Nam P. Suh
Focus Area: Design Principles, Objectives, and Guidelines
As we enter into a new era of the U.S. space exploration, NASA is facing unprecedented challenges and opportunities. The scale and scope of the new space missions, i.e. sending people to the Moon, Mars and other destinations, demands that NASA use a scientific design methodology that assures the successful achievement of its missions at the lowest possible cost, with the highest certainty, and within the schedule. Such a methodology must be used to achieve the following three specific goals: (1) creation of reliable and fully functional CEV and other hardware at a minimum cost and within schedule, (2) foster technology innovation, and (3) integrate the management process with the technological development. This is consistent with the objective of the RFI of NASA and the recent recommendations of the Presidential Commission for NASA.
This paper addresses “Design Principles, Objectives, and Guidelines”. The Axiomatic Design discussed in this paper is a general methodology that can deal with the design of complex systems, system architecture, technology innovation, and program management. It can be used in designing diverse products – software, hardware, materials, etc. – and organizations. Its use in developing software creates a software system quickly that is compatible with the hardware, since both are done using the same tools. It is a fundamental, universal tool that can be used in all synthesis processes. The following questions are answered by AD:
In the first section of this report, a brief introduction to Axiomatic Design theory is presented, in particular, some of the unique aspects of the Axiomatic Design process. The second section describes its use in system design/management. Finally, several examples drawn from a wide range of application areas are presented to illustrate how the theory has become an effective enabler for innovations and successful system designs.
INTRODUCTION TO AXIOMATIC DESIGN FRAMEWORK
Axiomatic design is a design theory and methodology that has been used in complex system design and for technology innovation. It enables mapping from customer needs to functional requirements, to design parameters, and finally to process variables. It is driven by functional requirements and assures that the design parameters in the physical domain are properly selected. Designs done based on the fundamental design principles eliminate the coupling of functions that bedevil the many products that are created based on experience and ad hoc. This systematic way of designing complex systems yielded innovative products at a fraction of typical cost within the allotted time. By analyzing the structure of the design axiomatically, complexity can be minimized and a modular, robust design can be achieved. Axiomatic design should be a vital tool in reducing the complexity of NASA’s CEV. We have demonstrated through a number of projects, including the Orbital Space Plane design, that Axiomatic Design can be a powerful tool in the hands of engineers.
The design world is made up of four domains, i.e., the customer domain, the functional domain, the physical domain, and the process domain. In the functional domain, the customer’s needs are specified in terms of FRs (Functional Requirements) and Cs (Constraints). To satisfy the FRs, we conceive DPs (Design Parameters) in the physical domain. From the customer domain, a designer must establish the minimum set of FRs required to meet each customer’s need. Thus, the designer must create a map from the customer’s domain to the functional domain. The FRs are defined as a minimum set of independent requirements that completely characterizes the functional needs of the system (or product) while DPs are defined as the key physical variables in the physical domain that characterize the design that satisfies the specified FRs. The relationship between each functional requirement and design parameter is captured by the design matrix. These physical parameters are carefully varied in the proper sequence in order to achieve the desired functions. By using axiomatic design, therefore, one can design a product or system that satisfies the FRs in the best way given by the FR/DP relationships. Its aim is to avoid the need to optimize by achieving one of the FRs at the expense of another. These four domains are present in many different kinds of design: product, materials, organizations, manufacturing, software, and universities.
The first design axiom, the Independence Axiom, states that the designer should maintain the independence of the FRs. Similarly, as each FR is defined, a DP must be defined in order to satisfy that FR. When design parameter cannot be implemented because it lacks details, the corresponding FR and the DP are decomposed to the next level until the FRs and DPs reach the lowest level called the leaf level. This decomposition process requires zigzagging between the domains as shown in Figure 1. Hierarchies of FRs and DPs are made by the zigzagging, which enables the systematic design of a complicated system with multi-level FRs and DPs.
The relationship between FRs and DPs is represented by the design matrix. The X at ijth position of the matrix in the design matrix denotes that a relationship between the ith FR and the jth DP exists. Also, when FRi and DPj are related by equations of parameters, there can exist a variable, Aij, at the ijth position that represents the equation. Ideally, each DP should only affect a single FR. The design matrix of such a system is said to be uncoupled (Figure 2a). Having one DP affect multiple FRs causes many problems. The design matrix of such a system is said to be decoupled (Figure 2b) or coupled (Figure 2c). Notice in Figure 2b that if DP3 is changed, then it affects FR1, FR2, and FR3. A decoupled design must be implemented in a certain sequence in order to prevent iteration. A coupled design requires multiple iterations in order to satisfy the FRs if it converges. It has been shown that each time an off-diagonal coupling term appears, the system’s robustness is sacrificed, even in a decoupled design. In a coupled solution, any variation during the life-time of the system may bring about the system failure because such a system operates only at a unique operating point.
(a) uncoupled (b) decoupled (c) coupled
Figure 2. Varying degrees of coupling in design matrices. (X’s mark a relationship, 0’s mark no relationship)
In general, the design range is the acceptable range of values that an FR can take, and the system range is the actual range of values that the FR takes, typically represented by a probability density function, seen in Figure 3. The probability of success, , is the area underneath the curve of the probability density function, fFR, of the FR on the design range (DR). This relationship is captured in the following equation.
The uncertainty can also be represented by information. The information of the uncoupled FRi is defined in terms of the probability Pi of Satisfying FRi, as seen in the following equation:
The foregoing description of Axiomatic Design constitutes the left leg of the V-model of the system design shown in Figure . When AD is completed, we have leaf-level design parameters that satisfy functional requirements. These leaf-level DPs must be integrated to create a system, which is depicted by the right leg of the V-model for system design. To integrate the system along the bottom up process shown in the right leg of the V-model, we need the information created during the FR/DP decomposition process shown by the left leg. To integrate DPs, the geometric interactions and proximity will be identified by creating a DP/DP matrix.
Complexity is defined as the uncertainty in achieving the FRs. In launching complicated systems such as CEV, we must reduce complexity based on a scientific basis, which has been developed in recent years at MIT. The goal of complexity theory is to show how the complexity can be reduced to increase the certainty of achieving the stated requirements within the constraints given and create a stable system for a long period of time. The entire ESE endeavor must be sure that unnecessary complexity is not built into the system to achieve its multi-pronged, multi-year, multi-purpose goals.
Axiomatic design defines complexity as the uncertainty in fulfilling the functional requirements. It has been shown that the complexity takes on four different forms:
Time-independent real complexity is the uncertainty that an FR of a designed system can be satisfiedwithin the design range. It can be measured for each FRi as the area of the system range of FRi within the design range. It is equal to the information content. The range for which the system range of FRi and the design range overlap is called the common range. See Figure 5. According to the Information Axiom, a good design is one that has the least information content (uncertainty). Therefore, the designer should always be diligent in keeping the system ranges of FRs within the design ranges.
Time-independent imaginary complexity is a result of the lack of knowledge about a design. Many organizations waste a great deal of resource on imaginary complexity. For example, consider the complexity of unlocking a combination lock. If nothing is known about the numbers and the sequence of the numbers, it will be a difficult task. If the numbers are known, the complexity is associated with the sequence of numbers. If both the numbers and sequences are given, it is not difficult at all. The complexity associated with this type of problem is imaginary complexity.
Figure 5. A graph of an FR with time-independent
real complexity. The p.d.f. of the system range of
FRi and the design range do not change with
Figure 5. A graph of an FR with time-independent real complexity. The p.d.f. of the system range of FRi and the design range do not change with time.
Suppose a designer developed a design that had the following design matrix:
Time-dependent combinatorial complexity means that the uncertainty in a design increases in time. This is typically experienced during the operation of an engineered product. The product during operation experiences different effects such as fatigue, corrosion, friction, impact, fouling, etc. Or, in the case of software, these effects may include memory leaks, data corruption, etc. The overall result of these degrading effects is that the FRs fall farther and farther out of the design range. The degrading effects combine and, therefore, the uncertainty increases in time. Suppose that the system range of an FR has a normal PDF with mean μ0 and standard deviation σ0. As time progresses, a degrading mechanism can increase the mean, as seen in Figure 6, or the standard deviation, as seen in Figure 7. As a result, the common range decreases in time. Actually, in real-life applications, the change of the PDF of the system range over time is a combination of changes to the standard deviation and to the mean. The change in time of uncertainty due to degrading mechanisms is combinatorial complexity.
Figure 6: The drift of the mean increases uncertainty over time.
Figure 7: The drift of the standard deviation increases uncertainty over time.
When the system range drifts out of the design range and thus makes the real complexity increase, we can restore the system by introducing functional periodicity. A system with time-dependent periodic complexity renews itself by identifying a set of repeating FRs and reinitializing the FRs at the beginning of each period. Many natural systems and engineered systems rely on functional periodicity to have stability. A simple example is the periodic maintenance of machines and cars to bring back their functions to their original state. Similarly, the entire operating system of a computer must be periodically reinitialized (i.e., rebooted) to make the computer stable and operational. Rebooting eliminates unnecessary information stored in the memory to allow normal operation. The idea of creating a functional periodicity for a long-term stable operation has been used to create advanced electrical connectors, low friction surfaces, etc.
Interestingly, periodic complexity is also necessary in all living creatures. Cell cycle is one form of periodic complexity. A single cell splits into two cells in a very complicated cycle, which reinitializes cell functions periodically. A human life is another example in which a human experiences various outside degrading mechanisms: exposure to harmful radiation, toxins, bacteria, viruses, accidents. A natural death is one in which combinatorial complexity causes a vital organ to malfunction. Without reproduction, a form of periodic complexity, the human race would be finished. But instead every 20-30 years a new generation of humans are produced, and humankind perseveres. When the time-dependent periodic complexity fails to reduce the combinatorial complexity, eventually the system fails. However, we can prolong the serviceability of complicated systems such as CEV by intentionally introducing functional periodicity.
Based on the complexity theory and axiomatic design theory, we can build a system with the minimum complexity. For an extended operation envisioned in space exploration, the idea of designing-in a means of eliminating system failures by taking appropriate action at the design stage is compelling.
AXIOMATIC DESIGN: Powerful and Convenient System-Design and System-Management Tool
Axiomatic design theory is a powerful and convenient tool for system-design and system-management issues. It offers a consistent and unified framework for high-level system design issues as well as leaf-level component designs through its functional approach. It also provides a logical framework in integrating the high-level system design with leaf-level component designs. This unified approach to system design and component design and the logical decomposition process, make Axiomatic Design applicable across many areas of technical (engineering, design and R&D), business, and management. This makes it an ideal tool for the design and management of the “system of systems”.
Systematic Framework and Open Architecture
As NASA develops its long-term projects, the systems it creates must have an open architecture to allow the adoption of yet-to-be created new technologies easily without a major modification of the entire system. This is allowed when the design is done within the Axiomatic Design framework because of the automatic modularity guaranteed by the design process and the design axioms. Axiomatic Design does not allow the population of children-level FRs and DPs without appropriate higher-level FRs and DPs. It also automatically creates the flow chart that provides a sequential operational chart based on the design matrix.
In short, the hierarchical nature of Axiomatic Design and the Independence Axiom provide three important things that are important in designing an open architecture for complex systems: (1) the complete relationships between all FRs through the design matrix, (2) a completely modular design that can enable the easy substitution of modules when technological advances justify replacing DPs, and (3) complete and automatic documentation of the all the reasons for design decisions. It provides specific tools for managing large systems that result from axiomatic design, i.e., flow diagrams, etc.
Benefits to Management
Tracking of system interactions: System architecture representations and efficient documentation
Axiomatic design is ideally suited to large-scale system design as it forces the designer to think about and indicate the system interactions in the form of a design matrix. The FR-DP hierarchy, the design matrix, “junction-mode” diagram and the “flow chart” (also called “flow diagram”) are convenient representations of system architecture, which make the tracking of system interactions convenient. Software capabilities to directly convert the information incorporated in the FR-DP hierarchies and design matrix to a “junction-mode” diagram or a “flow chart” have been developed. This makes it possible for different participants in the system-design team to access the system interactions in a manner that is most convenient. The flow diagram can be used for many different tasks: design, construction, operation, modification and maintenance of the system. It is also useful for distributed design and operation of the system, diagnosis of failures and archival documentation. Software capability to facilitate the clear documentation and communication of the design process have been developed and incorporated in AD. This documentation emphasizes the “how and why” of a design, not just the “what” of conventional documentation of engineered systems.
Efficient design function
A formal way of representing system architecture is important for communication between individuals in a team and between distributed teams, without possibility of misunderstanding. Axiomatic design enables the use of a common language and shared information between members, within and across teams, which preserves institutional learning.
Efficient project work-flow management and resource allocation
Axiomatic design helps to identify tasks, set a task sequence from the system architecture (flow-chart), and assign resources effectively. This process also allows checking progress made for each FR. Time consuming iterations and dead ends can be avoided by use of the system architecture.
Effective change management
When creating change in a large system, the biggest challenge for the system-designer is to predict the effect of the change on the entire system. This is a daunting task in a large, complex system. Axiomatic design contributes in this area in two ways. Firstly, it guides the designer to come up with an uncoupled or decoupled design to minimize system interactions. An uncoupled design minimizes (or sometimes eliminates) the need to consider the effect of a change on the rest of the system. For an uncoupled design, the design matrix or the flow chart exactly indicated the modules of the system affected by the change and the exact sequence in which the DPs must be changed to achieve a desired change. Secondly, Axiomatic design theory makes the system architecture representation and the documentation available to the system-designer in order to easily track the effect of the change on the entire system.
There are a number of techniques used today in design such as QFD, TRIZ and robust design. The use of these techniques and others is completely consistent with axiomatic design. In fact, axiomatic design can help the designer apply these techniques better. Figure 8 shows how they all fit together.
Figure 8. Using Other Design Tools Within the Axiomatic Design Framework
Some examples of what these techniques can do are:
The designer follows the axiomatic design process and uses the various techniques when appropriate. Axiomatic design helps the designer avoid mistakes such as unknowingly attempting to optimize a coupled design.
AXIOMATIC DESIGN: Powerful Tool that Leads to Innovations
Axiomatic design has proven itself to be an appealing tool for innovations. A clear separation of objectives (functional requirements) and solutions (design parameters) and a concept of coupling as a problem identification tool make it very effective in leading toward innovative solutions. Several examples from various technology disciplines are presented here.
Axiomatic design: Versatile Tool Applicable to a Design Task in Non-technical Domains
Axiomatic design is not limited to applications in technical design domains. Non-technical domains, in fact, showcase many of the strengths inherent in the axiomatic design framework. For instance, government policy design is often plagued by an inability to agree on the policy’s goals (functional requirements). If such a policy is completed anyway, the result is usually poor with few or none of the goals properly satisfied. Axiomatic design combats this compromise strategy of policy design by requiring the specific enumeration of goals in the customer domain and then in the functional domain. This forces policy designers (government) to stay accountable to their customers (the people) and to their functional goals when they put together the final policy. The end result is a policy with clear goals and a clear mapping from those goals to a proposed solution. In this fashion, Axiomatic design has driven innovation in many non-technical fields. Two examples are presented below.
Why do we need a disciplined, systematic framework for the new space mission? The scale and scope of the new space missions, i.e. sending people to the Moon, Mars and other destinations, render the program development and management to inevitably involve numerous components and subsystems that interact in complicated fashions. Thus it is impractical to evolve such a large complicated system as an assemblage of subsystems and components bottom up, and still expect to successfully achieve its missions. It has to be designed as a system top down. We therefore need a structured and systematic design process, if we are to carry out the task with the highest certainty, within the schedule, and at the lowest possible cost.
How do we design a large complex system? The Axiomatic Design technique as a general system design methodology is effective in a large complex system design as it
In this paper, we articulated, as concisely as we can, how the unique aspects of the Axiomatic Design process have been able to help system designs and lead to technical innovations. We believe each of those aspects will be an essential enabler in creating reliable and fully functional CEV and other hardware at a minimum cost and within schedule, fostering technology innovations, and integrating the management process with the technological development.