Functional Decomposition in Engineering: a Survey

Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2007 September 4-7, 2007, Las Vegas, Nevada, USA

DETC2007-34232

FUNCTIONAL DECOMPOSITION IN ENGINEERING: A SURVEY

Dingmar van Eck∗∗∗ Daniel A. McAdams Department of Philosophy Department of Mechanical & Delft University of Technology Aerospace Engineering Jaffalaan 5, 2628 BX Delft The University of Missouri-Rolla The Netherlands Rolla, MO 65409, USA

Pieter E. Vermaas Department of Philosophy Delft University of Technology Jaffalaan 5, 2628 BX Delft The Netherlands

ABSTRACT redesigning of existing products, functional reasoning Functional reasoning is regarded as an important asset to complements physical descriptions of the products indicating the engineering designers’ conceptual toolkit. Yet despite the the roles and uses of products and their components. Moreover, value of functional reasoning for engineering design, a functional reasoning is increasingly regarded as a common consensus view is lacking and several distinct proposals have technique, which is shared in engineering communication about been formulated. In this paper some of the main models for functional structures of products that are (collaboratively) functional reasoning that are currently in use or discussed in designed or redesigned, and in the archiving and use of engineering are surveyed and some of their differences clarified. functional structures of existing products in knowledge bases. The models included the Functional Basis approach by Stone This importance of functional reasoning in engineering and Wood [1], the Function Behavior State approach by Umeda warrants an ongoing effort at formalization to arrive at uniform et al. [2, 3, 4], and the Functional Reasoning approach of and commonly shared methods for the modeling of functions, to Chakrabarti and Bligh [5, 6]. This paper explicates differences fix the relations that hold between functions, and to define between these approaches relating to: (1) representations of algorithms that support reasoning about functions. Such function and how they are influenced by design aims and form formalization would not only facilitate the above-mentioned solutions, and (2) functional decomposition strategies, taken as uses of functional reasoning, but also allow for the next step of the reasoning from overall artifact functions to sub-functions, automating functional reasoning in computer tools, ranging and how these decomposition strategies are influenced by the from CAD-CAM systems to engineering knowledge bases. use of existing engineering design knowledge bases. Yet, despite the broadly accepted value of a common and uniform language for functional reasoning, the current situation 1 INTRODUCTION in the engineering sciences is rather one of plurality. Just as that Functional reasoning is increasingly regarded as an important there is no consensus in engineering about the meaning of the technique in engineering [7, 8]. For instance, in engineering term function itself [9, 10, 11], there is currently a series of designing of innovative products functional reasoning is functional reasoning models being proposed and developed that required in the initial conceptual phase of the design process to are distinct rather than convergent. fix the functional structure of a product relatively independently This plurality has – apparently – not hampered engineering of specific design solutions, and in engineering descriptions and and designing so far. Yet, with the increasing use of computer

∗ Author of correspondence, Phone: + 31 15 278-5417, Fax: + 31 15 278-6233, Email: [email protected].

1 Copyright © 2007 by ASME tools such as CAD-CAM systems and engineering knowledge supported since functional modeling allows designers to make bases, and with the increasing effort to couple these systems by critical design decisions about the product’s architecture in the communication or integration, it may be envisaged that this lack early conceptual stage of designing at which only functional of consensus may play up at some point in the near future. If, descriptions are considered. for instance, the current models for functional reasoning are Functions and sub-functions in the Functional Basis developed successfully in competition with one another, and approach are captured in terms of operations on flows of then incorporated in separate engineering computer systems, materials, energies, and signals. This operation on flows one is bound to end up with design tools and knowledge bases description of functions is reminiscent of the work on functions that are difficult to integrate. The source of this problem will by Pahl and Beitz [12]. then be identified as consisting of the different models of functional reasoning underlying these computer systems, which 2.1 Functions as Operations on Flows will then become topic of analysis. Anticipating these problems, In the Functional Basis approach an overall product function and – possibly somewhat ideally – trying to prevent them, we refers to a general input/output relationship of a products’ here set out in this paper to give this analysis immediately by overall task, which is described in a verb-object form and surveying a number of the main models of functional reasoning, represented by a black-boxed operation on flows of materials, as currently discussed in the engineering literature. energies, and signals. A sub-function is also described in a verb- We focus in this survey on conceptual differences between object form but represented by a well-defined basic operation three models of functional reasoning, specifically on how the on well-defined basic flows of materials, energies, and signals. term function itself is understood in these models, on how The black-boxed operations on general flows representing functional decomposition taken as the reasoning from overall product functions are derived from customer needs, and the functions to sub-functions is captured, and on how this basic operations and basic flows representing sub-functions are decomposition of functions is related to engineering knowledge laid down in common and limited libraries that span the about design solutions to functions. These models are the functional design space. These libraries are called a functional Functional Basis approach by Robert Stone and Kristin Wood basis (the current libraries have been fixed in [8] by integrating [1], the Function Behavior State approach by Yasushi Umeda et the libraries proposed in [1] with similar libraries developed at al. [2, 3, 4], and the Functional Reasoning approach by the US National Institute of Standards and Technology [13]). Amaresh Chakrabarti and Thomas Bligh [5, 6]. These three To give an idea on how overall product functions and models were chosen because they describe functional reasoning connected sub-functions are represented in the Functional Basis explicitly but reveal already on first inspection relevant approach, consider the example of a power screwdriver differences. First, in the Function Behavior State approach (adapted from [1]); the overall product function of the design reasoning from functions to physical structure takes screwdriver is represented (in verb-object form) as the place via the intermediate notion of behavior, whereas in the operation “loosen/tighten screws”, and has input and output other two approaches this reasoning is done without an flows of energies, materials, and signals. This overall product intermediate concept. Second, the Functional Basis approach function representation thus black boxes the internal flows of advances functional reasoning that is independent of existing the power screwdriver that transform the input flows into output design solutions to functions, whereas in the other two flows. Focusing on the energy flow, the input side consists of functional reasoning explicitly depends on such solutions. flows of electricity, human force, relative rotation, and weight, The sections 2, 3, and 4 are used for this presentation. and the output flows consist of torque, heat, noise, human force, Then, in section 5, we briefly compare the key elements of these and weight. Extracting the electricity part of the (internal) models and in section 6 we end with conclusions. energy flow, the representation of the detailed (temporally ordered) sub-functions operating on the incoming electricity 2 THE FUNCTIONAL BASIS APPROACH flow are represented as “store electricity”, “supply electricity”, The Functional Basis approach by Robert Stone and Kristin “transmit electricity”, “actuate electricity”, and “regulate Wood is an approach to that aims at creating a common and electricity”, respectively. These sub-functions are thus consistent functional design language, dubbed a functional represented as basic operations on basic flows and transform an basis, which allows designers to describe overall product input flow step-by-step into an output flow. functions in terms of interconnected sub-functions [1]. The Functional Basis approach is focused on especially the Table 1. Primary basic operations and flows in the electromechanical and mechanical domain and is presented as functional basis [8]. supporting the archiving, comparison, and communication of Primary basic Branch, Channel, Connect, functional descriptions of existing products, as well as the operations Control Magnitude, Convert, engineering designing of new products. Archiving, comparison, Provision, Signal, Support and communication are assisted since the sub-functions into Primary basic flows Material, Signal, Energy which overall product functions are decomposed, are described in a common universal language. Designing of new products is

2 Copyright © 2007 by ASME 2.2 Developing Sub-Function Chains to sub-functions from a repository archiving functional models The Functional Basis approach of Stone and Wood allows, as of products. It thus is a tool that aids in and implements a main said, to model overall product functions as sets of connected objective of functional decomposition, i.e., the generation of sub-functions. Their functional modeling framework provides functional design solutions. The other functional decomposition the means to decompose overall product functions into what approaches surveyed in this paper also employ such archived they call ‘small, easily solvable sub-functions’, i.e., sub- design knowledge bases in generating functional models, and functions for which solutions exist such that ‘the [structural] we therefore include the Concept Generator in our survey in form of the device [product to be designed] follows from the order to be able to discuss in section 5 the different ways in assembly of all sub-function solutions’ [1]. which knowledge bases assist in developing functional models. These sub-function assemblies, i.e., function structures, result from the following decomposition steps or tasks: Table 2. Function definitions, decomposition strategy, The first task is to arrive at an overall product function of a and design knowledge in the Functional Basis approach. product to be designed, described in a verb-object form and Function General input/output relationship of a represented by a black-boxed operation on flows of materials, product having the purpose of energies, and signals. This black-boxed operation originates performing an overall task, represented from customer needs and may initially be quite general, and is by a black box operation on flows of later on in the design process refined. The verb-object material, energy, and signal, determined description of the product function and this (black-boxed) by costumer needs operation-on-flows representation are related in the sense that Sub-function Part of a product’s overall task, the verb corresponds with the operation and the object represented by a basic operation on basic corresponds with (parts of) the flows. flows of material, energy, or signal, as The second task is to define for each input flow a chain of defined by the functional basis libraries sub-functions that transform that flow step-by-step into an of basic operations and basic flows output flow. These sub-functions are also described in verb- Decomposition Analysis of the black-box operation on object forms and represented by operations on flows. But now strategy flows corresponding to the overall the verbs are to be chosen from the functional basis. The sub- product function in terms of connected functions part of the different chains must be ordered in time basic operations on basic flows with respect to one another. corresponding to the sub-functions The third task is then to integrate these temporally ordered Design Archived functional models of products chains of sub-functions by connecting them, thereby arriving at knowledge base and archived components that counts as the functional model. In this three-step process the designer thus design solutions to sub-functions has to analyze the input flows of the overall function in terms of basic flows from the library of basic flows, and come up with a The Concept Generator can be found at a site created at the series of operations from the library of basic operations that Design Engineering Lab of the University of Missouri-Rolla, sequentially and/or in parallel transform the input flows step-by- which hosts also a web-based repository that contains functional step into the output flows. This transition from input to output is models of up to 102 products and their components, and that expressed by Stone and Wood thus: “think of each operation on stores the design solutions – the physical structures that can the flow from entrance until exit of the product (or perform these sub-functions – for the sub-functions part of these transformation to another flow) and express it as a sub-function models [15]. The Concept Generator is now aimed at creating in verb-object form” [1]. new functional models for any overall product function that is The Stone-Wood approach allows functional models to be fed into it, and at generating design solutions for these overall developed with a high level of detail. It is argued that the product functions on the basis of the design solutions of their functional basis defines a comprehensive set of basic functions, sub-functions that are already stored in the repository. able to fully span the mechanical (and electromechanical) In the first step of the algorithm, the Concept Generator design space, and that these basic functions have a level of translates the functional model of the overall product function detail, which allows them to be “easily solvable” [1]. (only models consisting of single chains of sub-functions are considered in [14]) into information about the sub-functions and 2.3 Design Repositories and the Concept Generator their adjacency. Secondly, the Concept Generator collects for Having discussed the function definitions and functional each individual sub-function in the chain design solutions decomposition strategy of the Functional Basis approach, we consisting of components that are stored in the repository as discuss in this section a design tool called the Concept having that specific sub-function. In the third step, all design Generator that can be taken as a natural extension of the solutions for the product as a whole are generated by Functional Basis approach [14]. The Concept Generator is an describing, on the basis of the information gathered in the first automated, mathematically based design tool that aids in the two steps, all theoretically possible component chains that solve development of functional models by retrieving design solutions

3 Copyright © 2007 by ASME the overall product function. Fourthly, additional information is Functions are archived in so-called function prototypes. collected from the repository on which sets of components have Function prototypes are designer knowledge bases which been actually combined in existing products, and in that sense represent and store typical patterns of functions that often can be taken as sets of compatible components. Finally, in a appear in a certain design domain [4]. Instead of defining fifth step, this information about the compatibility of functional primitives, in the FBS approach, functions are components is used to prune the set of theoretically possible defined by developing and archiving various function component chains to a set of feasible component chains that prototypes from existing product designs, basing solve the overall product function. In this final step a ranking is representations of functions on them. Function prototypes also added to these feasible chains, to “bubble the most represent, amongst others, functions and networks of sub- promising solutions to the top”. The algorithm puts constraints functions into which the function can be decomposed, which the on the functional modeling of overall product functions: the FBS modeler employs in developing functional models of algorithm selects only those functional models that consists of design objects (see section 3.3). sub-functions for which there are components available in the An example (adapted from [2, 4]) of function, behavior, design repository that have these sub-functions, and the and state representations in the FBS modeler is, for instance, the algorithm selects only those models that combine sub-functions function “to charge drum” in the design of a photocopier. In the that are actually combined in functional models of products in FBS modeler, this function is decomposed into the sub- the repository. functions “to rotate drum” and “to discharge voltage to drum”, To be sure, there is more to be said on the algorithm of the of which the latter sub-function is achieved by the behaviors Concept Generator and on the way it is implemented in “electrical charging” and “electrical discharging”, occurring on computer systems. For the purposes of this paper, i.e., the entities (states) “drum” and “discharger”, respectively. comparing the conceptual differences between models of functional reasoning, the above description suffices (but see 3.2 Developing Function-Behavior-State Mappings [14, 15] for more details). Functional design in the FBS approach, employing the FBS modeler, consists of six steps that involve two distinct types and 3 THE FUNCTION BEHAVIOR STATE APPROACH phases of functional decomposition in which two distinct Like the Functional Basis approach, the Function Behavior knowledge bases are used [2, 3]: First, the designer specifies a State (FBS) approach developed by Yasushi Umeda et al. [2, 3, required function by selecting an appropriate function prototype 4] aims to support and facilitate functional design. In particular, [2]. This specification and selection is somewhat unclear in the the FBS approach is reported to support the synthetic phase of FBS approach, but the authors seem to suggest that choosing a functional design, described by its developers as the process by function prototype fixes what the required function will be, which functional descriptions representing user intentions are instead of an appropriate function prototype being selected transformed into structural descriptions of products-to-be [2]. based on the (prior) formulation of a required function (see To support such synthetic design tasks, the FBS approach section 3.1). Second, the required function is then, by applying employs a computer-based design tool, called the FBS modeler, decomposition knowledge stored in the selected function which generates functional models that represent mappings prototype, decomposed into sub-functions, a procedure coined amongst functions, behaviors, and product structures. Structures “task decomposition” [2]. Third, these sub-functions are then are referred to as states in the FBS approach and the state of a mapped onto design solutions by instantiating appropriate design object is represented by entities, their attributes, and physical features selected by the designer. Physical features, relations between entities [2]. The FBS modeler thus is a design also archived in the selected function prototypes, refer to sets of tool supporting “the embodiment process of a function” [4], in components, their relations, and physical phenomena that which the concept of behavior is used as an intermediate step in together instantiate specific behavior(s) and thus particular transforming functions into states or structures. function(s) [2]. Fourth, after instantiation of physical features it may be the 3.1 Functions as Intended Behaviors case that some of them cannot occur because not all the In the FBS approach functions are equated with intended requisite physical conditions to instantiate the physical behaviors and described thus: “a description of behavior phenomena are met. For instance, for a particular physical abstracted by human through recognition of the behavior in phenomenon to occur, additional components might be needed, order to utilize it” [16] and elsewhere as “a function is an and connected to the ones already selected via physical feature association between the designer’s intention and a behavior that instantiation. Resultantly, not all task-decomposed functions can realizes the function” [3]. A function is represented by an be mapped onto design solutions. If this occurs, a subsystem of association of two concepts; a verb-object pair that represents the FBS modeler, coined Qualitative Process Abduction System designer intentions, expressed in the form of “to do something” (QPAS), reasons out additional physical features to realize these [2, 4], and behavior(s) that can instantiate the function. conditions, thereby realizing the embodiment of the sub- Behaviors in the FBS approach are defined as “sequential state functions that remained un-instantiated after the task transitions along time” [2]. decomposition. This procedure is dubbed “causal

4 Copyright © 2007 by ASME decomposition”. QPAS is a knowledge-based reasoning system represent task functions that include a symbol for the designer’s that generates design solution candidates by using physical intention, a network of sub-functions into which the task phenomenon and physical feature knowledge bases [17]. It function can be decomposed, as well as function-behavior takes as input a particular (series of) state transition(s), relations that are represented in the form of physical features, including relevant entities and physical conditions, and then thus specifying candidate embodiments of the (sub) functions. derives candidate physical phenomena that can achieve the state Function prototypes thus contain archived function-behavior- transition(s). Subsequently, QPAS derives physical features that state relations or mappings, derived from previous design include the physical phenomenon, after which the designer can results. Physical features are viewed as “building blocks” of select an appropriate one, thus instantiating the physical functions, and consist of entities, relations between entities, and phenomenon [17] (see also [18] for additional details on physical phenomena occurring on them. In the FBS modeler QPAS). these elements of physical features are dubbed behavioral Then, after physical feature selection and instantiation, the nodes, which together comprise a behavioral network [2]. As FBS modeler again employs the function prototypes knowledge discussed in the last section, the FBS approach relies on these base and reasons out and selects a function prototype that has function prototypes in specifying required functions and in the the added physical feature in its function-behavior relation and first phase (steps 1-3) of its functional decomposition scheme thus explains the function(s) of the added physical feature. The where function-behavior-state-mappings are developed. Next to function(s) is (are) then incorporated in the FBS model, and these function prototypes, in the second phase of the FBS connected as a cause to the initially un-instantiated sub- decomposition strategy (steps 4-6), the FBS modeler employs function(s) of the task decomposition. QPAS that uses physical phenomenon and physical feature In the next fifth step, the designer constructs a behavioral knowledge bases to realize un-instantiated functions from the network by connecting the instantiated physical features, first phase by finding out “appropriate mechanisms for realizing completing the functional hierarchy. Then, in the sixth step, a task-decomposed functions with physical knowledge” [2]. behavior simulation is run that evaluates the FBS model. If the simulation is unsatisfactory the designer can make adjustments Table 3. Function definitions, decomposition strategy, in either the functional hierarchy or in the behavioral network. and design knowledge in the FBS approach. This six-step functional decomposition strategy thus Function Intended behavior, expressed as a involves two distinct decomposition phases and types; a task combination of designer intentions and decomposition in the first phase (step 2) based on knowledge behavior(s) that can exhibit the function stored in function prototypes, and a causal decomposition in the Sub-function No separate definition given: sub- second phase (step 4) based on knowledge derived from QPAS functions are part of an overall function, [2]. The difference between the decomposition types seems to derived from either causal decomposition be one of detail; in task decomposition, the (sub) functions or task decomposition reflect designer intentions (“to do something”) and their Decomposition Function-state mapping via behaviors instantiating behaviors are not causally dependent on one strategy and physical features. Two distinct another and cannot be derived from physical knowledge [2]. By decomposition phases and types: first, contrast, (sub) functions in causal decompositions are task decomposition and resulting physically derivable and their instantiating behaviors are function-state mapping; second, causal causally related [2]. Umeda et al. [2] explain this difference decomposition and resulting function- thus: “the task-decomposed functional hierarchy can be state mapping of task-decomposed considered as a description of the designer’s intention, the functions that could not be mapped onto extracted functions by the causal decomposition can be states in the first phase considered as additional functions for explaining the mechanism Design Archived function-behavior-state to realize the designer’s intention” [2]. Their reference to knowledge base mappings mechanisms realizing a functional hierarchy suggests that functions in casual decomposition are more specific than 4 THE CHAKRABARTI-BLIGH APPROACH functions in task decomposition. The Functional Reasoning approach developed by Amaresh Chakrabarti and Thomas Bligh [5, 6] is yet another framework 3.3 Function Prototypes for functional reasoning in the conceptual mechanical design The abovementioned function prototypes refer to designer space, in particular the domain of mechanical transmission knowledge bases that archive and represent typical patterns of design [5]. It aims to facilitate computational approaches to functions for a certain design domain [4]. The FBS strategy for design and takes a prescriptive stance towards designing. defining functions, instead of an a priori method, consists in Chakrabarti and Bligh [6] identify three requirements of an collecting various function prototypes from existing design ideal functional reasoning approach: it should support design of results, and then to base representations of function on these any nature, from routine to innovative, it should support the prototypes [2]. The schemes within function prototypes

5 Copyright © 2007 by ASME synthesis of design solutions at a given level of design, and it included in their Functional Reasoning approach to arrive at a should support the elaboration of solution concepts through design solution for an overall design problem are [6]: First, the levels of detail [6]. They argue in [6] that these aims can only overall problem is described in terms of the intended function(s) be met when function based reasoning approaches employ a of the physical design to be developed. A part of this problem, known set of design solutions (structures) in its reasoning the sub-function, is then chosen for synthesis, i.e., for function- schemes. These solutions or structures are to be represented in structure mapping. Then, second, from a known set of terms of the functions they provide or require (to operate structures, alternative solutions are chosen that can instantiate properly). In the Chakrabarti-Bligh approach, the aim of the sub-function. Third, the first of these alternative solutions is functional reasoning is taken to provide “physical descriptions chosen and its (sub) function is evaluated with respect to the of designs, sufficient for their implementation, which would overall function or design problem. By incorporating the chosen provide the intended functions of the problem” [6]. This part-solution, the overall function is revised and narrowed approach consists of a piecemeal approach in which function- down; the number of sub-functions for which solutions have to component mappings are integrated from the outset (and step by be found is decreased. Fourthly, another sub-function of the step) in a functional reasoning process until the solution space now revised overall function is selected for synthesis, i.e., (of known structures) has been searched completely. It thus structure-function mapping. This step-by-step recursive tackles the design problem, i.e., the realization of the overall procedure continues until all the sub-functions of the overall product function, in parts. function are solved, i.e., all realizing structures are found. These steps thus solve a problem part (sub-function) of the overall 4.1 Function as Action or Effect design problem (overall function) at a time, thereby reducing In the Chakrabarti-Bligh approach, function is understood as a the overall problem space, until the overall function is description of the action or effect required by a design problem completely solved and implementing structures are identified or supplied by a solution [6]. In earlier work of Chakrabarti and for each sub-function. This four-step procedure leads to the Bligh, function is exclusively tied to an artifact’s structure or generation of a single solution structure, being an aggregate of solution and expressed as a “description of the action or effect the partial solutions chosen. (The Chakrabarti-Bligh approach is (intended to be) produced by an object, i.e., what it (is intended prescriptive in nature; the steps above are abstractly defined and to do or) does” [5]. So, functional representations in this the authors do not present rules of thumb on how to select approach describe what a structure does, or is supposed to do partial solutions for an overall design problem). [6], i.e., objects are described in terms of their known functions These steps lead to the development of a single solution [5]. structure. Then, to find alternative solution structures, the Functions are, moreover, defined in terms of mathematical functional reasoning strategy continues by going back one step expressions [5, 6] that express transformations between a set of and choosing another partial solution resulting in another input characteristics and a set of output characteristics. For revision of the overall function. Then one repeats this step by instance, in [5] the example of a bicycle drive is presented going back yet another step and choosing again another partial where a particular structure of this device has the function “to solution which solves a part of the revised overall function, transform input torque into output torque” and a connected thereby revising it again. These steps continue until the structure has the function “to transform input torque into output complete solution space has been searched, i.e., all possible force”. These functions of physical entities are, moreover, partial solutions for sub-functions have been identified and thus classified into three distinct types: structures that have as their all possible configurations of solution aggregates (component primary role the transmitting or transforming of force and configurations) have been identified that can solve the overall energy (like in the example above); structures that have couple design problem or function [6]. or connect functions; and structures that take unwanted forces To summarize, the functional reasoning scheme of away [5]. These function types are defined for the domain of Chakrabarti and Bligh amounts to a piecemeal, sub-function to mechanical transmission design for which they take input- component mapping approach incorporating these function- output motion transformations as functional primitives. Such a component mappings at each successive stage of the reasoning classification of functions into distinct types has also been process (and then back again) until the solution space (of known proposed by other design methodologies such as Pahl and structures) has been searched completely. It thus thereby tackles Beitz’s [12] and Hubka and Eder’s [19]. Pahl and Beitz, for the problem, i.e., the realization of the overall device function, instance, distinguish main functions from auxiliary functions. in parts.

4.2 Recursive Problem Redefinition 4.3 Known Physical Solutions Chakrabarti and Bligh’s model for functional reasoning consists The inclusion of known solutions in the Functional Reasoning of several steps and presupposes the existence of a given set of approach of Chakrabarti and Bligh is derived from the idea that design solutions, and a design problem defined in terms of a function structures cannot be developed usefully in a solution- function or a set of functions. Moreover it is required that these neutral way [6]; without known solutions for function design solutions can solve the design problem. The steps realization there is no guarantee that one moves from problem

6 Copyright © 2007 by ASME state towards solution space. The lynchpin of this argument is 5.1 Diverging Function Definitions: Form- what they refer to as the “problem of partitioning” [6]: the same Independency component may support multiple sub-functions and thus there is Whereas the three approaches take a product function to be not always a one-to-one mapping between components and sub- intended or required entities that are derived from user or functions. A set of sub-functions together can have one solution customer demands (although the latter is not made explicit in and this many-one mapping would remain undetectable in a the Chakrabarti-Bligh approach [5, 6], we assume that their solution-neutral reasoning scheme, the argument goes. scheme underwrites this), they nevertheless put forward Moreover, a given function vocabulary is likely to be somewhat different definitions of functions. incomplete and therefore, when it would be developed in a solution-neutral way, the possibility exists that it cannot express Table 5. Function in the Functional Basis, FBS, and the functions of all structures. The other way around, by Chakrabarti-Bligh approaches. ignoring solution concepts from the outset, the possibility exists Functional General input/output relationship of a that function structures are developed which cannot be solved in Basis product having the purpose of performing an terms of known solutions or structures. To circumvent these overall task, represented by a black box possible problems, Chakrabarti and Bligh [6] incorporate operation on flows of material, energy, and function-structure relations, based on known mappings, from signal determined by customer needs the outset; structure-function couplings are incorporated from FBS Intended behavior, expressed as a start to finish in their recursive problem reformulation combination of designer intentions and approach. behavior(s) that can exhibit the function The approach of Chakrabarti-Bligh is prescriptive in nature Chakrabarti- The intended action or effect of a physical and suggests how functional reasoning schemes ought to be Bligh object, expressed in terms of mathematical developed and used. Their approach, at least as laid down in [5] input-output transformations and [6], does not employ existing design knowledge bases, but instead prescribes that such knowledge bases are to be used in Table 6. Sub-function in the Functional Basis, FBS, and functional reasoning schemes. Chakrabarti-Bligh approaches. Functional Part of a product’s overall task, represented Table 4. Function definitions, decomposition strategy, Basis by a basic operation on basic flows of and design knowledge in the Chakrabarti-Bligh approach. material, energy, or signal, as defined by the Function The intended action or effect of a functional basis libraries of basic operations physical object, expressed in terms of and basic flows mathematical input-output FBS No separate definition given: sub-functions transformations are part of an overall function, derived from Sub-function Function of a component of a design either causal decomposition or task object, expressed in terms of decomposition mathematical input-output Chakrabarti- Function of a component of a design object, transformations Bligh expressed in terms of mathematical input- Decomposition Recursive function-structure mapping, output transformations strategy incorporating partial function-structure solutions in each successive stage of the A main difference between these approaches concerns the reasoning process manner in which they implement forms or objects in their Design Known function-structure mappings definitions of function, as will become clear below. This knowledge base difference is likely related to the different aims that the respective approaches associate with function-based designing. 5 COMPARISON Whereas a functional model in the Functional Basis approach is Having discussed all three approaches, in this section they will regarded as a “form-independent blueprint” [1] of an artifact, be compared. We will focus in particular on how the term the main task of functional design is in the FBS approach function itself is understood in these approaches, how regarded as “the embodiment process of required functions” functional decomposition taken as the reasoning from overall [4]. In line with this, Chakrabarti and Bligh [6] argue that functions to sub-functions is captured, and on how this known structure-function solutions are to be incorporated from decomposition of functions is related to engineering knowledge the outset in functional reasoning schemes, if the solution space about design solutions to functions. is to be searched exhaustively. More schematically, the three approaches take functions, respectively, as form-independent operations on flows , as intended behaviors of forms or objects , and as intended transformations of forms or objects .

7 Copyright © 2007 by ASME The Functional Basis approach defines a function as “a the former defines the function of an object (shaft), the latter description of an operation to be performed by a device or description explicates that an object (motor) will be used to artifact” [1] and, in accordance with the aim to deliver form move another object (table), but does not stipulate a precise independent functional models, its descriptions of basic object function. operations on basic flows do not include reference to form So, summing up, these three approaches differ somewhat in solutions. Functions in this approach thus refer to form- how they represent functions, to wit: in the Functional Basis independent operations. For instance, in the power screwdriver approach functions are form-independently defined, in the FBS example given in section 2.1 the sub-functions operating on the approach representations of function include object or form electricity flow are all defined independently from any solutions, and in the approach of Chakrabarti and Bligh component solutions that can implement them. functions are represented as the functions of physical objects. In By contrast, in the FBS approach form assumptions are the next section we suggest that these different definitions have incorporated in its representation of function. Consider, for an effect on the proposed strategies regarding the development instance, the example provided in section 3.1 where the overall of function structures. function “to charge drum” is decomposed, in the FBS modeler, into the sub-functions “to rotate drum” and “to discharge 5.2 Decomposition Strategies Decomposed: Using voltage to drum”. This example shows that, in the FBS Design Knowledge Bases in Different Ways approach, functional descriptions of overall functions and sub- The inclusion or exclusion of form assumptions in functional functions already include form solutions. This is in line with the definitions seems to lead to different steps taken in the FBS design aim to arrive at the embodiment level of functions. reasoning from overall product functions to sub-function Moreover, function representations in the FBS approach do assemblies. not have the level of detail or granularity that the basic functions of the functional basis have, and are not expressed in Table 7. Decomposition strategy in the Functional Basis, an input-output operation-on-flow type style, but instead FBS, and Chakrabarti-Bligh approaches. represented in terms of the above generic functional Functional Analysis of the black-box operation on flows descriptions. Basis corresponding to the overall product In the Functional Reasoning approach of Chakrabarti and function in terms of connected basic Bligh, functional representations describe what structures do or operations on basic flows corresponding to are supposed to do, and thus refer to the functions of objects. the sub-functions These are furthermore expressed as transformations between a FBS Function-state mapping via behaviors and set of input characteristics and a set of output characteristics. physical features. Two distinct Recall the bicycle drive example of section 4.1, in which decomposition phases and types: first, task structures of the bicycle drive are ascribed a certain function, decomposition and resulting function-state such as “to transform input torque into output force” [5]. In one mapping; second, causal decomposition and way, this resembles the Functional Basis notion of functions in resulting function-state mapping of task- the sense that function representations in the Chakrabarti-Bligh decomposed functions that could not be approach [5, 6] are, like functions in the Functional Basis mapped onto states in the first phase approach, defined in terms of transformations/operations. On Chakrabarti- Recursive function-structure mapping, the other hand, there is a difference; whereas the Functional Bligh incorporating partial function-structure Basis approach defines functions in a form-independent manner, solutions in each successive stage of the Chakrabarti and Bligh speak explicitly of the functions of reasoning process physical parts or objects. This definition of functions (likely) relates to the prescriptive aims that are associated with Table 8 Functional knowledge bases in the Functional functional designing, i.e., the development of meaningful Basis, FBS, and Chakrabarti-Bligh approaches. function structures is contingent on using known structure- Functional Archived functional models of products and function couplings, i.e., object functions (see section 4.3). Basis archived components that counts as design The object function definition of the Chakrabarti-Bligh solutions to sub-functions approach is similar to the FBS approach in the sense that in the FBS Archived function-behavior-state mappings latter function definitions also include (assumptions about) Chakrabarti- Known function-structure mappings. The forms. There are however also some differences: as said, the Bligh approach is prescriptive and does not FBS framework does not express functions in terms of employ existing knowledge bases transformations and, moreover, its functional descriptions are more broadly defined than object functions in the Chakrabarti- The Functional Basis approach of functional modeling Bligh approach. For instance, the object function “a shaft translates overall product functions in a three-step sequence into transmits torque” [5] is more specific than the functional functional models consisting of highly specific and form- description “to move the table with a motor fast” [2]. Whereas

8 Copyright © 2007 by ASME independent sub-functions. These functional models consist of Whereas in the Functional Basis approach the use of knowledge temporally organized and interconnected basic operations on bases is not primary in developing functional models, these basic flows, excluding references to implementation details. knowledge bases are an integral part in the FBS approach and After these functional models have been developed, the the Chakrabarti-Bligh approach. As a result, form solutions are Concept Generator produces design solutions for the individual interwoven in the decomposition strategies of the latter two sub-functions on the basis of existing design solutions of sub- approaches, whereas in the former approach they are not; functions that are stored in a repository. Use of this repository function-component solutions are stored in the design in the Functional Basis approach does not commence in the repository, but are not employed in functional model early three-step phase of developing functional models, at least development. not in innovative designing (and not in [1]). The repository is essentially a knowledge base which stores known functional 6 CONCLUSIONS AND OUTLOOK models and sub-function to component mappings from actual In this paper we have surveyed the Functional Basis approach products, but is not a necessary add-on in the development of of Stone and Wood [1], the FBS approach of Umeda et al. [2, 3, functional models, i.e., function structures of products-to-be. 4], and the Functional Reasoning approach of Chakrabarti and These functional models are developed, using the functional Bligh [5, 6]. The focus in this survey was on conceptual basis libraries and without employing design repositories. differences between these approaches, specifically on how the In contrast, in the FBS approach the use of function term function itself is understood, on how functional prototypes, from which function definitions are derived, is an decomposition taken as the reasoning from overall functions to integral and necessary part of functional designing. From the sub-functions is captured, and on how this decomposition of start, and in the different decomposition phases, the FBS functions is related to engineering knowledge about design approach employs archived function relations and function- solutions to functions. It is argued that the Functional Basis structure couplings in its functional decomposition scheme. approach defines functions in a form-independent fashion, that Consider, for instance, the following example of functional in the FBS approach representations of function include object decomposition knowledge extracted from a function prototype or form solutions, and that in the approach of Chakrabarti and [2]: the function “to move a table fast and precisely” is Bligh functions are represented as the functions of physical decomposed into the sub-functions “to move the table with a objects. It has further been argued that these function definitions motor fast” and “to stop the table precisely”. This example are related to the manner in which the respective approaches shows that, in the FBS approach, functional descriptions of employ design knowledge bases in developing functional overall functions and sub-functions already include form decomposition schemes. Whereas in the Functional Basis solutions and that the possible functional decompositions in the approach the use of knowledge bases is not primary in FBS approach are constrained by archived solutions regarding developing functional models, these knowledge bases are an the embodiment of overall functions and sub-functions, i.e., in integral part in the FBS approach and the Chakrabarti-Bligh the above example that a motor should be used to move the approach. As a result, form solutions are interwoven in the table fast. This thus shows that, in the FBS approach, function decomposition strategies of the latter two approaches, whereas definitions and the ways in which an overall function is in the former approach they are not. decomposed are constrained by the use of design knowledge The starting point for this survey is the observation that bases. there is no consensus in engineering about the meaning of the The Chakrabarti-Bligh approach of functional reasoning is term function itself, and that despite the broadly accepted value similar to the FBS approach (and different from the Functional of a common and uniform language for functional reasoning, Basis approach) in the sense that it also, from the outset, there is currently a series of functional reasoning models being employs design knowledge bases, storing structure-function proposed and developed that are distinct rather than convergent. relations, in its functional reasoning scheme. A difference with Our aim was to make this lack of consensus explicit, primarily the FBS approach is that in the Chakrabarti and Bligh approach, since we estimate that the existing differences between current alternative function-structure solutions must be incorporated in approaches towards functional reasoning will eventually hamper the functional reasoning steps in order to search the complete the development of engineering computer tools and knowledge design solution space. It must be said that this suggestion is bases that can deal with functional reasoning. prescriptive in nature and not descriptive; in contrast with the The two steps that naturally succeed our analysis are, first, Functional Basis approach and the FBS approach, the approach expanding our survey to other approaches towards functional of Chakrabarti and Bligh suggests how function based reasoning, and, second, making an attempt to overcome the reasoning ought to proceed and does not employ existing design identified differences, either by integrating the approaches or by knowledge databases [6]. embracing some at the expense of others. The first step defines To sum up, whether functions are form-independently our next project, and also the second is one that we cannot take defined or not seems, in the surveyed approaches at least, to be here. We finish instead with remarking that both options to related to the manner in which design knowledge bases are overcome differences may in the end be one and the same. employed in developing functional decomposition schemes. There is some room to integrate the three analyzed approaches.

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