Managing functional coupling sequences to reduce complexity and increase modularity in conceptual design

According to the Axiomatic Design Theory (ADT), a design concept that can satisfy the upstream objectives under downstream constraints with the minimal relative complexity can lead to the most ideal design. As stated by Suh’s Complexity Theory, the relative complexity of a design concept is caused by couplings between functional requirements (FRs) and design parameters (DPs), and can be reduced by strategically ordering the execution (i.e., implementation) sequence of DPs. However, it is generally very difficult in the current design practice to obtain this “execution sequence” with existing methods due to their inherent limitations and/or many real-world restrictions. Meanwhile, many practical methods, such as the modular design approach, have been widely used in industries to produce real-world design results that don’t necessarily conform with the principles required by those ideal design theories. As a result, from the perspectives of design theories, most real-world designs are “not ideal” (i.e., having some relative complexities due to FR-DP couplings) and therefore can (and should) be improved by better sequencing their DPs. This is the motivation under which the Design Coupling Sequence (DCS) method was developed in this thesis research. The DCS method can assist designers to automatically obtain the “execution sequences,” in the forms of functional sets, that can yield the minimal relative complexity, hence making a practical design concept most ideal (i.e., as close to the ideal concept with the minimal relative complexity as possible) while taking into practical considerations (such as increasing the modularity to lower the production costs) in real-world conceptual designs. ❧ The DCS method defines the ‘precedence’ between ‘functional sets’ to manage coupled design concepts to support the modular approach during conceptual design. It identifies the ‘precedence’ by the level of functional coupling to determine the proper sequencing order to minimize the overall complexity. Two types of functional sets are defined in DCS as 1) the complete independently set U: the collection of all the functionally dependent DPs in the system so that the set is independent to other U sets, and 2) the indivisible coupled set C: the collection of coupled concepts that can’t be decoupled by sequencing, so it prescribes the designer to consider the group of DPs together as a set to match existing modules in the database. To handle the real complexity of design concepts which require redesign, the DCS algorithm helps to determine the proper execution sequence. To minimize the imaginary complexity, which occurs when design concepts “appear” to be functionally coupled due to a lack of understanding of the system structure, the DCS method provides a formula to reveal the number of acceptable execution sequences that can lead to the simplest design implementation. Compared with existing methods, the DCS method is applicable for any design cases with known design matrices, including the square, rectangular, zero-at-diagonal, large, and/or numerical matrices. In short, for all practical design cases, DCS can organize functional-coupled design concepts as “functional sets” with execution sequences of DPs that lead to the minimal complexity of this design concept. ❧ The foundation, hypothesis, algorithm and its usability of the DCS method are validated by four case studies in this research. The faucet design case demonstrates how to apply the DCS method and shows the differences between ADT and DCS results. The case of coffee maker design shows how the DCS method manages the functional sets based on the design matrices reengineered from existing design concepts. The vehicle tire design case demonstrates how different DCS strategies within the Innovative Design Thinking (IDT framework during the conceptual design stage can work in a real-world product development situation. The IDT framework prescribes four consecutive steps: (1) following the top-down process to ideate new design concepts that satisfy the principles/axioms suggested by the design theory to reach a certain layer of details, (2) following the bottom-up process to identify some existing design modules from available engineering database (or catalogs) that can satisfy the functional requirements at this detail layer, (3) constructing the design matrix that shows the couplings between FRs and DPs at this detail layer, and (4) apply the DCS algorithm to determine the execution sequence of DPs based on the above design matrix. This will yield a new design concept with an execution sequence that is most creative (because it satisfies the design principles at the top layers) and most practical (because it utilizes the existing modules at the bottom layers). Finally, a case of collision avoidance planning presents one of the possible extensions of the DCS algorithm. ❧ The results of this research have significant impacts on both design theory and design practice. Theoretically, the approach in this research 1) guides designers to improve concepts not only organizing design matrix but also extract additional coupling information to increase modularity and 2) is a more generalized approach than the previous methods that can be applied to any design cases with design matrix. Practically, the research 1) demonstrates the usability of the DCS algorithm within an executive program to generate the DCS functional sets automatically for large design system and 2) allows the principle of functional dependency and the practice of modular design to be considered simultaneously as much as possible during the conceptual design stage. It is a fundamental contribution that demonstrates how the ideal principles (or axioms) of design theories can be used together strategically with practical design methods (or considerations) in industry practices to generate real-world design results that are both most practical and creative. For future research, there would be three aspects- DCS algorithm, DCS sets, and DCS strategies. Number one, DCS algorithm would be further revised to extend to software design or machine learning with functional sets in terms of a component diagram. Number two, with DCS sets, the three-dimensional design matrix could be studied further. Number three, DCS strategies would be investigated further for applying on detailed design cases. ❧ As a recap, the research prescribes a functional coupling managing algorithm with functional sets for suggesting acceptable execution sequences in conceptual design. It not only helps designers with complexity reduction but also bridges the ideal design theory to practical modules. The designer can create better designs that are most creative and yet practical by using the DCS strategies.