An important element of successful engineering design is the effective management of resources to support design decisions. Design decisions can be thought of as having two phases—a formulation phase and a solution phase. As part of the formulation phase, engineers must decide what information to collect and use to support the design decision. Since information comes at a cost, a cost-benefit tradeoff must be made. Previous work has considered such tradeoffs in cases in which all relevant probability distributions were precisely known. However, engineers frequently must characterize these distributions by gathering sample data during the information collection phase of the decision process. This characterization is crucial in high-risk design problems where uncommon events with severe consequences play a significant role in decisions. In this paper, we introduce the principles of information economics to guide decisions on information collection. We investigate how designers can bound the value of information in the case of distributions with unknown parameters by using imprecise probabilities to characterize the current state of information. We explore the basic performance, subtleties, and limitations of the approach in the context of characterizing the strength of a novel material for the design of a pressure vessel.