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Managers of complex engineering development projects face a challenge when deciding how to allocate scarce resources to minimize the risks of project failure. As resource constraints become tighter, balancing these failure risks is more critical, less intuitive, and can benefit from the power of quantitative analysis. This paper describes the Advanced Programmatic Risk Analysis and Management model (APRAM), a decision-support framework for the management of the risk of failures of dependent engineering projects within programs. Our goal is to guide the management of the design, the development, and the budget of dependent projects. Considering first a single project, our approach is to optimize the use of the budget reserves and of the funds dedicated to the system itself for each possible budget allocation. This phase involves separate optimizations of the system design and a strategy for resolving development problems based on a chosen objective function. The model also allows checking that specified thresholds of maximum acceptable risks are met, and if not, indicates how much is required to satisfy them. It is then extended to include project dependencies within a program. Finally, it allows checking that the level of resources available is appropriate by computing the shadow "risk cost" of the budget constraint. The NASA Jet Propulsion Laboratory has supported the development of this model, so each step of APRAM is illustrated by the schematic case of an unmanned space program involving two dependent projects. Also, where applicable, we discuss our experiences working with the APRAM concepts for the management of unmanned space missions.