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Ever since its beginning, systems engineering has been influencing every application in our daily life. Consistent with the evolution of IT and electronics, systems design has been shaped by several structured design methodologies including Six Sigma, lean and including data analytics. Though the development of applications using systems concepts has been rapid, the focus has been limited to the fundamental methodologies leading to better system design. In this paper, a methodology, EMBED-X, is proposed for design of human-robotic systems using the concepts of systems engineering where the phases of system development are effected using Lean Six Sigma and analytics. The EMBED-X methodology encapsulates an Internet of Things (IoT) based environment. The case studies of a weather display system and development of a rover-drone are considered here. The EMBED-X framework allows flexibility in implementation and combines the principles of Six Sigma and Lean in the context of human-centered development. The human interface is accomplished using the Habermas's theory of communicative action. This methodology presents several advantages over traditional systems design. The key advantages include better coordination between human designers, design reuse, prediction of faults or failure modes and optimized cost. Therefore, the design of robotic systems, in particular, would benefit from a combined methodology, not only as a means for system development but also during training and workshops. The paper draws conclusions on the limitations of the present work and discusses the wide scope for future research.