Dependability evaluation plays a key role in the design of a broad range of systems, where related properties have to be carefully analyzed in or-der to meet the requirements. This is particularly challenging in distributed con-texts, where several entities may interact influencing each other. In this paper, we present an analytical framework that allows the study of a class of phenomena where different working conditions alternate, changing the stochastic behavior of the system. The proposed solution technique, based on phase type distributions and on ad-hoc fitting algorithms, can be applied in dependability evaluation of a wide class of distributed systems. Examples are provided to show the usefulness and the applicability of the framework, characterizing and investigating differ-ent dependability aspects of two distributed computing systems, i.e., connection-oriented networks and Internet of Things.