The evolving technology and state of art research have provided various platforms for transforming engineering design by merging product and process design with materials. This merger gives us an extended design space and a larger search space with a potential benefit of discovering engineering solutions that include better-quality product without compromising performances. The opportunities also pose serious challenges. The realization and modeling of the extended design space in itself is very complex as result of numerous interacting decisions (coupled decisions) at varying levels of priority. With a plethora of materials and manufacturing processes to choose from, the need for decision support to aid designers to efficiently explore the design space becomes imperative. Furthermore, the uncertainty that lies at each stage of decision making need to be properly addressed to render the effectiveness and accuracy of the undertaken decisions. The design of engineered systems, in context of this thesis, is viewed from the Decision-Based Design (DBD) perspective. In Decision-Based Design (DBD), the principal role of a human designer is to make decisions and engineering design is recognized as a decision- making process. The implementation of Decision-Based Design can take many forms, one manifestation of the Decision-Based Design (DBD) construct is the Decision Support Problem Technique (DSPT) developed to provide support to human designers in exercising judgment in making design decisions. All decisions identified in the DSPT are categorized as selection, compromise, or a combination of these. Selection decisions are modeled as selection Decision Support Problems (sDSP) and the compromise decisions are modeled as compromise Decision Support Problems (cDSP). In this thesis, a framework for modeling design decisions involving multiple interacting decisions, called the Multilevel Decision Scenario Matrix (MDSM) is proposed. The decision pattern pertaining to several interacting decisions is identified for a given engineering design problem using MDSM and a mathematical formulation with robustness metrics is implemented for the identified decision pattern to explore decisions that are relatively insensitive to uncertainties. Then, a generic robust decision method, based on compromise Decision Support Problem Construct is proposed. The integration of coupled decisions with robustness metrics, specifically, Design Capability Index (DCI) and Error Margin Index (EMI) is detailed as a method for designing engineered systems under uncertainty. The proposed method is applied in designing of fender, one-stage reduction gearbox and, composite structures.