This paper presents the requirements and needs for establishing a benchmarking protocol that considers representation characteristics, supported cognitive criteria, and enabled reasoning activities for the systematic comparison of function modeling representations. Problem types are defined as reverse engineering, familiar products, novel products, and single-component systems. As different modeling approaches share elements, a comparison of modeling approaches on multiple levels was also undertaken. It is recommended that researchers and developers of function modeling representations collaborate to define a canonically acceptable set of benchmark tests and evaluations so that clear benefits and weaknesses for the disparate collection of approaches can be compared. This paper is written as a call to action for the research community to begin establishing a benchmarking standard protocol for function modeling comparison purposes. This protocol should be refined with input from developers of the competing approaches in an academically open environment. At the same time, the benchmarking criteria identified should also serve as a guide for validating a modeling approach or analyzing its failure.

This paper introduces a rigorous framework for function modeling of complex multidisciplinary systems based on the system state flow diagram (SSFD). The work addresses the need for a consistent methodology to support solution-neutral function-based system decomposition analysis, facilitating the design, modeling, and analysis of complex systems architectures. A rigorous basis for the SSFD is established by defining conventions for states and function definitions and a representation scheme, underpinned by a critical review of existing literature. A set of heuristics are introduced to support the function decomposition analysis and to facilitate the deployment of the methodology with strong practitioner guidelines. The SSFD heuristics extend the existing framework of Otto and Wood (2001) by introducing a conditional fork node heuristic, to facilitate analysis and aggregation of function models across multiple modes of operation of the system. The empirical validation of the SSFD function modeling framework is discussed in relation to its application to two case studies: a benchmark problem (glue gun) set for the engineering design community; and an industrial case study of an electric vehicle powertrain. Based on the evidence from the two case studies presented in the paper, a critical evaluation of the SSFD function modeling methodology is discussed based on the function benchmarking framework established by Summers et al. (2013), considering the representation, modeling, cognitive, and reasoning characteristics. The significance of this paper is that it establishes a rigorous reference framework for the SSFD function representation and a consistent methodology to guide the practitioner with its deployment, facilitating its impact to industrial practice.

Research and industrial practice have produced a host of function models and modeling approaches over the last decades. Each of these is meant to support designers in their design endeavors. Industrial practice is excessively diversified in terms of contextual requirements, aims, and adopted processes; this automatically begs the question which of the existing models should be selected for application in a specific situation. This paper sets out to contribute to this discourse. It strives to benchmark the fairly novel integrated function modeling (IFM) framework against the well-established function structures modeling approach. The paper comparatively investigates the respective capabilities of the approaches, following the benchmarking protocol used earlier in relation to this Special Issue. Function structures are used as reference as they represent one of the most widespread function modeling approaches in research and practice. Both function structures and the IFM framework are exemplarily applied for modeling a glue gun. The gradual generation and refinement of the models is used to showcase their respective benefits and shortcomings. Eventually, the IFM framework is found to excel over function structures in terms of comprehensiveness and support for different types of function analyses. Finally, future research directions are proposed.

Functional modeling is an effective method of depicting products in the design process. Using this approach, product architecture, concept generation, and physical modeling all contribute to the design process to generate a result full of quality and functionality. The functional basis approach provides taxonomy of uniform vocabulary to produce function structures with consistent functions (verbs) and flows (nouns). Material and energy flows dominate function structures in the mechanical engineering domain with only a small percentage including signal flows. Research suggests that the signal flow gap is due to the requirement of “carrier” flows of either material or energy to transport the signals between functions. This research suggests that incorporating controls engineering methodologies may increase the number of signal flows in function structures. We show correlations between the functional modeling and controls engineering in four facets: schematic similarities, performance matching through flows, mathematical function creation using bond graphs, and isomorphic matching of the aforementioned characteristics allows for analogical solutions. Controls systems use block diagrams to represent the sequential steps of the system. These block diagrams parallel the function structures of engineering design. Performance metrics between the two domains can be complimentary when decomposed down to nondimensional engineering units. Mathematical functions of the actions in controls systems can resemble the functional basis functions with bond graphs by identifying characteristic behavior of the functions on the flows. Isomorphic matching, using the schematic diagrams, produces analogies based upon similar functionality and target performance metrics. These four similarities bridge the mechanical and electrical domains via the controls domain. We provide concepts and contextualization for the methodology using domain-agnostic examples. We conclude with suggestion of pathways forward for this preliminary research.

Functional modeling is an analytical approach to design problems that is widely taught in certain academic communities but not often used by practitioners. This approach can be applied in multiple ways to formalize the understanding of the systems, to support the synthesis of the design in the development of a new product, or to support the analysis and improvement of existing systems incrementally. The type of usage depends on the objectives that are targeted. The objectives can be categorized into two key groups: discovering a totally new solution, or improving an existing one. This article proposes to use the functional modeling approach to achieve three goals: to support the representation of physics-based reasoning, to use this physics-based reasoning to assess design options, and finally to support innovative ideation. The exemplification of the function-based approach is presented via a case study of a glue gun proposed for this Special Issue. A reverse engineering approach is applied, and the authors seek an incremental improvement of the solution. As the physics-based reasoning model presented in this article is heavily dependent on the quality of the functional model, the authors propose a general approach to limit the interpretability of the functional representations by mapping the functional vocabulary with elementary structural blocks derived from bond graph theory. The physics-based reasoning approach is supported by a mathematical framework that is summarized in the article. The physics-based reasoning model is used for discovering the limitations of solutions in the form of internal contradictions and guiding the design ideation effort.

Critical chains composed of critical flows and functions have been demonstrated as an effective qualitative analogy retrieval approach based on performance metrics. In prior work, engineers used expert knowledge to transform functional models into critical chain models, which are abstractions of the functional model. Automating this transformation process is highly desirable so as to provide for a robust transformation method. Within this paper, two paradigms for functional modeling abstraction are compared. A series of pruning rules provide an automated transformation approach, and this is compared to the results generated previously through an expert knowledge approach. These two approaches are evaluated against a set of published functional models. The similarity of the resulting transformation of the functional models into critical chain models is evaluated using a functional chain similarity metric, developed in previous work. Once critical chain models are identified, additional model evaluation criteria are used to evaluate the utility of the critical chain models for design analogy identification. Since the functional vocabulary acts as a common language among designers and engineers to abstract and represent critical design artifact information, analogous matching can be made about the functional vocabulary. Thus, the transformation of functional models into critical chain models enables engineers to use functional abstraction as a mechanism to identify design analogies. The critical flow rule is the most effective first step when automatically transforming a functional model to a critical chain model. Further research into more complex critical chain model architectures and the interactions between criteria is merited.

Modular product design is an efficient strategy to let manufacturing companies meet the customers’ requirements by offering a wide variety and customization of products and significantly saving time and cost during engineering and production (Fei et al., 2011). Despite numerous approaches for function modeling and modular product design (Srinivasan et al., 2012; Eckert, 2013; Vermaas, 2013) that have been developed in the last decades, carrying out an efficient product variants’ design process is still an open issue for many manufacturing companies. The proposed approaches offer numerous ways to model information about product functionality, but each approach is useful and particularly well suited for different applications and domains (Summers et al., 2013). The present research compares the existing approaches for product variants design and defines a function-based model to support product design and redesign according to a modular framework, merging qualitative technical issues with business-oriented evaluation. Such a framework has been used to develop a multiuser IT platform, composed of a knowledge-based engine and four different tools to support designers and engineers in product variants creation, management, and configuration, from product functional modeling to cost estimation and life cycle assessment. The proposed model has been tested on industrial cases in the context of household appliances. Experimental results demonstrates that, after a preliminary context analysis and a proper knowledge base creation, such a model supports a more conscious decision-making and promote collaboration within an interdisciplinary design team. Finally, the case study shows the necessity, but in the meanwhile the insufficiency, of a functional decomposition as the only representation viewpoint.

This paper aims to situate functional abstraction in light of systems thinking. While function does not extensively appear in systems thinking literature, the literature does identify function as part of systems thinking that enables us to recognize and connect that function has a role in building a systems thinking approach for students. A systems thinking approach is valuable for students since it helps them view a system holistically. In this research, we measure how well students are able to abstract function. We asked students to generate functions for two different products and examined how students taught functional modeling and function enumeration compare to students who are only taught function enumeration. The student responses were examined using a rubric that we developed and validated for assessing function. This rubric may be used to classify functions by correctness (correct, partially correct, and incorrect) and categories (high level, interface, low level, and ambiguous). On questions where students were not explicitly asked to write a high-level function or low-level function, and so on, students who were taught functional modeling were able to better demonstrate systems thinking in their responses (low-level and interface functions) than those students who were only taught function enumeration.

Benchmarking function modeling and representation approaches requires a direct comparison, including the inferencing support by the different approaches. To this end, this paper explores the value of a representation by comparing the ability of a representation to support reasoning based on varying amounts of information stored in the representational components of a function structure: vocabulary, grammar, and topology. This is done by classifying the previously developed functional pruning rules into vocabulary, grammatical, and topological classes and applying them to function structures available from an external design repository. The original and pruned function structures of electromechanical devices are then evaluated for how accurately market values can be predicted using the graph complexity connectivity method. The accuracy is found to be inversely related to the amount of information and level of detail. Applying the topological rule does not significantly impact the predictive power of the models, while applying the vocabulary rules and the grammar rules reduces the accuracy of the predictions. Finally, the least predictive model set is that which had all rules applied. In this manner, the value of a representation to predict or answer questions is quantified.