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Provably conservative (and optimistic) reliability models can be systematically derived from more complex models. These derived models incorporate a reduced state space and fewer transitions, and, therefore, have solutions that are more cost- effective than those of the original complex models. The designer can extensively explore the design space without incurring the expense of solving multiple complex models. A conservative- optimistic pair of derived models produces a band that includes the solution to the complex model. Sensitivity analysis can be performed on this pair of models to determine those parameters of the original model that are most sensitive to change (i.e., uncertainty) and hence warrant further expense in obtaining tighter specifications.