an approach for selecting cloud computing infrastructures, in terms of dependability and cost that best suits both company and customer needs. We use stochastic models to calculate dependability-related metrics for different cloud infrastructures. We then use a Multiple-Criteria Decision-Making (MCDM) method to rank the best cloud infrastructures, taking customer service constraints such as reliability, downtime, and cost into consideration. A case study demonstrates the practicability and usefulness of the proposed approach.