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Dependability is an important consideration during the design and development of IT systems and services. But in services computing systems, the traditional definition and evaluation methods from the systems' and components' point of view meet challenges. In this paper, we veer from the angle of view, and study the dependability and their attributes from the service-oriented perspective. A stochastic model using semi-Markov process is put forward, and the quantitative analysis of the dependability attributes is carried out. By extending and transforming this model, the mean time to dependability attributes failure is calculated. Based on the analysis and calculations, some theorems are proposed and proved, to show the inter-relationships and comparisons of the different dependability attributes. Furthermore, we model the service composition and conduct workflow analysis to show how this model could deal with complex services. In addition, LANL service systems are analyzed as a case study to show how the proposed model and calculation methods could apply to real systems, and sensitivity analysis is also performed to identify the bottlenecks and find effective ways for dependability optimization.