Cloud computing has attracted more and more attention and has been used in more and more applications in many different fields. As we know, cloud computing delivers computing as a service. Its adoption widely depends upon the reliability of its systems. However, self-monitoring and adaptation are overlooked by most system designers and architects. Extant system accounting functionalities mainly focus on recent error causes, which is insufficient for long-term history analysis and event prediction. Our approach not only analyzes system events from both service consumers and providers, but also provides a layered composable system accounting framework in cloud computing environments. By self-monitoring, history analysis, event prediction and recovery, a new refined quality of reliability (QoR) for cloud computing is essentially provided. An implementation of this framework in an education services environment confirms the advantages over extant system accounting systems