Application of Axiomatic Design and Design Structure Matrix to the Decomposition of Engineering Systems

Transcription

1 Application of Axiomatic Design and Design Structure Matrix to the Decomposition of Engineering Systems M. D. Guenov* and S. G. Barker Regular Paper Department of Power, Propulsion and Aerospace Engineering, School of Engineering, Cranfield University, Wharley End, Bedfordshire, MK43 0AL, United Kingdom DECOMPOSITION OF ENGINEERING SYSTEMS Received 25 February 2004; Accepted 1 August 2004, after one or more revisions Published online in Wiley InterScience ( DOI /sys ABSTRACT A design decomposition-integration model, named COPE, is proposed in which Axiomatic Design Matrices (DM) map Functional Requirements to Design Parameters while Design Structure Matrices (DSM) provide structured representation of the system development context. In COPE, the DM and the DSM co-evolve. Traversing between the two types of matrices allows for some control in the application of the system knowledge which surrounds the decision making process and the definition of the system architecture. It is argued that this approach describes better the design process of complex products which is constrained by the need to utilise existing manufacturing processes, to apply discrete technological innovations and to accommodate work-share and supply chain agreements. Presented is an industrial case study which demonstrated the feasibility of the model Wiley Periodicals, Inc. Syst Eng 8: 29 40, 2005 Key words: axiomatic design, design structure matrix, systems decomposition, systems integration *Author to whom all correspondence should be addressed ( m.d.guenov@cranfield.ac.uk). Contract grant sponsor: UK EPSRC Research Grant GR/R37067 under the Systems Integration Initiative. Systems Engineering, Vol. 8, No. 1, Wiley Periodicals, Inc. 1. INTRODUCTION Standards for the engineering of systems such as EIA 632 and ISO/IEC support a seamless process of converting customer needs into systems/technical requirements, which are subsequently transformed into logical representations (architectural design) and fi- 29

2 30 GUENOV AND BARKER nally into physical solution representations. The process is iterative (see Fig. 1) due to the incomplete information available at the outset of the project and also the large number of constraints involved technical, economic and even political. The systems approach of tackling the problem includes the deployment of Integrated Product Teams (IPT). These are composed of a variety of specialists from different functional disciplines, ideally representing different phases of the product lifecycle to ensure that the design process will consider, as early as possible, all relevant requirements and constraints. IPTs are now a common practice in industries such as the defense and aerospace. What seems to be lacking, however, are high-level support tools which could help the systems teams and architects draw together consistently a vast amount of information needed for the requirements and the design decomposition of the system. Currently there exist a number of requirements management tools, which fulfill only partially this need. For instance, Acclaro [Suh, 2001; Axiomatic Design Software Inc. website] is designed to evolve the systems design in accordance with the rules of Axiomatic Design Theory (ADT). The software allows the systems designer to enter the top-level Functional Requirements (FRs) and Design Parameters (DPs), and to decompose and map those in two tree hierarchies and associated design matrices. However, Acclaro is concerned primarily with functional decomposition, and not with explicit constraint mitigation and control. SLATE, on the other hand [Talbott et al., 1994a, 1994b], now part of the EDS Team Center suite of software, is a good example of a powerful requirements management system. It provides constructs not only to build requirements and product hierarchies, but also allows the designer to attach constraints and text fragments to each item within each layer of the system decomposition, and also provides a good level of traceability of nonfunctional requirements throughout the design decomposition. SLATE, however, would only produce results which reflect the experience of those using it. Observations made during the industrial case study suggest that, in practice, even experienced systems designers are too quick to follow a particular solution path, relying heavily on existing knowledge and past concepts. There are also other methods of structuring the design process, such as the N 2 chart [Lano, 1977, 1979], and the Design Structure Matrix (DSM) approach [Steward, 1967, 1981]. The latter approach provides the ability to group related design elements. There are software tools available which are based on the DSM. These include DeMAID [Rogers, 1999], which was developed by NASA to facilitate the decomposition and sequencing of design activities, and more recently, PlanWeaver (ADePT [Adept Management website]) which has been applied mainly in the construction industry. This paper presents work which has concentrated particularly on the integration of ADT and DSM. The conjecture is that ADT and DSM are complementary parts of the decomposition integration problem, where the former is more concerned with mapping of functional requirements to design parameters, while the latter is better suited to modeling the interactions and the integration of the design parameters. The main objective of the work is to investigate to what extent those two methods can be integrated and to evaluate the approach in a realistic industrial setting. The potential value of this work is that it provides a means of relating component integration to system functionality, which otherwise is not available but is essential during the early stages of the design process. The following two sections present a brief summary of ADT and DSM, respectively. Section 4 outlines the Methodology, while Section 5 describes the industrial case study undertaken to test and evaluate the approach. Finally conclusions are drawn and future work outlined. 2. AXIOMATIC DESIGN THEORY (ADT) Figure 1. High-level view of the systems engineering process (adapted from ANSI/EIA ). The underlying hypothesis of the Axiomatic Design [Suh, 1990, 2001] is that there exist fundamental principles that govern good design practice. The main distinguishable components of the ADT are domains, hierarchies, and design axioms. The foundation axioms are:

3 DECOMPOSITION OF ENGINEERING SYSTEMS 31 Figure 2. Decomposition by zigzagging. Axiom 1. Maintain the independence of the functional requirements. 1 Axiom 2. Minimize the information content of the design. Axiom 1 requires that Functional Requirements (FRs) be independent of one another, which enables each FR to be satisfied without affecting any of the other FRs. Thus there is no coupling of function where it can be avoided, and the design remains as uncomplicated as possible. Axiom 2 provides a quantitative measure of the merits of a given design, and thus it is useful in selecting the best among the designs which satisfy axiom one [Suh, 2001]. Generally, the design that uses the least information is superior. This is explained in more detail later in this section. According to the ADT, the design process takes place in four domains (Fig. 2, adapted from Tate [1999] and Suh [2001]): Customer, Functional, Physical and Process. Through a series of iterations, the design process converts customer s needs (CNs) into Functional Requirements (FRs) and constraints (Cs), which in turn are embodied into Design Parameters (DPs). Functional Requirements can be defined as a minimum set of independent requirements that completely characterises the functional needs of the product in the functional domain ; Design Parameters are the key physical variables in the physical domain that characterise the design that specifies the FRs [Suh, 2001, p 14]. DPs determine (but also can be affected by) the manufacturing or Process Variables (PVs). The decomposition process starts with the decomposition of the overall functional requirement in practice this should correspond to the top system requirement. Before decomposing a FR at a particular hierarchical level in the functional domain, the corresponding DP must 1 It appears that software engineers realized this earlier, while learning from some bad designs in the automotive industry [see Stevens, Myers, and Constantine, 1974: 139]. be determined for the same hierarchical level in the physical domain. This iterative process is called zigzagging (see also Tate [1999] for a more thorough treatment of the decomposition problem). Zigzagging also involves the other domains since manufacturing considerations may constrain design decisions, while over-specified requirements could virtually prohibit the discovery of feasible design solutions. At each level of the design hierarchy, the relations (the dependencies) between the FRs and the DPs can be represented in an equation of the form: FR = [A]DP, (1) where each element of the design matrix [A] can be expressed as A ij = FR i / DP j (i = 1,, m and j = 1,, n). Equation (1) is called the design equation and can be interpreted as choosing the right set of DPs to satisfy given FRs. This is required by Axiom 1 (Independence). Each element A ij is represented as a partial derivative to indicate dependency of a FR i on a DP j. For simplicity the value of an element A ij can be expressed as 0 (i.e., the functional requirement does not depend on the particular design parameter), or otherwise X. Depending on the type of resulting design matrix [A], three types of designs exist: uncoupled, decoupled and coupled (Fig. 3). Uncoupled design occurs when each FR is satisfied by exactly one DP. The resulting matrix is diagonal, and the design equation has an exact solution; i.e., Axiom 1 is satisfied. When the design matrix is lower triangular, the resulting design is decoupled, which means that a sequence exists, where by adjusting DPs in a certain order, the FRs can be satisfied. The design matrix of a coupled design contains mostly nonzero elements, and thus the FRs cannot be satisfied independently. A coupled design can be decoupled, for example, by adding components to carry out specific functions however, this comes at a price.

4 32 GUENOV AND BARKER Figure 4. Probability distribution of a design parameter. The solid line represents uniform distribution, the dotted line a nonuniform distribution (adapted from Suh [1990]). Figure 3. Examples of design types. From top to bottom: Uncoupled, Decoupled, and Coupled Design. One additional factor that affects coupling is the number of FRs, m, relative to the number of DPs, n. If m > n, then the design is either coupled or the FRs cannot be satisfied. If m < n, then the design is redundant. (Note that in both cases the design matrix [A] is not square.) In addition to the design axioms, ADT is governed by a set of rules, which are formalized into theorems and corollaries. Of particularly relevance to this research are Corollary 3 and Theorem 5 which originate from the first axiom (Independence): Corollary 3 states: Integrate design features in a single physical part if the functional requirements (FRs) can be independently satisfied in the proposed solution. Theorem 5 states: When a given set of FRs is changed by the addition of a new FR, by substituting one of the FRs with a new one, or by selection of a completely different set of FRs, the design solution given by the original DPs cannot satisfy the new set of FRs. Consequently, a new design solution must be sought. The Second Design Axiom states that minimizing the information content of a DP increases the probability of success of satisfying a function. The information content is defined by the equation I = log system common range. (2) In Figure 4 design range is the tolerance within which the DP can vary; system range is the capability of the (manufacturing) system; common range is the overlap between design and system ranges, and specifies the range within which the FR(s) can be met [Suh, 2001]. The information content of a system can be computed by summation of the individual information contents of all DPs only if the latter are probabilistically independent. Frey, Jahangir, and Engelhard [2000] proved that simple summation cannot be performed for decoupled designs and offered a method for computing information content. There is no exact method for computing the information content of coupled designs. 3. DESIGN STRUCTURE MATRIX (DSM) The DSM can be seen as a successor to the N2 chart [Lano, 1977, 1979, Becker, Ben-Asher, and Ackerman, 2000], which was used for some years by the Systems Engineering community, before the introduction of the DSM. The DSM has become increasingly popular as a means of planning product development, project planning and management, systems engineering, and organizational development [Browning, 2001, 2002]. The concept dates back to the 1960s and was not actually published until 1981 [Steward, 1981]. The Design Structure Matrix (DSM) is a compact, matrix representation of a system/project. The matrix contains a list of all constituent subsystems/activities and the corresponding information exchange and dependency patterns. That is, what information pieces (parameters) are required to start a certain activity and where does the information generated by the activity feed into i.e., which other tasks within the matrix utilize the output information [Design Structure Matrix website]. There are three different configurations of the matrix (Fig. 5). The simple, parallel configuration, in which the design

5 DECOMPOSITION OF ENGINEERING SYSTEMS 33 Figure 5. DSM configurations. elements (e.g., design parameters or activities) are fully independent of each other, the sequential, decoupled configuration, in which the second parameter is dependent upon the output of the first, and the fully coupled configuration, in which parameters are interdependent upon each other. Figure 6 shows how a DSM may be used. The crosses below the diagonal in figure 6a represent a forward flow of information, while those above the diagonal depict a feedback loop. The DSM can be used to reorder, or partition design elements, to minimize feedback loops (Fig. 6b). This is achieved by a process of triangularization [Browning, 2002], to render the matrix as lower-triangular as possible. Sets of feedback loops can also be removed, by tearing them from the matrix in practice this means producing a set of assumptions for the (as yet) unknown information. The DSM must then be repartitioned. DSMs can also be used to create and sequence modules or clusters [Sharman and Yassine, 2004], which are either mutually exclusive, or minimally interacting. This absorbs any (remaining) iteration within the system. This is shown in Figure 6c. There are two types of DSM in terms of application: The static DSM, essentially a square matrix, used for the representation of systems design architecture interface, design decomposition and modularization, and planning of organizational topologies The temporal DSM, which is primarily used for mapping of design processes and for scheduling and management of activities, over time This research is concerned with the use of DSM to model the integration and connectivity (logical and physical) between design embodiments of system architectures, and to trace the effects of this integration on the functionality of the system. While DSM provides a powerful technique for the analysis of design interactions within a complex development program, it appears to be less effective in innovative design. As Dong and Whitney [2001, p 11] point out, it is not possible to obtain a DSM for a new product that has never been designed before. Additionally, Dong and Whitney maintain that, although the DSM captures the interactions between elements within a system, it fails to record explicitly the reasons for these interactions. 4. DECOMPOSITION-INTEGRATION PROCESS USING ADT AND DSM ADT postulates that a zigzagging process for FR-DP mapping that takes place in a solution neutral envi- Figure 6. Examples of DSM forms: (a) Basic, (b) Partitioned, (c) Clustered.

6 34 GUENOV AND BARKER ronment ensures better design. This, however, can rarely happen in practice, particularly in complex product environments, where economic considerations dictate maximum possible utilization of mature designs and existing manufacturing processes [Guenov, 2002]. In addition, the design process must capture the interactions among the design parameters, including geometry, spatial layout, interfaces (e.g., logical and physical connectivity), and so forth. As discussed in the previous section, DSM is a mature method capable of capturing the interaction between design parameters, but by definition, it is fully known only for products that have already been designed. These considerations led us to the idea that the decomposition integration problem would be better modeled as a co-evolution of ADT matrices and DSMs. The generic representation of the process which we named COPE (decomposition-integration of COmplex Product Environments) is depicted in Figure 7. In COPE, ADT is used to map the decomposition of functional requirements to design parameters (FR-DP). At each decomposition level various knowledge sources are consulted in order to take into consideration constraints originating from all stakeholders. The knowledge sources include unstructured ones (e.g., employees tacit knowledge and various unpublished documents) as well as structured/coded sources. Examples of the latter include government regulations, DSMs of past designs (also processes), company s own design standards, synthetic and analytical models, knowledge bases, and so forth. Technology bricks is a generic term which encompasses chunks of new technology which is mature enough to be applied in the new product with potential competitive advantage. As the decomposition progresses, essential design studies must be performed, including spatial layout, performance and capacity constraints checks, and/or more detailed design of particular, riskier aspects of the product, resulting in more interactions between the design parameters. As a consequence, Corollary 3 of ADT may be violated or requirements may need to be added or changed at a higher level, which would require a repetition of the decomposition phase (see Theorem 5 of ADT). The first step to linking ADT and DSM was made by Dong and Whitney [2001], who showed that if the Axiomatic design matrix (DM) can be expressed analytically and one design parameter (DP) is dominant in satisfying a particular functional requirement (FR), then the triangulated design matrix is equivalent to the DSM of the design parameters. The algorithm consists of three major steps: 1. Construct the Design Matrix (DM). 2. In each row of the DM choose the dominant (the largest) entry. 3. Permute the matrix by exchanging rows and columns so that all dominant entries appear on the main diagonal. The authors show that choosing the dominant entries is important as it ensures the convergence of the design process. Figure 7. Schematic representation of the COPE Decomposition-Integration process.

7 DECOMPOSITION OF ENGINEERING SYSTEMS 35 Unfortunately, when designing complex (physical or software) systems the FRs are satisfied by modules or other (sub)systems or components and therefore the design matrix cannot be represented analytically; and it may not necessarily be square either. In order to overcome this restriction, we have devised a decomposition procedure (Fig. 8) in which the design and structure matrices co-evolve. The procedure starts with the construction of the DM of the FR-DP hierarchy. At this level the dominant DPs are identified. The DM is manipulated [see Dong and Whitney, 2001] so that it becomes lower triangular with dominant entries, X, on the main diagonal. The result is the Architectural DSM, that is, a DSM derived only from the functional view of the product. At this stage a certain amount of layout/spatial design may need to be done, including possible integration of components. This will be subjected to considerations regarding innovation, cost, weight, capacity and other constraints, which are taken into account by applying the knowledge sources, as discussed above (see also Fig. 4). The resulting design may affect the functionality of the systems, for example, grouping components together may couple functions. If that is the case, requirements may need to change or more design parameters may need to be added. This means that the design decompo- Figure 8. COPE decomposition integration procedure.

8 36 GUENOV AND BARKER sition has to be reconsidered from the highest level (see Theorem 5). The decomposition ends when a leaf node is encountered, that is, further decomposition will change the subject of the requirement. In terms of systems engineering standards (see, e.g., ANSI/EIA- 632), a leaf node can be approximately described as a specified/assigned requirement. Perhaps it is worth emphasising that the COPE procedure aims to retrace the AD-DSM connection at each level of the decomposition rather than at reaching a leaf node of the DP hierarchy. This is justified by the fact that in practice one can be very restricted in performing the entire decomposition in a solution neutral environment (as advocated by ADT) there are, for example, cost considerations at the outset of the project which result in targets on reusability of components and manufacturing processes from previous products and /or targets on commonality of components with other existing product lines. Furthermore, one sometimes needs to decompose much deeper one branch of the FR-DP hierarchy relative to other branches in order to de-risk the solution. For example, one may need to know if a particular material can be used before continuing further with the decomposition since this particular material may affect performance constraints or interfaces with other components. Thus we see our approach as compliant with the deeper localized studies that need to be preformed in practice at the conceptual and preliminary design stages before proceeding further with the development process. 5. CASE STUDY In order to test our approach regarding ADT (and, subsequently, DSM), a case study was undertaken in conjunction with COPE Project sponsor BAE SYS- TEMS. The chosen study concerns the upgrading of an air defense system. The primary form taken by our research was a series of interviews with key members of the project. These ascertained the nature of the requirements, and the structure of the design. This information was then decomposed using axiomatic design techniques to identify connectivity between requirements and design, and how each impacted the other. This was known as the As Is solution. Impacting factors, or constraints, both within the system of design, and of an organizational nature, were studied to model their effect on the process of system design. This was validated with the BAE SYSTEMS Project. A parallel analysis was conducted to determine how the system could have been designed, had ADT [Suh, 1990, 2001] and engineering design standards been applied. This became the As Could Be solution. It was intended that the comparison between As Is and As Could Be would indicate any areas where the existing design could have been improved, thus confirming (or not) our initial hypothesis. Additionally, we expected that the comparison would identify a set of potentially useful features that have not yet been addressed by the existing systems engineering tools. The findings of the study noted that possibly the key constraint was that this was an update rather than a new system, and that any design was therefore constrained by what already existed. However, the analysis of requirements by the BAE SYSTEMS Project appears to have been relatively unstructured and, indeed, an ongoing process. This, when coupled to a predominantly bottom-up rather than top-down analysis technique, meant that the requirements were not decomposed fully, and therefore the relation of requirements to design was not fully analyzed. This has the potential for delay in the form of extended or unnecessary rework or iteration the need for which the Project admitted was not accounted for. The work breakdown was described as being intuitive, and based largely on previous experience. Thus work appeared to be assigned to teams without consideration of how all of the modules could be integrated together successfully. The design of the system was forced down specific avenues. This was mainly because it was time constrained and there was a history of rival bids, which, through the prime contractor, led to decisions regarding the design being taken that were beyond the control of the BAE SYSTEMS team. Furthermore, the fact that certain data was provided much later than scheduled, has also placed certain restraints upon the system design process. The organizational need requiring the design, initially at least, to be planned in conjunction with two specific suppliers, also applied certain constraints. The need to trace and analyze design decisions and changes has been a central requirement in the design of complex products for quite some time [Guenov, 1996]. In the context of this case study, the DSM offered a potential solution to the problem of tracing the effect of contextual issues such as project scheduling, and event sequencing, upon the system design (Pimmler and Eppinger, 1994; Ulrich and Eppinger, 1999). Through the application of ADT and DSM, our case study research discovered elements of the system design and its context which required integration to provide a successful design solution. For example, given that the chosen design utilized two sensors, one to track the position of incoming targets, the other to track an outgoing missile, with the outgoing missile potentially being able to be seen by both sensors simultaneously, could be seen as an integration issue which requires the application of

9 DECOMPOSITION OF ENGINEERING SYSTEMS 37 Figure 9. 2nd-level Design Matrix (DM). both ADT and DSM. An example of such an application is described below. The approach for deriving the DSM from the DM is leveled so that each hierarchical level of the FR-DP decomposition hierarchy is evaluated in turn. The first step is to construct the Design Matrix (DM). For the purposes of demonstrating the approach, a 2nd-level abstraction of the ADT decomposition hierarchy will be concentrated upon. A sample of the 2nd-level BAE SYSTEMS DM is shown in Figure 9. The design appears to be a redundant one as the number of design parameters is greater than the number of functional requirements. At this stage it is important to identify the primary relationships between requirements and design i.e., if more than one design parameter is used to satisfy a requirement, identify the dominant one, and where appropriate, secondary relationships if they exist (they do not in this example). This is step two of the approach. The primary relationships are marked with large X s, while secondary relationships could be depicted with small x s. The DM now describes the functional linkages between the Functional Requirements (FRs) and the Design Parameters (DPs). This serves to define the manner in which the DPs will satisfy the FRs. However, the effects of decisions relating to the system such as cost, capacity, and physical integration are not dealt with particularly well. As a result, a DSM structure can be generated to accommodate these issues. The next step of the approach concerns the derivation of an Architectural DSM. This is illustrated in Figure 10. A dummy FR, denoted by?, is added to make the matrix square. Asterisks are used to denote blank cells on the diagonal. The Architectural DSM is created through a combination of a method proposed by Dong and Whitney [2001], and triangulation. Thus the rows and columns are permuted to produce a (predominantly) lower triangular matrix. The vertical axis is renumbered according to the DP order, and the Architectural DSM is the result. This is the equivalent of the DM, in DSM form, and provides the interface between the DM and DSM. This stage of the case study analysis revealed a problem with the design solution. Figure 10 shows a feedback loop between DPs and 2.2.2, and a Figure 10. 2nd-level Architectural DSM. second between and However, these feedback loops had not been anticipated in the design. Analysis of the model revealed that the likely reason for their appearance in the structural DSM was a leveling issue: DP verifies that the output of previous DPs is correct. But the corresponding FR for this DP occurs at a lower level of decomposition in the DM. This raised an issue with the As Is model (this being the existing solution, modeled in Figs. 9 and 10). A review of the requirements then led to the creation of an As Could Be solution, which is shown in Figure 11a. This attempted to use axiomatic design method [Suh, 1990, 2001] to create a design independently of the existing As Is model, to see if improvements were theoretically possible to the design. The main changes (the original FR/DP nomenclature has been retained for ease of comparison) are an additional FR, stating the need to verify the output of processing tasks, and an additional DP which enables a further verification task, that of comparing successive outputs to enhance reliability of Figure 11. (a) 2nd-level As Could Be Design Matrix; (b) 2nd-level As Could Be Architectural DSM.

10 38 GUENOV AND BARKER missile/target detection, up from a lower level of the decomposition. This simplifies the FR-DP relationship whereas, previously, FR had been satisfied by three DPs which embodied the verification algorithms at a lower level of decomposition, the requirement can now be met independently of processing operations. This may incur a cost overhead, depending on the technology used to implement it, but is representative of the ADT design philosophy, being in accordance with corollary three of axiomatic design [Suh, 1990, 2001]. Finally, FRs and of the As Is solution (Fig. 9) perform the same operation. These have therefore been combined into one. The design solution remains uncompromised as the DPs can be scheduled to cater for the newly compressed FR. It can be seen in Figure 11b that this has resolved the feedback issue. The effects of decision-making on the matrices now need to be modeled. The decisions can regard a range of criteria, such as constraints, physical and logical connectivity, and software or hardware integration. In the BAE SYSTEMS case, the need exists to combine software functionality onto processor cards. The physical connectivity of the design and the interaction of the functions across the processors are therefore relevant. Using the As Is solution as a basis, the creation of these DSM can be demonstrated by Figures 12 and 13. For the physical connectivity (denoted by 0 s), it can be seen that of the processing DPs (2.2.1, 2.2.2, and 2.2.3), operates independently, while provides data to DPs and then feed The verification DPs (2.2.4 and 2.2.5) also operate independently, with both passing information to the output channel (DP 2.2.6) on completion of the verification task. This completes an operational cycle. The integration between software cards, shown in Figure 13, is described by numbers. The numbers on the diagonal indicate which of three processors the DP is assigned to. Thereafter, numbers separated by a comma indicates that two DPs communicate over separate Figure 12. 2nd-level physical connectivity between design parameters. Figure 13. 2nd-level interaction between processor cards. processors. The first number denotes the card from which the communication is initiated, and the second number indicates which card receives the communication. An example is that DP 2.2.1, stationed on card 3, communicates with DP 2.2.5, which appears on card 2. The DSM can be separated out into layers (shown by Figs. 12 and 13), to give the system engineer a filtered view of how each of the design elements interacts with each other in regard to a different design perspective. This is illustrated in Figure 14. So far, we have shown that the model can highlight the effect of integration issues of a system design. This is shown by the unbroken arrow in Figure 14. However, it is also necessary to be able to understand how the nature of the design is affected by these issues. This necessitates backtracking from the layered DSM to the DM, to understand changes which may have been caused to the original FR-DP relationship. This is indicated by the dotted arrow to the right hand side of Figure 14, illustrating how the effect of a constraint or decision regarding integration may alter the balance between FRs and DPs on the original DM. To provide an example, currently, the processing is verified prior to output. This involves two DPs (2.2.5 and 2.2.4), which currently appear on processor cards two and three, as shown in Figure 13. If, however, the capacity and speed constraints of the processor cards dictated that they be positioned on the same card, then new physical connectivity would appear on the appropriate DSM, as both DPs would now be linked via the same processor card. This is denoted by the shaded area upon the layered DSM in Figure 14. This in turn would dictate a new sequence in which the two DPs could be executed, bringing about a coupling, and altering the structural DSM/DM, as indicated by the dashed arrow and letter A. A further example of this is that an FR specified the need to detect objects a, b, and c at range x in climate condition y. To meet this requirement, a DP provides the required capability. However, cost and capability constraints applied to the DSM mean that it is not possible to use the DP. The alternative is a DP which,

11 DECOMPOSITION OF ENGINEERING SYSTEMS 39 Figure 14. Layered DSM and its effect upon the DM. unfortunately, can only detect objects a and c at range x, and not in condition y. It can be seen that the process of deriving the DSM to study constraints etc. and their effects has now revealed that the FR on the original DM cannot be met. Thus the FR must be changed to accommodate the DSM constraints, and this changes the design, as dictated by theorem five of ADT [Suh, 1990, 2001]. Consequently, a new design solution must be sought. 6. CONCLUSIONS A novel design decomposition model for complex product environments (COPE) is presented. It combines Axiomatic Design with Design Structure Matrix to accommodate the iterative nature of the decomposition-integration process. The research to date has demonstrated that this approach can bring significant benefits. An industrial Case Study, conducted as part of the research and reported here, has shown that the DM-DSM arrangement can be used to identify the existence of potential conflicts in the design solution, and allows groups of design parameters to be explored in greater detail. This approach also appears to provide a level of control and transparency to the systems design process, and gives the systems architect the opportunity to study proposed changes before they are made, and to understand how any such change(s) may produce a knock-on effect throughout the design solution. Despite the potential which COPE has demonstrated so far, we have not yet solved completely the problem of mixing various levels of details during the decomposition process. This is important since deeper localized design studies cannot be avoided in practical situations, it is a part of the de-risking process. Secondly, the decomposition process forms only a subset of the engineering life cycle and therefore COPE must be evaluated in a wider context. So far we have consulted and tried to take into account the established standards for engineering of systems, however, standards implementation is company dependent. In this view, further development, evaluation and validation of the method, as well as a specification of the requirements for a decomposition tool form the scope of our future work. Currently we are experimenting with the integration of ADT, DSM, and Requirements Management tools [Guenov and Barker, 2004]. ACKNOWLEDGMENTS This work is funded by UK EPSRC Research Grant GR/R37067 under the Systems Integration Initiative. We are indebted to BAE SYSTEMS for their help with the Case Study. We thank the anonymous referees for their helpful comments. REFERENCES Adept Management website: com/ ANSI/EIA , Processes for engineering a system, Electronic Industries Alliance, Government Electronics and Information Technology Association, Engineering Department, Arlington, VA (approved January 7, 1999). Axiomatic Design Software Incorporated website: O. Becker, J. Ben-Asher, and I. Ackerman, A method for system interface reduction using N2 charts, Syst Eng 3(1) (2000), T.R. Browning, Applying the design structure matrix to system decomposition and integration problems: A review and new directions, IEEE Trans Eng Management 48 (2001), 3,

12 40 GUENOV AND BARKER T.R. Browning, Process integration using the design structure matrix, Syst Eng 5(3) (2002), Qi Dong and D. Whitney, Designing a requirement driven product development process, Proc 13th Int Conf Des Theory Methodol (DTM 2001), September 9 12, 2001, 11 20, Pittsburgh, PA. Design Structure Matrix website: D.D. Frey, E. Jahangir, and F. Engelhard, Computing the information content of decoupled designs, Res Eng Des 12 (2000), M.D. Guenov and S. Barker, Requirements-driven design decomposition: A method for exploring complex system architecture, Proc ASME 2004 Int Des Eng Tech Conf Comput Inform Eng Conf (DETC 04), Salt Lake City, UT, September 28 October 2, 2004, to appear. M.D. Guenov, Complexity and cost effectiveness measures for systems design, Manufacturing Complexity Network Conf, Downing College, Cambridge, UK, April 9 10, 2002, M.D. Guenov, Modelling design change propagation in an integrated design environment, Computer Model Simulation Eng 1 (1996), ISO/IEC (System Life Cycle Processes), DPC: 01/647707, Version 6.0, Bsi, London, R.J. Lano, The N2 Chart, Informational Report, TRW, 1977, California. R.J. Lano, A technique for software and systems design, North-Holland, Amsterdam, K.R. McCord and S.D. Eppinger, Managing the integration problem in concurrent engineering, Working Paper MSA, MIT Sloan School of Management, Cambridge, MA, T.U. Pimmler and S.D. Eppinger, Integration analysis of product decompositions, ASME Des Theory Methodol Conf, Minneapolis, MN, September 1994, J.L. Rogers, Tools and techniques for decomposing and managing complex design projects, J Aircraft 36(1) (1999), D.M. Sharman and A. Yassine, Characterizing complex product architectures, Syst Eng 7(1) (2004), W.P. Stevens, G.J. Myers, and L.L. Constantine, Structured design, IBM Syst J 13(2) (1974), D.V. Steward, The design structure system, Document 67APE6, General Electric, Schenectady, NY, September D.V. Steward, The design structure system: A method for managing the design of complex systems, IEEE Trans Eng Management EM-28, 3 (August 1981), N.P. Suh, The principles of design, Oxford University Press, New York, N.P. Suh, Axiomatic design: Advances and applications, Oxford University Press, New York, M.T. Talbott, H.L. Burks, R.W. Shaw, M. Amundsen, K.K. Hutchison, and D.D. Strasburg, Method and Apparatus for System Design, U.S. Pat. No. 5,355,317, October 11, 1994(a). M.T. Talbott, H.L. Burks, R.W. Shaw, M. Amundsen, K.K. Hutchison, and D.D. Strasburg, Method and Apparatus for Aiding System Design, U.S. Pat. No. 5,357,440, October 18, 1994(b). D. Tate, A roadmap for decomposition: Activities, theories, and tools for system design, Ph.D. Thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, February K.T. Ulrich and S.D. Eppinger, Product design and development, 2nd edition, McGraw-Hill Education (ISE Editions), New York, Marin D. Guenov is a Senior Lecturer (Advanced Engineering Methods) in the School of Engineering, Department of Power Propulsion and Aerospace Engineering at Cranfield University, UK. He holds an MEng in Mechanical Engineering and a Ph.D. in Materials Handling Systems and Operational Research. Currently Dr. Guenov leads national and international multidisciplinary research projects supported by the European aerospace industry in the areas of design of complex systems, modeling and simulation for synthetic environments, multidisciplinary design analysis and optimization, and infrastructures for collaborative design. Dr. Guenov is a member of the Royal Aeronautical Society and The Association of Cost Engineers and is a Charted Engineer. Stephen G. Barker is a Research Officer in the School of Engineering, Department of Power Propulsion and Aerospace Engineering at Cranfield University, UK. Dr. Barker holds a BSc. (Hons.) in Computer Studies, and researched Applied Engineering Process Management for his Ph.D. Currently, Dr. Barker is part of the COPE (COmplex Product Environment) research team, which investigates Decomposition- Integration issues within Complex Product Development programs. Dr. Barker has previously worked as a lecturer and tutor in the fields of Network Communications and Operations Management.