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In this paper, new bounding strategies are presented to improve confidence interval estimation for system reliability based on component level reliability, and associated uncertainty data. Research efforts have been focused on two interdependent areas: 1) development & improvement of analytical approaches for quantifying the uncertainty associated with the system reliability estimate when data regarding component reliability is available; and 2) based on these analytical approaches, generating statistical inference methods that can be used to make accurate estimations about the reliability of a system. The analytical approach presented relies on a recursive rationale that can be applied to obtain the variance associated with the system reliability estimate, provided the system can be decomposed into a series-parallel configuration. The bounding procedure is independent of parametric assumptions regarding component time to failure, and can be applied whenever component reliability data are available. To assess the validity of the proposed procedure, three test cases have been analyzed. For each case, Monte-Carlo simulation has been used to generate component failure data, based on nominal component reliability values. Based on these simulated data, lower bounds have been constructed, and then compared against nominal system reliability to generate an expected confidence level. The results obtained exhibit a significant improvement in the accuracy of the confidence intervals for the system reliability when compared with existing approximation methods. The procedure described is effective, relatively simple, and widely applicable.