The demands of clients in context of business application have always been high in distributed environments. With these ever increasing demands there comes the requirement for change. Service-Oriented Architecture is an architecture style that is used for the development and integration of functionality of services provided by different stakeholders. To provide refined solutions for designing business enterprise, Service-Oriented Architecture approach is adopted without affecting overall functionality of organization. For designing a Service-Oriented Architecture, there are many quality attributes like reliability, flexibility, reusability and maintainability. Among of all these, reliability is a primary concern. This survey explains three important reliability models: state-base, path-based and additive model. This paper discusses some literature for composite reliability of Service-Oriented Architecture. For this literature we have selected research articles on Service-Oriented Architecture from 2005 to 2013.