2.1. Task-oriented approaches

Task-oriented approaches represent the flows of functions through the system with respect to causality in the chain sequence, focusing on structure-independent description of what needs to be achieved. The functional flow block diagram (NASA, 2007; Chourey & Sharma, Reference Chourey and Sharma2016) provides a network structure of functions of the system in a sequential relationship that leads to the achievement of overall system function. The functional flow block diagram is well supported by tools, for example, the SysML activity diagram (Friedenthal et al., Reference Friedenthal, Moore and Steiner2008). The function analysis system technique (Kaufman & Woodhead, Reference Kaufman and Woodhead2006), commonly used in industrial practice through brainstorming-based techniques, promotes the top-down decomposition of a main function into subfunctions, by iteratively applying how–why–when questions of the higher level function. The integrated function modeling (Eisenbart, Reference Eisenbart2014; Eisenbart et al., Reference Eisenbart, Gericke, Lucienne, Blessing and Timothy2016) represents the functional model of a system through six connected views: use case view, state view, interaction view, actor view, effect view, and process flow view. The process flow view represents the sequence of processes required for the fulfillment of a use case, illustrating both sequential and parallel transformation processes.

Task-oriented approaches promote a hierarchical decomposition for system functions. However, they lack a structured approach to the development of the function chains describing the achievement of function at a certain level of the hierarchy, and the combination of chains within the overall functional structure of the system.

2.2. Flow-oriented approaches

Pahl et al. (Reference Pahl, Beitz, Feldhusen and Grote2007) underpin the development of “function structures” by introducing a concise taxonomy for the flows through a system in terms of energy, material, and signal (information). The basis for function representation is the block diagram (i.e., black box) in which the function is articulated in verb–noun structure. The development of the function model starts by identifying the main flow, followed by the identification of the auxiliary flows with their subfunctions (Pahl et al., Reference Pahl, Beitz, Feldhusen and Grote2007). The basic principles of the function modeling approach proposed by Pahl et al. underpin the functional basis of Stone and Wood (Reference Stone and Wood2000), widely adopted in mechanical engineering, electrical engineering, mechatronic system development, and product service system design literature (see Eisenbart, Reference Eisenbart2014, for detail). Pahl et al. (Reference Pahl, Beitz, Feldhusen and Grote2007) do not focus on the flow characteristics; therefore, multiple operation modes that depend on different parameter values of the flows cannot be captured in a single model (Schultz et al., Reference Schultz, Sen, Caldwell, Mathieson, Summers and Mocko2010). For the same reason, it is difficult to ensure that the functional model complies with the conservation laws of physics and therefore that it is “mathematically correct” (also questioned by Vermaas, Reference Vermaas2008, Reference Vermaas2009).

Bond graphs model physical systems through a network (McBride, Reference McBride2005; Silva et al., Reference Silva, Bouscayrol, De Angelo and Lemaire-Semail2014), whose vertices represent physical elements (analogous to design elements and referred to by the number of energy ports that they possess) and whose edges (known as power bonds or simply bonds) represent power flow. Each bond implicitly carries an effort variable (e.g., force or voltage) and a corresponding flow variable (e.g., velocity or current). There are also two special types of vertices called junctions that represent series and parallel connection. Bond graphs support the analysis of complex systems across disciplines (Summers et al., Reference Summers, Hernandez-Vargas, Zhao, Shah and Lacroix2001). Triengo and Bos (Reference Triengo and Bos1985) note that it is difficult to model mechanical systems, while Umeda et al. (Reference Umeda, Takeda, Tomiyama, Yoshikawa and Gero1990) pointed out that the model focuses on structure and behavior of a system, but not on its functions. Recent work has focused on addressing this shortcoming, as evidenced by Lucero et al. (Reference Lucero, Adams and Turner2017) and Mokhtarian et al. (Reference Mokhtarian, Coatanea and Paris2017), who both tabulate mappings of the five bond graph elements to the functional taxonomy of Stone and Wood (Reference Stone and Wood2000).

2.3. Function-structure oriented approaches

Function–structure oriented approaches attempt to address the “what” and the “how” concurrently. The integration definition for function modeling (IDEF0; Buede, Reference Buede2009; Ally & Ning, Reference Ally and Ning2015) also represents controls and mechanisms associated with a function box, in addition to the inputs and the outputs (of material, energy, and information). The top-level function is decomposed into subfunctions by preserving the bounding arrows (input, output, control, and mechanism) of the top-level function box (Buede, Reference Buede2009). While the IDEF0 can represent the operation of a system in terms of a chain of functions in detail, function modeling using the IDEF0 can become complicated even in the analysis of a simple system (King & Sivaloganathan, Reference King and Sivaloganathan1998; Eisenbart, Reference Eisenbart2014).

Functions can also be represented in relation to state transitions. A state machine characterizes the behavior of a system in terms of a state at a particular time, and it is visually represented by a state-transition diagram (Harel, Reference Harel1987). Harel (Reference Harel1987; see Jaelson et al., Reference Jaelson, Mylopoulos and Silva Souza2014) extended the state transition diagrams to statecharts by introducing the notions of clustering, concurrency, refinement, and zooming. However, as noted by Buede (Reference Buede2009), semantics and syntax of statecharts are limited in the modeling of complex systems. Statecharts are useful in the analysis of a known configuration, and they are used in the popular graphical modeling languages, Universal Modeling Language (UML) and SysML, that are commonly employed for the model-based representation of multidisciplinary systems (Friedenthal et al., Reference Friedenthal, Moore and Steiner2008; Albers & Zingel, Reference Albers and Zingel2013). UML/SysML state machines introduce a strong formalism, but do not cover the way of defining, articulating, and decomposing functions (Eisenbart et al., Reference Eisenbart, Mandel, Gericke and Blessing2015). The SAPPhIRE model (Srinivasan & Chakrabarti, Reference Srinivasan and Chakrabarti2009; Srinivasan et al., Reference Srinivasan, Chakrabarti and Lindemann2012) uses state transitions as one of its entities (i.e., state change, action, part, phenomenon, input, organ, effect) in the analysis of an engineering system. Srinivasan and Chakrabarti (Reference Srinivasan and Chakrabarti2009) introduced a model of causality used to explain the causality of engineered systems through these entities.

Matthiesen and Ruckpaul (Reference Matthiesen and Ruckpaul2012) represented modeling of systems with logical states in the contact and channel approach (C&C²-A). They introduce the “sequence model” in which a sequence consists of at least two states and it determines the operational mode of a system. A state can be part of different sequences and can address the fulfillment of several functions. A function includes at least two working surface pairs, connecting channel and support structure, and at least two connectors to embed the model into its environment. Design decomposition is carried out through describing the basic elements working surface pairs, connecting channel and support structure, and connectors at different levels of the system (Matthiesen & Ruckpaul, Reference Matthiesen and Ruckpaul2012; Albers & Wintergerst, Reference Albers, Wintergerst, Chakrabarti and Blessing2014; Freund et al., Reference Freund, Kloberdanz, Lotz and Würtenberger2015). The development of a functional model for a reasonable large system through C&C²-A may become difficult due to the use of multiple elements in the representation of a function.

2.4. FBS-oriented approaches

FBS approaches introduce the concept of “behavior” to establish a link between “what” and “how” in relation to function modeling. The FBS model of Umeda (Umeda et al., Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996; Umeda & Tomiyama, Reference Umeda, Tomiyama, Chkrabarti and Lindemann2015) considers that a function cannot be represented independent of behavior so they represent a function as an association of “to do something” and “a set of behaviors” that exhibit this function. A function is expressed in verb–object–modifier format, while behavior is defined as sequential state transitions over time where a state consists of entities, attributes of entities, and relations between entities. Physical phenomena regulate the changes of entity attributes by relating them to physical laws (Alvarez Cabrera et al., Reference Alvarez Cabrera, Erden and Tomiyama2009). The representation of a functional model using the FBS model can easily and quickly become complicated and bulky, as the model consists of too many nodes and edges (van Beek & Tomiyama, Reference van Beek and Tomiyama2009).

The SBF model of Goel (Goel et al., Reference Goel, Rugaber and Vattam2009; Goel, Reference Goel2013) uses the concept of behavior to map structural elements of a known device to functions. The behavior concept represents the change in structure in terms of a sequence of state transitions. Each state transition is annotated by the reasons for the transition, for example, physical laws. The SBF model provides a structured methodology in the decomposition of given input and output states into sequential state transitions. This also limits the model to the development of nonbranching state transitions.

Object–process methodology (OPM) of Dori (Reference Dori2002, Reference Dori2016) describes function, structure, and behavior of a system in a single model through its basic elements, objects, and processes. The OPM can represent a system at any level through its complexity management mechanisms (Dori, Reference Dori2002).

3.1. Conventions for state definitions and representations

Several function modeling tools, such as statecharts (Harel, Reference Harel1987), FBS (Umeda et al., Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996), SBF (Goel et al., Reference Goel, Rugaber and Vattam2009), and OPM (Dori, Reference Dori2002), use states for the function modeling and representation of a system. Figure 3 summarizes some of the key definitions and representations of states based on the cited authors' examples.

Fig. 3. Summary of definitions and representations of states.

With the exception of FBS (Umeda et al., Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996), which uses multiple elements in the representation of a state, representations of states are based on a rectangular box. The state representation of Harel (Reference Harel1987) is prevalent in the software-based graphical representations of multidisciplinary systems, for example, the UML/SysML state machine diagram (Weilkiens, Reference Weilkiens2006), and it was therefore adopted for the SSFD representation.

In relation to the definition of state, it is apparent from Figure 3 that the reviewed approaches, while using different terms, are generally consistent with each other. The term state is associated with a specific situation of a given element (Harel, Reference Harel1987), an entity (Umeda et al., Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996), substance/component (Goel et al., Reference Goel, Rugaber and Vattam2009), and an object (Dori, Reference Dori2002). Umeda et al. (Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996) and Dori (Reference Dori2002) point out that the situation of an entity and an object can be specified in terms of a set of “attributes” that have values, while Goel et al. (Reference Goel, Rugaber and Vattam2009) use the term parameter instead. This requires a critical analysis to establish a consistent approach for both the definition of states in relation to objects and the description of states via attributes.

3.1.2. Attributes in the definition of a state

The statecharts of Harel (Reference Harel1987) and the implicit state representation of Dori (Reference Dori2002) in Figure 3 directly show the value of a given element and an object, while Umeda et al. (Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996) and the explicit state representation of Dori (Reference Dori2002) in the same figure describe the value of an entity and an object through attributes. Goel et al. (Reference Goel, Rugaber and Vattam2009) use the term parameter with the same meaning.

Coherent with the attribute description of Tomiyama and Yoshikawa (Reference Tomiyama and Yoshikawa1986), Umeda et al. (Reference Umeda, Takeda, Tomiyama, Yoshikawa and Gero1990) suggested that an attribute should be measurable to be observed by scientific means. All approaches in Figure 3 use the term value in the articulation of a measurable object attribute. According to Dori (Reference Dori2002), a value is the concrete specification of an attribute. The SSFD uses the concepts of Umeda et al. (Reference Umeda, Takeda, Tomiyama, Yoshikawa and Gero1990) and Dori (Reference Dori2002) in the description of “measurable” attributes of both physical and conceptual existence of an object. Sickafus (Reference Sickafus1997) suggested that a tangible object should possess at least the attributes of mass and volume, while for Dori (Reference Dori2002), a physical object should have mass and occupy coordinates in space and time. Some controversy exists in literature in relation to objects that may not possess mass and volume (e.g., light).

However, it could be hypothesized that space and time can be referred to as “global attributes” of an object, meaning that each object should possess these attributes. The design approach of Pahl et al. (Reference Pahl, Beitz, Feldhusen and Grote2007) and the functional basis of Stone and Wood (Reference Stone and Wood2000) reflect the global attribute “time” by representing subfunctions of a system in respect of causality, while the FBS of Umeda et al. (Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996) and the SBF of Goel et al. (Reference Goel, Rugaber and Vattam2009) embed the time dimension into the function definition through behavior, which is described as sequential state transitions.

The SSFD incorporates “time” and “space” as “global attributes” of an object. The global attribute “time” is embedded into the state definition by representing transfer between states with respect to causality, that is, an input state of a state transition is the output state of another state transition, and vice versa. The global attribute “space” is referred to as the “location” of an object in which it is acted on and it is specified along with the object's attributes (i.e., local attributes) in italic. Figure 4 summarizes the convention for the representation of a state in the SSFD.

Fig. 4. State representation in the system state flow diagram.

The SSFD state box in Figure 4 consists of two parts; the upper part contains the name of the object in bold, while the lower part contains the object attributes including local measurable attribute(s) and global attribute “location.”

For illustration, the last column in Figure 3 shows the SSFD state representations for the examples considered based on the reviewed approaches. This shows that the SSFD state model provides a compact state definition and representation in a structured way by differentiating between local attributes (e.g., size) and global attributes (i.e., location and time) of an object. For example, in contrast to the OPM, the SSFD model represents the state of the lamp in a single representation.

3.2. Function modeling in the SSFD

There is no uniform function definition in the literature (Umeda et al., Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996); however, the meaning of function can be generalized based on the design method used (Vermaas, Reference Vermaas2013). Coherent with the proposed SSFD state model, the OAF framework of Sickafus (Reference Sickafus1997) was adapted for the SSFD in the definition of a function. Thus, in the SSFD, a function is conceptually defined in terms of the triad of an input state of an object, an output state of an object, and an object (the design solution) that has to be provided in order to achieve the transfer between states, by addressing relevant attribute(s) of the input state. The associated graphical representation is illustrated in Figure 5.

Fig. 5. Comparison of the system state flow diagram function model with the approaches in Figure 1.

The use of an arrow in the representation of a function is common practice in state-based approaches, for example, the statecharts (Harel, Reference Harel1987). Coherent with the principles of Harel (Reference Harel1987), an open arrow with the function text below is used to denote a function in the SSFD, as shown in Figure 5. The head of the arrow is located on the output state. The function text indicates that the attribute(s) of the output object is modified through combining relevant attribute(s) of the design solution with the attribute(s) of the input object. The design solution is represented in a gray box in Figure 5.

A function is commonly articulated in verb–noun format in respect of the flows of material, energy, and information. For the SSFD, this articulation is related to the transfer between states. Considering the SSFD state model, the articulation of a function in verb–noun format is coherent the OAF framework of Sickafus (Reference Sickafus1997), that is, based on the rule that the verb corresponds to the operation on the object attribute(s), whereas the noun relates to the object or the object attribute.

Figure 6 summarizes the comparison of the SSFD function model with the approaches previously considered in Figure 3. Comparative representations in Figure 6 shows that the SSFD supports a compact function representation. The SSFD function model divorces the consideration of function from the consideration of the design solution by including the design solution conceptually in function modeling. Therefore, only the flow of state transitions is represented, initially without an explicit reference to a design solution. For example, in the second row of Figure 6, the SSFD models the FBS “paper weight” example (a) in terms of the input state and the output state of the paper instead of the paper weight; the function “stabilize paper” is articulated based on the specification of the paper location. If a specific design solution is chosen (e.g., a paper weight), coherent with the SSFD function model, the paper weight can fulfill this function as long as its relevant attribute (i.e., mass) combines with the relevant attribute of the paper, leading to a specific output state. The SSFD function definition triad is used to illustrate this, see the SSFD Model (b) in the second row of Figure 6. Different design solutions can be used to achieve the same objective, and can be illustrated in a similar way. The main advantages of the SSFD over the FBS are the representation of the state in a single box and the clear separation between function and design solution.

Fig. 6. System state flow diagram function model.

An SSFD functional model of a system can be developed by defining all functions of the system on the basis of the triad defined in Figure 5. Coherent with Suh's (Reference Suh2005) complexity definition, it can be suggested that the more flows of material, energy, and information a system addresses, the more complicated the functional model of the system becomes. This shows the need for a set of steps for the establishment of functional model of a system using the SSFD function model.

4.1. SSFD main flow heuristic

Pahl et al. (Reference Pahl, Beitz, Feldhusen and Grote2007) have introduced the term main flow to represent the main functions of a system, that is, those that directly address the fulfillment of its overall function. In a similar vein, Otto and Wood (Reference Otto and Wood2001) have used the term dominant flow. Complex multidisciplinary systems often present difficulties with the identification of the main flow, as they have multiple interconnected flows. The identification of a main flow to start the analysis is therefore the first challenge that needs to be addressed by the analyst. The decomposition of the main flow into a functional chain is the next step. The following sections outline the SSFD methodology for completing these tasks.

4.1.1. Identification of the main flow

Chandrasekaran and Josephson (Reference Chandrasekaran and Josephson2000) have discussed that there are two views in function modeling of a system: device centric and environment centric. The effect of the device on the environment in which it operates (i.e., environment-centric view) is a result of the way of working of the device (i.e., device-centric view) related to the intended effect on the environment. The environment is the user or an object related to the intended effect on the user. Coherent with Deng's (Reference Deng2002) description of user-focused purpose of design, and based on the methodology of Chandrasekaran and Josephson (Reference Chandrasekaran and Josephson2000), the main flow heuristic in the SSFD is introduced to describe the purpose of a system by determining the flow related to the intended effect of the system on the user.

Figure 7 illustrates this concept for the glue gun example. In relation to the use of the glue gun, the main intent of the user is to join two or more elements to create craftwork or to close and seal a parcel or box. Figure 7 shows an environmental-centric SSFD representation, capturing the input state “open box” and the output state “closed box” of the object of interest, associated with the main intent of the user. The SSFD “triad” representation includes the main function, for example, to “join box” (e.g., by joining the two surfaces of the box top flaps), and the “glue” as the design solution for the use case illustrated.

Fig. 7. Environment-centric system state flow diagram for the glue gun in relation to the main function “Join box.”

The fundamental working principle of the gun is that a quantity of melted glue is deposited on the desired location of the box flap; the two flap surfaces are then joined and held together until the glue is fully solid and thus the box is sealed. Thus, from a device-centric perspective, the main flow is a material flow, that is, the glue. The input state is the glue stick at room temperature (temperature T1) located in storage, while the intended output state is a quantity M2 of melted glue (temperature T2) deposited on the surface of the box, in the desired location. The function of the glue gun is therefore to deliver a quantity of glue in melted state on the desired location on the box, such that the required environment-centric function “join box” can be achieved. The corresponding SSFD for the glue gun device is shown in Figure 8. Attribute values are denoted by symbols for the sake of simplicity of the analysis (e.g., M1 for glue stick mass).

Fig. 8. Device-centric high-level system state flow diagram for the glue gun.

4.1.2. State-based decomposition of the main flow

Coherent with the conversion–transmission module heuristic of Otto and Wood (Reference Otto and Wood2001), operation types on a state transition can be categorized into conversion and transmission. The former addresses the change in the attributes of an object that the function is applied to, while the latter is about changing the location of an object through the applied function. The glue stick, which is the input material, undergoes multiple conversion and transmission operations to achieve the specified output state of “glue” described in Figure 8. These operations can be addressed by describing intermediate state transitions between the input and output states in Figure 8. The identification of these state transitions requires the description of the way of achievement (see Kitamura & Mizoguchi, Reference Kitamura and Mizoguchi2003) of the state transition in Figure 8, that is, the physical phenomena that regulate the changes of the object attributes. As noted by Umeda et al. (Reference Umeda, Ishii, Yoshioka, Shimomura and Tomiyama1996), we can reason out intermediate states between the input state and the output state based on description of the physical phenomena. Like the input and the output states, an intermediate state is thought of as an object described by its measurable attributes. Once intermediate states are identified, the flow through these states is mapped between the input state and the output state with respect to causality. Finally, functions are iteratively articulated to achieve the sequence of state transitions.

Solution-neutral decomposition reasoning usually starts with identifying the key conversions that describe the “way of achievement.” For the glue flow, the main conversion required is to increase the temperature of the glue stick to the specified temperature (e.g., 120–180°C, depending on the material used) such that a physical state change (“melted” glue) is achieved. In order to deliver the device centric function discussed in Figure 8, a specified quantity (M2) of melted glue needs to be extracted and deposited at the desired location; this can be achieved by subsequent conversions like applying a force to pressurize the melted glue, followed by extrusion of melted glue to atmospheric pressure. In order to apply these conversion operations, the glue stick must be “imported” into the device, which is a transmission operation.

Figure 9 shows the sequence of transmission and conversions on the main flow in an SSFD format, that is, representing each intermediate state described in terms of the values of the relevant attributes, linked to the previous state with an arrow that denotes the function (transmission or conversion) that needs to be achieved. The attributes involved are consistently indicated for all intermediate states, to support the subsequent specification of the functional requirements.

Fig. 9. The “main flow” through the glue gun device.

The device-centric SSFD for the main flow of the glue shown in Figure 9 can be aggregated into the environment-centric functional model showed as an SSFD state transition in Figure 7. Thus, the output state of “glue” in Figure 9 denotes the design solution, which combines with the input state of the box (open) in Figure 7, to achieve the output state of box (closed), fulfilling the user-required function to “join box.” Figure 7 showed this link by using two types of arrows (i.e., one and double headed) for the purpose of clarifying the triad, but in practice this link can be shown by one arrow, as illustrated in Figure 10. The arrow from the output state is pointed to the function text related to the conversion, showing extruded glue as the design solution in this function triad. This arrow is represented with a dashed line to distinguish it from the function arrow, as shown in Figure 10.

Fig. 10. System state flow diagram for the glue gun: the flow of glue.

4.2. SSFD connecting flow heuristic

The main flow in Figure 10 shows the conversion and the transmission operations between the input state and the output state of the gun. In order to achieve the conversion operations, flows of additional resources need to be “connected” to the main flow to complete the function “triads,” showing the way of achievement of the function. The “connecting flow” heuristic relates to the systematic identification and analysis of the flows associated with the conceptual, solution-independent “design solution” that delivers the functions identified on the main flow.

The functions “heat GS” and “apply linear force” are conversion functions on the main flow of the glue gun in Figure 10, which require additional flows. The way of achievement in the process of melting glue is associated with an increase of the glue temperature. A common glue gun uses conduction to transmit the heat between the heat source (which can be an electric heat converter, e.g., a Nichrome wire) and the glue stick, via a conducting rigid body (the glue gun barrel), which also plays a role in the “apply linear force” conversion. Thus the flow of energy, from the electricity source to the heat transmitted through conduction to the glue stick, must be mapped using the SSFD and “connected” to the main flow of the glue gun device. Figure 11 illustrates the SSFD for this flow, based on the assumption that mains electrical energy is used as a source. Intermediate state transitions on this flow can be determined using the same SSFD principles followed in the decomposition of the main flow of the glue gun. The functions required, as shown in Figure 11, are to import electrical energy to the glue gun, and then to convert electric energy into heat, which is transmitted (through conduction) to the glue stick.

Fig. 11. System state flow diagram for the flow of electrical energy through the glue gun.

In terms of the function “apply linear force,” for the common glue gun, the user is the source of energy. The glue gun device converts energy from the user to linear force applied to the cold end of the glue stick; the rigid glue stick acts as a piston, transmitting force and converting it into pressure/fluid energy for the melted glue. Figure 12 illustrates this energy flow.

Fig. 12. System state flow diagram for the conversion of user energy in the glue gun.

Figure 13 shows an updated SSFD that connects the electrical and user energy flows with the main flow through the device. This shows the design solutions for achieving the desired behaviors as functions on the main flow as follows:

• • the heat energy converted from mains electrical energy combines with the glue stick to deliver an increase in the stick temperature to the point where part of the stick becomes fluid (melted); and

• • the linear force (generated from the user energy) applied to the glue by the glue stick pressurizes the melted glue.

Fig. 13. System state flow diagram for the glue gun: the flow of electrical and user energy.

4.3. SSFD branching flow heuristic

Some technical systems require the flows to be split and allocated to different functions. For example, the hydraulic brake system for a vehicle distributes the fluid energy from a master cylinder to more than one wheel to simultaneously generate a retardation force for the vehicle. It is also the case that the real behavior of electromechanical systems means that the transmission and conversion functions cannot be achieved without loss; the flow of the resources that are diverted away from the intended function need to be mapped and accounted for, as these can cause issues elsewhere in the system or at the interface with other systems. For example, not all the energy of the heat source is transmitted to the glue stick; a part of it is transmitted to the environment via convection. The quantity of heat that is transmitted to the environment increases as the temperature of the glue increases, and thus the temperature gradient between the heat source and the glue decreases. The SSFD branching flow heuristic provides a mechanism to represent flows that branch out of the considered flow, and to ensure that the SSFD functional model is “mathematically correct,” that is, observes the conservation laws of physics. The correctness of the model in relation to branching flows can be checked via the balance of the attributes.

Figure 14 shows an updated SSFD, which illustrates the flow of heat branching out of the energy flow, with heat energy being exported to the environment from the glue gun through convection. The effect of this energy export to the environment needs to be investigated from an engineering point of view, to ensure than no detrimental effects are allowed and reduce system efficiency. For example, the effect of this heat energy on the environmental air temperature is very likely negligible; however, if we consider the impact on other environmental factors, such as the user, or another object like the box itself, the effect could be severe, leading to injury of the user and damage (or even fire) to the box.

Fig. 14. Glue gun system state flow diagram: branching flow of thermal radiation.

The representation in Figure 14 also shows the “system boundary”; this is denoted by the rectangular box that contains the states and functions that must be achieved by the device, confirming the demarcation between the environment-centric view and the device-centric view.

4.4. SSFD conditional fork node heuristic

Complex multidisciplinary systems often have multiple modes of operation, corresponding to different use cases. While each operation of the system can be independently described by a functional chain, aggregating all functional chains into a global functional model for the system that captures the complex functionality of the system is a challenge, often not appropriately addressed by conventional functional models. The aggregation of functional chains often requires the identification of logical or parametric conditions. A functional model that is capable of representing such a complex system needs to capture the logic of the system. In order to address this challenge, a special SSFD heuristic is introduced to indicate the flow operation (either connecting type or branching type) that is subject to a logical or parametric condition. Coherent with the statecharts (Harel, Reference Harel1987) convention and the SysML state machine “fork node” (Friedenthal et al., Reference Friedenthal, Moore and Steiner2008), this SSFD heuristic is called the “conditional fork node.” Figure 15 illustrates the representation of the fork node for two distinct cases:

1. 1. there can be multiple possible output states distinguished by the attribute values involved, which depend, through the stated condition, on the attribute value of the input state and the attributes or parameters of the function; and

2. 2. there can be multiple input states distinguished by attribute values, which depending on the operating conditions and the function attribute or parameter value, determine the output state attribute value.

In order to illustrate this for the glue gun case study, a glue gun that offers low-temperature and high-temperature operation modes to serve multiple use cases/user requirements in terms of the strength of the bond is considered. Such devices provide the option of low temperature (around 120°C, suitable for working with more delicate materials) or high temperature (operating at approximately 190–210°C, providing a stronger bond), which can be selected by the user via a switch positioned on the body of the device. Different glue stick materials are employed for the two modes of operation. For both operation modes, the device operates based on the same fundamental working principle, and with the same functional chain, although the specified attribute values (including the temperature of the glue at the output state) will be different depending on the conditions. Figure 16 illustrates the SSFD of the whole system, using several fork nodes to implement the operating logic of the system.

1. 1. Fork node F1 indicates that the input state can be either low- or high-temperature glue stick, differentiated by the material composition and attributes (e.g., mass, denoted by M1 and M3, respectively). The geometric dimensions are similar, and the way in which the sticks are imported to the glue gun is the same, as shown by the fork F1. The value of the mass attribute corresponding to the output state of the function “import GS” is denoted by M and it can be either M1 or M3, depending on the input state.

2. 2. The function “heat GS” is controlled by the attribute of the heat energy output state of the function “convert EE to heat energy”; in turn this is controlled by the current attribute value of the output state of the function “regulate current,” which is conditional on the heat gun control setting, as shown in fork node F2. The corresponding triad for this function consists of input state current (C), which combines with the control signal (if an electronic switch is used; otherwise, it could be a simple circuit breaker that modulates the resistance of the heater element by shorting out a section of it) to “regulate current” (assuming a constant supply voltage the current will be determined by the resistance) and deliver the output state attribute value, which is either C1 or C2.

3. 3. Fork node F3 illustrates the SSFD for the temperature control selector (switch), which is activated by the user.

4. 4. Fork node F4 illustrates that the output of the “heat GS” function depends on

   • • the attribute value of the input state, which can be either low-temperature or high-temperature glue stick; and

   • • the value of the attribute heat energy, which controls the function.

5. 5. Assuming that the trigger force is the same in all cases, the successful output from the system will be the specified amount of melted glue at low or high temperature.

6. 6. Heat energy exported to the environment from the glue gun will be different depending on the operation mode of the gun.

Fig. 15. System state flow diagram fork node.

Fig. 16. Glue gun system state flow diagram for low- and high-temperature operation modes.

6.1. Representation characteristics

6.2. Modeling characteristics

The SSFD heuristics play an essential role in the way the analyst interacts with the model, which is a strength of the framework. The main flow heuristic is arguably the most important step. The approach suggested in the SSFD is to start with the environment-centric perspective, focusing on the goal or utility that is required from the device. The main flow through the device should always be aligned with the main goal or utility. In the case of the glue gun analysis, this has immediately pointed to “glue” as being the main flow through the device. However, with large complex systems, the main flows are often not immediately obvious.

The input and output states for the main flow are defined next. If the analysis is driven by the environment-centric analysis, then the output state would have to be defined first; in the case of the glue gun, the mass, location, pattern, and temperature of the glue were defined as attributes of the output state. Identifying the input state requires design analysis and judgment; the benchmark glue gun considered the use of glue sticks, although pellets could also have been used.

Decomposition of the main flow within an SSFD is based on the identification of intermediate states, which can be “measured.” This can be pursued either from the input state to the output state or from the output state backward to the input state; in both cases, the consistency of the attributes describing the states must be ensured. For innovative design, when no reference solution is available or considered, the strategy of Pahl et al. (Reference Pahl, Beitz, Feldhusen and Grote2007) of starting with identifying the key transformative operation is the most robust strategy. In terms of SSFD, this would be equivalent to identifying a midstate of the flow, associated with the main transformation, and then identifying state transitions required before and after the main transformative step. For material flows, the visualization technique commonly used in process mapping was suggested by Campean, Henshall, and Rutter (Reference Campean, Henshall and Rutter2013) as an efficient strategy: “if I am a molecule of glue at the tip of the glue stick, what transformations do I go through to end up deposited in melted state in the required location on the box?”

This approach to guiding the analyst to correctly identify the main flow is much stronger than other functional modeling approaches, including the functional basis of Stone and Wood (Reference Stone and Wood2000). The engineers tend to focus on mapping the energy flows first, as illustrated by the example of glue gun function analysis based on mapping the flows of energy material and information in Eckert and Summers (Reference Eckert and Summers2014). While such a model might still be correct from an engineering point of view, it is not focused on the goal of the system. From a practical/industry application point of view, the focus on the goals is paramount. In order to address this, from an engineering point of view, we need to understand the use case goals, and to ensure that we have engineering measures consistent with the stakeholder measures of the delivered output, and that we focus the way of achievement on the delivery of the output.

The development of the SSFD model through the connecting, branching, and conditional fork node heuristics provides the analyst with the facility to develop models with increased levels of detail. In effect, this is equivalent to developing the model across successive levels of abstraction. The way this is managed in practice depends on the approach adopted for product development management. If the design development is carried out by one design unit, then the ability to develop the model with increased levels of detail and ultimately to have a detailed model of the whole system, which can be verified and simulated, would be of interest. However, if the design is carried out by a distributed organisation (e.g., involving suppliers), which is typically the case with many OEMs, then the analysis will be carried out at successive system levels based on the system architecture. In this case, a modular approach to the development of the SSFD can be taken.

6.3. Cognitive dimensions characteristics

Table 1 summarizes the evaluation of the SSFD function modeling framework against the key cognitive dimensions suggested by Summers et al. (Reference Summers, Eckert and Goel2013). A noteworthy point in relation to the analysis presented in Table 1 is that the sensitivity of the SSFD function modeling to the expertise of the analyst is an area that still requires research and development. While the SSFD provides a crisp focus on identification of measurable attributes to describe the states (input and output states to begin with), many real-world systems have such complexity that would require a large number of attributes and metrics to fully characterize the state of the object. This can be illustrated even in the case of the glue gun: the analysis in Figure 10 suggests that the relevant attributes to describe the output state of glue are mass, temperature, and location (XYZ). This would be appropriate if the use case goal is to have a blob of glue in the desired location, but if a pattern is required, then the mass flow rate would be a more appropriate attribute. This problem could be addressed with further research in two ways: develop a taxonomy for description of states; and develop a library of generic models for generic flows, which could be imported and customised for specific engineering problems.

Table 1. Evaluation of SSFD in relation to key cognitive dimensions

6.4. Reasoning characteristics

The original reason for developing the SSFD function modeling approach was to enhance the function failure reasoning (Campean et al., Reference Campean, Henshall, Brunson, Day, McLellan and Hartley2011; Campean, Henshall, & Rutter, Reference Campean, Henshall and Rutter2013). The automotive industry uses a model-based approach for function failure analysis (AIAG, 2008) early in the design process, which requires a robust functional model to carry out the function failure reasoning. The evidence from industry practice (Campean et al., Reference Campean, Henshall, Brunson, Day, McLellan and Hartley2011) is that functions are often brainstormed, and coherent function models are often not developed. It has also been observed that there is poor linkage between system levels in terms of function traceability; engineering teams would start to develop a functional model for a module based on the understanding of how the module works rather than what function it is required to deliver within the bigger system. This leads to poor integration and traceability within the system design development. The SSFD has delivered a fundamental underpinning for the development of a framework for robust engineering design based on failure mode avoidance, which has been comprehensively deployed within the automotive industry (Campean, Henshall, & Rutter, Reference Campean, Henshall and Rutter2013; Henshall et al., Reference Henshall, Campean and Rutter2014, Reference Henshall, Rutter and Souch2015; Dobryden et al., Reference Dobryden, Rutter, Hartl and Bramson2017; Naidu et al., Reference Naidu, Brittle, Ma and Rutter2017).

The subsequent development of the SSFD methodology, including the framework described in this paper, was driven by the need to develop consistent function models starting with the customer and logical layers of the system, and traceable across the levels of the systems, through robust functional requirements and function failure avoidance metrics. The SSFD provides a strong basis for exchange-based articulation of functional requirements and the associated requirements specification, underpinned by the state-based modeling and states description through attributes.