Reliability prediction of components operating in complex systems has historically been conducted in a statistically isolated manner. Current physics-based, i.e. mechanistic, component reliability approaches focus more on component-specific attributes and mathematical algorithms and not enough on the influence of the system. The result is that significant error can be introduced into the component reliability assessment process. The objective of this study is the development of a framework that infuses the influence of the system into the process of conducting mechanistic-based component reliability assessments. The formulated framework consists of six primary steps. The first three steps, identification, decomposition, and synthesis, are qualitative in nature and employ system reliability and safety engineering principles for an appropriate starting point for the component reliability assessment. The most unique steps of the framework are the steps used to quantify the system-driven local parameter space and a subsequent step using this information to guide the reduction of the component parameter space. The local statistical space quantification step is accomplished using two newly developed multivariate probability tools: Multi-Response First Order Second Moment and Taylor-Based Inverse Transformation. Where existing joint probability models require preliminary statistical information of the responses, these models combine statistical information of the input parameters with an efficient sampling of the response analyses to produce the multi-response joint probability distribution. Parameter space reduction is accomplished using Approximate Canonical Correlation Analysis (ACCA) employed as a multi-response screening technique. The novelty of this approach is that each individual local parameter and even subsets of parameters representing entire contributing analyses can now be rank ordered with respect to their contribution to not just one response, but the entire vector of component responses simultaneously. The final step of the framework is the actual probabilistic assessment of the component. Variations of this final step are given to allow for the utilization of existing probabilistic methods such as response surface Monte Carlo and Fast Probability Integration. The framework developed in this study is implemented to conduct the finite-element based reliability prediction of a gas turbine airfoil involving several failure responses. The framework, as implemented resulted in a considerable improvement to the accuracy of the part reliability assessment and an increased statistical understanding of the component failure behavior.