In this paper, we focus on the reliability and availability analysis of Web service (WS) compositions, orchestrated via the Business Process Execution Language (BPEL). Starting from the failure profiles of the services being composed, which take into account multiple possible failure modes, latent errors, and propagation effects, and from a BPEL process description, we provide an analytical technique for evaluating the composite process' reliability-availability metrics. This technique also takes into account BPEL's advanced composition features, including fault, compensation, termination, and event handling. The method is a design-time aid that can help users and third party providers reason, in the early stages of development, and in particular during WS selection, about a process' reliability and availability. A non-trivial case study in the area of travel management is used to illustrate the applicability and effectiveness of the proposed approach.