In this paper, we take an availability-centric view on Quality of Service (QoS) and focus on the issues of providing availability guarantees for widely distributed systems such as web servers and peer-to-peer (P2P) file sharing systems. We propose a concept called Quality of Availability (QoA) in which the availability is treated as a new controllable QoS parameter. The newly refined fine-grained availability definitions and QoA metrics enable the specification and evaluation of the different level of availability for different users and applications. We tackle specifically the replica placement (RP) problem where our focus is on choosing the number and location of replicas while (1) meeting different availability QoS requirement levels for all individual users and (2) taking the intermittent connectivity of system nodes explicitly into account. We decompose the RP problem into two sub-problems: (1) improving QoA and (2) guaranteeing QoA. We investigate a number of simulations - for full and partial replication models and static and dynamic placements - to compare and evaluate the achieved availability QoS of the developed RP algorithms. Our proposed QoA concept and model can be used as a base mechanism for further study on the effectiveness of realistic replication schemes on both availability and performance QoS for widely distributed systems.