We introduce an efficient parametric model checking (ePMC) method for the analysis of reliability, performance and other quality-of-service (QoS) properties of software systems. ePMC speeds up the analysis of parametric Markov chains modelling the behaviour of software by exploiting domain-specific modelling patterns for the software components. To this end, ePMC precomputes closed-form expressions for key QoS properties of such patterns, and uses these expressions in the analysis of whole-system models. To evaluate ePMC, we show that its application to service-based systems and multi-tier software architectures reduces analysis time by several orders of magnitude compared to current parametric model checking methods.