The fields of risk analysis and prognostics and health management (PHM) have developed in a largely independent fashion. However, both fields share a common core goal. They aspire to manage future adverse consequences associated with prospective dysfunctions of the systems under consideration due to internal or external forces. This paper describes how two prominent risk analysis theories and methodologies - Hierarchical Holographic Modeling (HHM) and Risk Filtering, Ranking, and Management (RFRM) - can be adapted to support the design of PHM systems in the context of smart manufacturing processes. Specifically, the proposed methodologies will be used to identify targets - components, subsystems, or systems - that would most benefit from a PHM system in regards to achieving the following objectives: minimizing cost, minimizing production/maintenance time, maximizing system remaining usable life (RUL), maximizing product quality, and maximizing product output. HHM is a comprehensive modeling theory and methodology that is grounded on the premise that no system can be modeled effectively from a single perspective. It can also be used as an inductive method for scenario structuring to identify emergent forced changes (EFCs) in a system. EFCs connote trends in external or internal sources of risk to a system that may adversely affect specific states of the system. An important aspect of proactive risk management includes bolstering the resilience of the system for specific EFCs by appropriately controlling the states. Risk scenarios for specific EFCs can be the basis for the design of prognostic and diagnostic systems that provide real-time predictions and recognition of scenario changes. The HHM methodology includes visual modeling techniques that can enhance stakeholders' understanding of shared states, resources, objectives and constraints among the interdependent and interconnected subsystems of smart manufacturing systems. In risk analysis, HHM is often paired with Risk Filtering, Ranking, and Management (RFRM). The RFRM process provides the users, (e.g., technology developers, original equipment manufacturers (OEMs), technology integrators, manufacturers), with the most critical risks to the objectives, which can be used to identify the most critical components and subsystems that would most benefit from a PHM system. A case study is presented in which HHM and RFRM are adapted for PHM in the context of an active manufacturing facility located in the United States. The methodologies help to identify the critical risks to the manufacturing process, and the major components and subsystems that would most benefit from a developed PHM system.