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Axiomatic Design: Achieve the Right Design

By Al Hamilton

Design is a science, and accordingly, the rules of good design practice can be distilled to their essence. Just as Newton’s laws of motion allowed humans to realize their dreams of space travel, so too will the laws of design usher in a renaissance of design.

A key aspect of axiomatic design is the separation between what a system has to achieve (functional requirements) and the design choices involved in how to achieve it (design parameters).

Independence Axiom

The independence axiom states that each function of a system and the design choice that satisfies it should not interfere with other functions of the system.

In the design matrix of Figure 1, each functional requirement of a system is uniquely satisfied by a design parameter (x’ed boxes), and that design parameter affects only that function. This is called an uncoupled design matrix. An uncoupled design that satisfies the customer’s requirements and has the minimum information content is an optimal design.

Figure 1: Uncoupled Design Matrix

Unfortunately, the real world is often not that clean. The choice of a design element might be constrained by several factors, including cost, size, weight, technology or corporate practice. Design matrices often indicate that a design element can have secondary effects on other functions of the system. This might not be a disaster, however. If the design matrix can be reorganized to be “triangular” or decoupled, then a satisfactory solution can be achieved.

In Figure 2, design parameter 1 (DP1) satisfies functional requirement 1 (FR1) but also impacts functional requirement 2 (FR2). By executing DP1 first, its impact on FR2 can be assessed so that that can be accommodated as design parameter 2 (DP2) is executed. If DP2 is worked on in isolation, it will almost certainly need to be redesigned once the impact of DP1 is known.

Figure 2: Decoupled Design Matrix

In traditional design programs, these interactions are found during testing, which is an expensive and inefficient way to resolve design contradictions that should be identified and corrected in the early phases of a design. One of the benefits of axiomatic design is its ability to to identify the correct order of design, mitigate these interactions and thereby avoid redesign.

An uncoupled design is a common form of an axiomatic design, and the careful assessment of the interactions and assessment of alternative design decisions to reduce or eliminate them is one of the most powerful benefits of the axiomatic design process.

The final design matrix class is called a coupled design (Figure 3). A coupled design is one that cannot be reorganized to a triangular matrix. In this case, the relationship between the design elements and their functions is circular.

Figure 3: Coupled Design Matrix

In this example, DP1 affects FR1 and FR2. Similarly, DP2 impacts the same functional requirements. The presence of a coupled relationship is represented in Figure 3 by the shaded squared. A coupled design, which is common, requires an iterative approach to design. The result is typically a singular design that is unstable and lacks robustness. When a designer encounters this type of design during design development, an extensive search for alternative ways of satisfying the functions should be sought. The Theory of Inventive Problem Solving (TRIZ) and trade studies are two methods that are used in an organized search for alternative solutions.

By applying the first axiom and working to limit functional interactions, a system can be designed to be inherently robust. The tools of traditional engineeringtypically are applied to an existing design to identify and quantify interactions and ultimately to find parameter values that can optimize some part of the performance space while minimizing the impact on others. Axiomatic design takes the radical notion that design interactions should be explicitly addressed much earlier in the design cycle and to the greatest extent designed out of the system from the start.

Information Axiom

The information axiom grounds axiomatic design in reality. The information axiom states that when choosing between two designs with similar functional properties, the design with the highest probability of success is the best. This apparently simple axiom requires further insight into how to determine the probability of success.

The process of satisfying a system function with a design element implies a transfer function. In its simplest form, the transfer function can be represented as a linear coefficient that transfers the acceptable functional performance into a design range, or design tolerance. This tolerance must then be compared to the available systems capability, represented as the systems probability density function (PDF).

Figure 4: Design Range and Systems Probability
Density Function
Figure 5: Impact of Coupling on Design Range

Once the relationship between functional range and design range is understood, the obvious questions are, “Can we produce the design element within the design range?” and, “Will it remain within the design range in various use cases and over its life?” If the answer to both is yes, then the design element has a 100 percent probability of success, or a “0” information content.

The formal definition of information content for a particular design parameter is:

To compare two different designs based on their information contents, it is necessary only to compare the sums of information contents of each design.

By decreasing the functional range, coupled designs of any form can significantly decrease the acceptable design range. With a decreased design range, a design element’s probability of success decreases, thereby increasing the information content of a system.

Design Is a Science

Axiomatic design is not a substitute for other Design for Six Sigma (DFSS) methodologies; rather, it is a way of integrating those methodologies into a coherent process to move logically and scientifically from voice of the customer (VOC) through to detailed technical decisions. The axiomatic design process provides a functionally-driven, solution-neutral way to develop design alternatives and and clear objective methods for choosing between those alternatives. With this process, designers can avoid the ad-hoc design-build-test-redesign cycles that typify current design processes. Axiomatic design ensures that robustness is designed in, not added on as an afterthought.

About the Author:

Al Hamilton is vice president of Axiomatic Design Solutions, a firm specializing in training, consulting and software to support the axiomatic design process. Mr. Hamilton has more than 20 years of industry experience in a variety of market, program and project management positions in the metrology and digital imaging fields. He is a member of the International Society of Six Sigma Professionals. Contact Al Hamilton at info (at)