(Academic)Reliability-Based Design Optimization (RBDO) approaches often use the First-Order Reliability Method (FORM) to efficiently obtain an estimate of the reliability of a system. This approach treats the reliability analysis as a nested optimization problem, where the objective is to compute the most probable point (MPP) by minimizing the distance between the failure surface and the origin of a normalized random space. Numeric gradient calculation of the solution of this nested problem requires an additional solution of the FORM problem for each design variable, an approach which quickly becomes computationally intractable for large scale problems including Reliability-Based Topology Optimization (RBTO). In this thesis, an alternative analytic approach to the analysis and sensitivity of nested optima derived from the Lagrange Multiplier Theorem is explored. This approach leads to a system of nonlinear equations for the MPP analysis for any given set of design variables. Taking the derivative of these equations with respect to a design variable gives a linear system of equations in terms of the implicit sensitivities of the MPP to the design variable where the coefficients of the linear equations depend only on the current MPP. By solving this system, these sensitivities can be obtained It is a common practice when designing a system to apply safety factors to the critical failure load or event. These safety factors provide a buffer against failure due to the random or unmodeled behavior, which may lead the system to exceed these limits. However these safety factors are not directly related to the likelihood of a failure event occurring. If the safety factors are poorly chosen, the system may fail unexpectedly or it may have a design which is too conservative. Reliability-Based Design Optimization (RBDO) is an alternative approach which directly considers the likelihood of failure by incorporating a reliability analysis step such as the