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In this paper, we discuss a Monte Carlo sampling based method for propagating the epistemic uncertainty in model parameters, through the system availability model. We also outline methods to compute the number of samples needed to obtain a desired confidence interval for various scenarios. We illustrate this method with a real system example and discuss the results obtained. While our example discusses confidence interval for system availability, this method can be directly applied to compute uncertainty for other dependability, performance and perform ability measures, computed by solving stochastic analytic models. We also emphasize the fact that no simulation is carried out in our method but a repeated sampling is performed over the parameter space followed by the execution of the analytic model with the final phase being the statistical analysis of the output vector.