Ontology Web Language for Services (OWL-S), one of the most significant semantic Web service ontologies proposed to date, provides a core ontological framework and guidelines for describing the properties and capabilities of services in an unambiguous computerinterpretable form. Analysis of the quality of service of composite service processes specified in OWL-S enables service users to decide whether the process meets nonfunctional requirements. In this paper, we propose a probabilistic approach for reliability analysis of OWL-S processes, employing the non-Markovian stochastic Petri net (NMSPN) as the fundamental model. Based on the NMSPN representations of the OWL-S elements, we introduce an analytical method for the calculation of the process-normal-completion probability as the reliability estimate. This method takes the probabilistic parameters of service invocations and messages as model inputs. To validate the feasibility and accuracy of our approach, we obtain runtime experimental data and conduct a confidence interval analysis in a case study. A sensitivity analysis is also performed to determine the impact of model parameters on reliability and to help identify the reliability bottlenecks.