Cloud-management infrastructure plays an important role as a part of cloud computing stacks, serving as the resource manager of cloud platforms. The complexity of cloud-management infrastructure makes its high availability (HA) one of the most critical requirements. Various technologies have been developed to increase the reliability and availability of cloud management infrastructure, however, little work focused on quantitative analysis of its availability. In this paper, we designed a new availability benchmarking method for cloud management infrastructure. By using our measurement method, a private cloud customer or public cloud provider can estimate the availability of deployment of its cloud management stack. We have evaluated our method on Open Stack cloud infrastructure. We show that with various HA technologies and configurations, the availability of the cloud management infrastructure can be greatly different.