Stochastic reliability analysis of composite services is challenging, primarily since it needs us to carefully balance accuracy of analysis and its computational complexity: Given stochastic models of service components, we often combine them and define a large complex model to accurately reflect the effects of failures of particular components on the reliability of the entire service. In this paper, we propose a new technique, based on the Markov reward model (MRM) foundation, to substantially reduce the computational complexity without losing accuracy. It evaluates, prior to analysis, the effects of the possible failures and represents them as scalar reward values attached to a single compact Markov model. Thus we can replace the component models with a compact model that retains the complete information for accurate analysis. We demonstrate the effectiveness of this technique for several cases, where failures are correlated with each other in different ways.