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A notable drawback of the existing architecture-based reliability assessment techniques is that they only obtain a point estimate of application reliability and do not attempt to quantify the variance in the estimate. The variance in the reliability estimate of an application represents the risk associated with the estimate. Ideally, the variance should be zero, but in practice it is inevitable due to the following two factors: (i) variances in the reliability estimates of components comprising the application, and (ii) architectural characteristics of the application. Quantifying the variance in the reliability estimate of an application provides an indication of the degree of risk associated with the estimate, and can also suggest an appropriate variance reduction strategy. We present a technique to quantify the variance in the reliability estimate of an application based on its architecture. Our technique generates analytical functions which express the mean and variance of application reliability in terms of the means and variances of the component reliabilities as well as the architectural characteristics of the application. Through a case study, we illustrate how the analytical functions generated using our technique could be used to evaluate the impact of individual components on the mean and the variance in the application reliability.