Design of a mechatronic system requires multidisciplinary knowledge. A designer should consider product lifecycle issues as well as design and manufacturing strategies simultaneously at conceptual design stage without missing any of the information. The proposed methodology concurrently considers all the x-abilities/design aspects along with interactions without missing any information and hence leads to a high quality product. A methodology which amalgamates concurrent design concepts, graph theory, matrix algebra, and permanent multinomial is proposed. Eight x-abilities namely, miniaturization, intelligence, integration, environment, quality, reliability, manufacturing, and assembly for concurrent design of a mechatronic system and the design parameters under each x-ability are identified. A colored graph useful for visual analysis is proposed. The design index derived is useful for researcher and designer in evaluating the conceptual design alternatives. The proposed step-by-step procedure would be useful for developing a new algorithm for software coding.