Cloud services with a multi-tiered architecture are often difficult to evaluate in terms of performance and dependability. The tiered architecture complicates the resource capacity decisions of the service provider, and makes it more demanding to maintain a good balance between capacity and quality of service. In this work we present an approximation of the response time distribution of a multi-tier service, which should help the providers in their planning and operation. The approximation also takes into account failures in the virtual machines in which the service runs, and acknowledges replication of the tiers. We demonstrate that the approximation can be used as decision support for service providers.