Significant technological advances in sensing promote the use of large sensor networks to monitor engineered systems, identify damages, and quantify damage levels. Prognostics and health management technique has been developed and applied for a variety of safety-critical engineered systems, given the critical needs of system health state awareness. The prognostics and health management performance highly relies on real-time sensory signals that convey system health-relevant information. Designing an optimal sensor network with high detectability of system health state is thus of great importance to the prognostics and health management performance. This article proposes a generic sensor network design framework using a detectability measure while accounting for uncertainties in material properties and geometric tolerances. Our contributions in this article are threefold: (1) the definition of a detectability measure to quantify the diagnostic/prognostic performance of a given sensor network, (2) the development of detectability analysis based on physics-based simulation and health state classification, and (3) the formulation of a generic sensor network design optimization problem as a mixed integer nonlinear programming. We employ the genetic algorithms to solve the sensor network design optimization problem. The merit of the proposed methodology is demonstrated with a power transformer system, which suffers from core and winding joint loosening due to consistent vibration.