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Correlated component failures (COCOF) may impact the reliability of a software application, and hence these types of failures must be explicitly incorporated into reliability analysis. The influence of COCOF on application reliability must be analyzed within the context of the application architecture. Contemporary reliability analysis approaches that incorporate COCOF, however, cannot scale to even moderate-sized software applications. This paper presents an efficient, scalable approach to analyze the reliability of a component-based software system, considering COCOF within the context of its architecture. The effectiveness of the approach is illustrated through two experimental studies. The results indicate that the approach is simple and efficient, and hence can be applied to large systems to identify correlations that impede system reliability.