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This article details a novel design optimization strategy for a prescribed vibration system (PVS) used to mechanically filter solids from fluids in oil and gas drilling operations. A dynamic model of the PVS is developed, and the effects of disturbance torques are detailed. This model is used to predict the effects of design parameters on system performance and efficiency, as quantified by system attributes. Conjoint value analysis, a statistical technique commonly used in marketing science, is utilized to incorporate designer preferences. This approach effectively quantifies and optimizes preference-based trade-offs in the design process. The effects of designer preferences on system performance and efficiency are simulated. This novel optimization strategy yields improvements in all system attributes across all simulated vibration profiles, and is applicable to other industrial electromechanical systems.