Compatiability Analysis and Case Studies of Axiomatic Design and TRIZ

This is part 2 of a 2-part article. Part 1 appeared in August, 2000. A Comparison of TRIZ and Axiomatic Design.

Kai Yang and Hongwei Zhang
Department of Industrial and Manufacturing Engineering
Wayne State University
Detroit, MI 48202, USA



This is our second research paper in comparisons of TRIZ and Axiomatic Design. In this paper, design problem solving approaches of Axiomatic Design and TRIZ are analyzed and compared in detail, and several case studies are discussed to support our point of view about these two methodologies.



The first research paper in comparisons of TRIZ and Axiomatic Design, these two methodologies are reviewed and briefly compared. The conclusion is that some design rules in AD and problem-solving tools in TRIZ are related and share the same ideas in essence. The objectives of this paper is to compare and contrast TRIZ and Axiomatic Design problem solving methods in detail, and to discuss the possibility of integration of them. The long-term goal of this work is to develop a generic framework and tools to help designers make and understand correct design decisions.

The body of this paper is divided into five parts. The first part discusses the domain mapping theory in AD and contradiction transformation idea in TRIZ. The second and third parts analyze two axioms and their possible corresponding techniques in TRIZ. The fourth part presents complementarity of these two methodologies using a case study, and the last part discusses the advantages and limitations of TRIZ and Axiomatic design.



AD states that design is the creation of synthesized solutions in the form of products, processes, or systems that satisfy perceived needs through the mapping between the FRs in functional domain and the DPs in physical domain, through the proper selection of DPs that satisfy FRs. To conduct design, one must determine the design objective by defining it in terms of functional requirements. Then to satisfy these functional requirements, a physical embodiment characterized in terms of design parameters must be created. The design process involves relating these FRs of the functional domain to the DPs of the physical domain.

TRIZ, on the other hand, states that some design problem may be modeled as a technical contradiction, which is the functional conflict or coupling. A problem requires creativity when attempts to improve some functional attributes lead to deterioration of other functional attributes. A design problem associated with a pair of functional contradiction can be resolved either by finding a trade-off between the contradictions, or by overcoming it. TRIZ does not accept trade-offs, and it stresses that an ideal design solution is to overcome the conflict.

Extensive studies in invention problem solving demonstrate that a functional contradiction is derived from a physical one. In order to overcome a functional conflict, one has to identify a physical element of the system that controls the competing attributes, and this element must be modified in such a way that it would meet the opposite requirements to its state. Transforming a functional contradiction in system level into a physical contradiction in component level is always required in TRIZ. Figure 1 illustrates this idea.



The following Ampoules Sealing case study demonstrates that TRIZ and AD theory offer the compatible ideas in problem solving.

Ampoules Sealing Case Study

In a manufacturing process a burner is used to seal ampoules containing drugs. The problem is that the flame may overheat the drug in ampoules and degrade the drugs. What should we do in this situation?

Let us use AD theory and TRIZ to analyze the manufacturing process and then compare their similarity and differences. From AD standpoint, the functional requirements in the functional domain of this manufacturing process may be expressed as two independent requirements that satisfy the Axiom 1.

FR1 = seal ampoules

FR2 = protect drugs from deterioration during the process

The original design selects only one design parameter in its physical domain, which is:

DP1 = heat by a burner.

There are two FRs but only one DP in the design solution. The number of DPs is less than the number of FRs. Based on the Theorem 1, the design is either a coupled design result, or the FRs cannot be satisfied. It is clearly that this is a coupled design because DP1 affects both FR1 and FR2. The design equation is:


In order to satisfy two FRs independently, the process design should be decoupled. Theorem 2 states: when a design is coupled due to the greater number of FRs than DPs (i.e, m>n), it may be decoupled by addition of new DPs so as to make the number of FRs and DPs equal to each other. If a subset of the design matrix containing n´n elements, one can constitute a triangular design matrix to decouple the previous design.

So, the coupled design represented by above equation can be modified into a decoupled design by adding a DP and changing the design matrix into a triangular one as follows:


If the burner represents DP1, what is DP2? It is obvious that DP2 should counteract the effect of the heat produced by the burner. In practice, water is an ideal component to offset the heat. So, the one possible design solution is given in figure 2.


From TRIZ standpoint, this design problem situation can be easily modeled as the technical contradiction (functional conflict) in the system level: we want to heat ampoule top (attribute “A”) to seal ampoules but it causes degradation to medicine (attribute “B”).


TRIZ contradiction analysis states that at the heart of a technical contradiction is hidden a physical one. In order to overcome the technical contradiction, a physical component should be modified in such a way that it would meet the opposite requirements. In this ampoule sealing case, the heat improves “A” (seal), but degrades “B”(medicine in the ampoule). So, the ampoules should be hot to improve seal, and it should be cold to not damage the medicine. Clearly the ampoule is the physical component that controls the technical contradiction.

TRIZ Knowledge Base tools provide several separation principles to overcome physical contradictions. Three most frequently used principles are separation of opposite properties in space, separation of opposite properties in time and separation of opposite properties between whole system and its components.

Careful examination of three separation principles, it is not difficulty to recognize that separation in space should be used in this situation. In order to make the top of an ampoule hot and other part cold, it is proposed to surround the ampoules with a water jacket. The water takes excess heat away from ampoules to prevent overheating the drag (see figure 2).



Independence Axiom in AD implies that the design matrix be of a special form. The consequences of applying Axiom 1 to the design matrix are as follows:

It is desirable to have a square matrix, i.e., n=m

The matrix should be either diagonal or triangular.

In real design situation, we need to search for DPs that yield a diagonal or triangular design matrix. The degree of independence can be treated as the definition of tolerance.

There are a hierarchy in both the functional domain and the physical domain, and a zigzagging process between two domains in design process. The domain process is most straightforward when the solution consists of uncoupled design at each level. When the design is uncoupled, we can deal with the individual FRs of a hierarchical level without considering other FRs of the same level and proceeding hierarchical levels. When the design is coupled, we must consider the effect of a decision on other FRs and DPs. Figure 3 shows the design matrices and structure models. Therefore, the designer should try to find solutions by attempting to uncouple or decoupled design in every level of design hierarchy.

The problem is how to decouple a coupled design. It is obvious to modify design matrix to be either diagonal or triangular. In practice, many coupled designs undergo changes and become a decoupled design through a trial and error process that is in opposition to TRIZ methodology.

In TRIZ methodology, a coupled design is defined as the existence of a contradiction. Removal of dependency of coupling means to overcome a technical or physical contradiction by applying inventive principles or separation principles. Thus, these principles can serve, with AD corollaries and theorems, as the guidelines of de-coupling a coupled design.

The design process of the Paper Handling Mechanism [11] illustrates how separation principles in TRIZ aid to satisfy Axiom 1 in AD.


Paper Handling Mechanism Case Study

The function of the paper handling mechanism used in an automatic teller machine is “isolate one bill from piled bills”, which is the first FR of the system. Several physical structures can be used to realize this functional requirement, such as friction, vacuum and leafing etc. Friction method is selected and its mechanism is showed in figure 4.


However, this DP does not always work correctly because the friction is changeable under some circumstances. If the friction force working on the tope of bill becomes too large by some accident, two or more bills will be sent forwards, and if it becomes too small the top bill may not be isolated. So, we have to decompose the first level functional requirement into two functional requirements: “give a forward force to the first bill” and “give a backward force to the second bill”. To satisfy these two requirements, the new DP of this design is a pair of rollers rotating in the same direction shown in figure 5. Furthermore, the friction coefficient of the upper roller is large than that of the lower roller.


So, the design equation is:

FR1: give the a forward force to the first bill

FR2: give a backward force to the second bill

DP1: upper roller

DP2: lower roller

A11 represents the friction between upper roller and the first bill; A22 is the friction between lower roller and the second bill. A12 and A21 represent the friction between two bills, so A12 is equal to A21. Compared to A11 and A22, A12 and A21 can be ignored, thus two requirements can be satisfied independently.

The remaining questions are:

To solve these problems, the following four more FRs are defined.

FR3: slant the cross section of the piled bills to make isolation easy.

FR4: pull out the isolate bill

FR5: adjust the friction force.

FR6: decrease the forward force after one bill is gone

In AD theory, these six FRs are the minimum set of independent requirements that completely characterize the design objectives for the specific needs of the paper handling mechanism. Six DPs in the physical domain are selected as follows and the mechanism is illustrated in figure 6A.

DP1: upper rollers

DP2: lower roller

DP3: wedge-shaped floor guide

DP4: carriage pinch rollers

DP5: press plate

DP6: cam

However, from TRIZ standpoint, FR1 and FR6 can be viewed as a functional contradiction because FR1 requires a forward force and FR6 requires a backward force. In order to satisfy FR1 and FR6, the friction between upper roller and the first bill should be large and small. Two factors control the friction force between the upper roller and the first bill: pressure and friction coefficient, which means either the pressure, or the friction coefficient should be large and small. Separation of opposite properties in time, one of TRIZ separation principles, can be utilized because the FR1 and FR6 are not required at the same time.



One design solution, making the pressure large and small, is given in figure 6A. Another design alternative is illustrated in figure 6B. In this design solution, a partial rubber roller is used to satisfy the requirements, because its friction coefficient is large at one time and small in another time. So, only five physical components are needed to realize the six functional requirements because the partial rubber roller can satisfy FR1 and FR6 independently. Compared with two design alternatives, it is clearly that the design expressed in figure 6B is better one because of its simple structure. Simple structure means less information is needed to produce the product (see the next part).




Axiomatic Design theory proposes two design axioms that provide the mechanism for assessing alternatives at each design. The first axiom is the independence axiom and the second is the information axiom. The axiom 1 requires that the functional requirements should be independent. However, the functional coupling should not be confused with physical coupling, which is often desirable as a consequence of Axiom 2. Integration of more than one function in a single physical part, as long as the functions remain independent, should reduce the information content, i.e., the design complex.

Professor Suh uses Bottle/Can opener design to illustrate the physical integration without comprising functional independence [1]. The functional requirements of the Bottle/Can Opener are:

FR1 = open beverage bottles

FR2 = open beverage cans

By definition, the two FRs are independent. We sometimes wish to open a bottle or a can, but not both simultaneously.

In the very simple design, the means for achieving the two FRs independently are embodied in the same physical device rather than in two separate components. Therefore minimal information content is required to manufacture device.


The design does not couple the FRs because the act of opening cans does not interfere with or compromise the requirement of opening bottles. The FRs would be coupled only if only there were a FR to open bottles and cans simultaneously, which is not the case here. So the design solution is that two separate functions are fulfilled by one physical piece without functional coupling. So, physical integration without functional coupling is advantageous, since the complexity of the product is reduced.

It is interesting that the same design solution could be obtained if we applied TRIZ methodology. More importantly and generally, TRIZ offers eight patterns of evolution of technological systems which allow one to identify the most effective direction for the system’s development.

In Bottle/Can opener example, at least two patterns might be used to predict or explain why two functions should be integrated into one physical device without coupling.

The first pattern is the Evolution toward Increase Ideality, which states that evolution of all the technological system proceeds in the direction of increasing degree of ideality. This means that in the process of evolution either the system of performing a certain functions gets less complicated/cost, or the system becomes capable of performing its function better or perform more functions than for which it was original designed. The ideality may be expressed as the equation as:

Based on this equation, it is clearly that the degree of ideality of Bottle/Can opener is bigger than that of two single openers (Bottle and Can). The reason is that functions of bottle/can opener are the same as that of two individual openers, but manufacturing cost is reduced. In terms of AD theory, the information content of one bottle/can is less than that of two individual openers. So, the conclusion is that the ideality in terms of TRIZ and the information axiom of AD theory are the compatible parameters in assessment of technological system and design solution. The pattern “Evolution toward Increase Ideality” in TRIZ is compatible with the Information Axiom in AD.

The second applicable pattern is “Increased Complexity Followed by Simplification”. This pattern consists of several evolution lines and “Line Mono-Bi-Poly” fits very well in predicting and interpreting this Bottle/Can Opener design solution. From TRIZ standpoint, bottle opener and can opener are two simple mono function systems. “Line Mono-Bi-Poly” states: if the technological system is a mono-system, it evolves by changing it to a bi-system. If it is a bi-system, it evolves to a poly-system. A single-barreled hunting rifle evolves to a two-barreled hunting rifle and its mono-functional performance is doubled. However, wristwatch calculator is a bi-function device by integrating two functions, measuring time and doing calculation, into a physical device. It is clearly that this pattern also satisfies the Axiom 2 because the new system enhances functions of the previous system in the limit cost. We should note that the evolution of technological system along the line of “Mono-Bi-Poly” does not violate the Independence Axiom.



Many case studies in applying AD theory, related to manufacturing process, material process, product design, software development, have been published in recent years. These applications illustrate how Axiom 1 and Axiom 2 can be used in solving real problems. By examination of these case studies, we find that many decisions can be made qualitatively if we understand the basic engineering principles, physical and chemical effects. To proceed with the design task, engineers need a database and computers. The database should contain sufficient knowledge to make the computer to communicate with the designer and to give the designer information about plausible design solution [12].

AD offers two design axioms and several theorems and corollaries, but it has not developed such a knowledge base yet to support these design rules. Therefor, in AD theory framework the engineering problem solving mainly depends on the engineer’s personal background and knowledge. A study shows that an average engineer knows usually 50-100 physical effects and phenomena, while there are more than 6,000 physical effects described in scientific literature [5]. Each effect may be a key to solving a large group of problems. Since engineering students are not usually taught how to apply these effects to practical situation, they often have problems with utilization of such well-know effects as thermal expansion or frequency resonance, let alone with less recognized effects. So, when applying AD to the product or manufacturing process design, an average engineer likely encounters problems such as what effects should be used and how to apply them.

Motivated by the need to help engineers to apply some physical and chemical effects in the engineering problem solving, TRIZ effect knowledge base has been developed in the past decades. This knowledge base is built on a functional principle: it contains a list of functions (applications) that commonly encountered in practice, and a corresponding list effects and application examples that serve as the guidelines to realize these functions. By integrating this TRIZ knowledge base into AD theory, the effectiveness of problem solving can be enhanced tremendously.

Here is the case study from the book [1]. We use this example to demonstrate how this TRIZ knowledge base can aid to solve real problems.


Method and Apparatus for Mixture Solid Particles Case Study

The dry mixing of fine powder is a very difficulty process, as they tend to segregation as a function of particle size; to agglomerate, forming clumps, and to compact into a cake. However, a “perfect” mixture is desired in many applications. A perfect mixture is defined as one in each component is evenly distributed throughout the mixture, so that with reference to the smallest sample, of interest, the ratio of particle components in every such sample is the same as the ratio of components in the entire mixture.

In order to realize a perfect mixture of two components, Professor Suh proposed a method and designed an apparatus [1]. Two different powder A and B, are stored in separate containers, through which air flows. The air stream carries the particles and conveys them to channels that direct the flow of particles past corona discharge devices. The corona devices have high voltage corona point electrodes and ground electrodes. One of the electrodes is supplied with a positive voltage with respect to ground, and other electrode is supplied with a negative voltage with respect to ground. The corona discharge across the electrode ionizes the air particles. The ionized air particles combined with the particle A and B as they pass between the electrodes, so as to impart a positive and negative charge on the particles, respectively.


Since the particles in each stream are charged with the same charge, the stream spreads as each stream leaves the region of each corona discharge device. As they enter a mixing chamber, the streams of oppositely charged particle attract each other, so particles of one charge tend to pair up with particles of the other charge as both streams are conveyed down through the mixing chamber (see figure 8).

Professor Suh and his associates considered all plausible solutions in physical domain, then they came to the conclusion that corona effects should be used. In the book Suh analyzed how the design solution satisfy Axiom 1 in detail, but how they came up with the idea of utilizing corona effect remained as somewhat nebulous and protracted.

At this point, applying TRIZ knowledge base may help us to generate the possible solution. In this case, the highest level functional requirement (FR) is to combine particle A with particle B. It is clearly that the problem is to realize the required function and TRIZ physical, chemical and geometric effect knowledge base can help to come up with design concept.


Effect Knowledge base in TRIZ does not offer “function of mixture of particles” but it does have the inverse function, “separation of substance”. In order to realize the function of “separating particles of substances”, the knowledge base offers us the following effects [10]:

The Effect Knowledge base suggests that these physical and chemical effects should be considered when you want to separate particles of substances. By careful examination of these effects and analysis of examples, it is not difficult for us to come to the conclusion that corona effect and Coulomb’s Law could be applied to both separate and mix particles of substance.

If particle A and B have same electrostatic charges, they are exclusive. However, opposite electrostatic charges provide internal forces among particles. So, a perfect mixture might be realized if component A takes positive charge and B negative charge. In order to make particles A and B have the opposite charges, they should combine with the ionized air particles as they pass between the electrodes, so as to impart a positive and negative charge on the particles, respectively.

The task of TRIZ is finished at this functional level once the design idea of mixing two powders by means of electric field is derived. The further design process, how the idea is realized by physical structure, depends on the proper application of AD analytical analysis method. Actually AD decomposes the highest functional requirements into several low-level requirements through zigzagging process. For each functional requirement at the low level, TRIZ may find its new applications. In this way, AD approach may be viewed as analytical tool and TRIZ as synthesis tool. They are complementary very well in the real problem solving.



Several examples given above have demonstrated that TRIZ fits very well into the “ideation and create” element of axiomatic design process. In these examples, TRIZ knowledge base tools make the nebulous searching process for an acceptable design solution clear if the design problem could be traced into a particular area of design hierarchy.

However, as the systematic design methodology, axiomatic design does have several advantages in creating and evaluating a system structure.

  1. In AD theory, the design process is defined as the development and selection of a means to satisfy objects, subject to constraints. It is series steps, or activities, by which inputs are transformed to an output. This transformation occurs by means of the designer assistant by design tools/methods and knowledge base. The design object may be a physical object, a manufacturing process, a software or an organization, whatever the customer is willing to accept. However, TRIZ confines its application to technological systems since its methods, tools and knowledge base are from patent database. There are very few case studies in the fields of software development and organization structure design.
  2. AD places careful emphasis on the importance of recognizing the hierarchical nature of design, and particularly to ensuring that the process of iteration between FRs in functional domain and DPs in physical domain is carried out in a systematic manner. In general, a system, especially a complex one, cannot be designed without zigzagging and decomposing to create FR and DP hierarchy. This systemization occurs through an essentially top-down approach. Definition of system level FRs permits derivation and iteration of system level DPs, and then most importantly-definition of the system level DPs is necessary before FRs at the next level down in the hierarchy may occur; and so on right through each level of the hierarchy. The designer follows this zigzagging approach, checking the correctness of the design at each level using two axioms, until he has decomposed the problem to a point where the solution to the remaining sub-problem is known. In effect, AD suggests that the final solution of top level FRs can only really be achieved after each layer of the problem hierarchy has been given due consideration and iterated accordingly. TRIZ methodology models a design problem either as a technical contradiction that might be overcome by the contradiction table, or as the substance-field model that 76 Standard Solutions may aid to find the design solutions. These two models do not pay much attention to the hierarchical nature of the product system, so they only work well in the individual design level.
  3. In AD, two design axioms provide a rational means for evaluating the quality of proposed designs so that design decision may be made on a rational basis, support by easily understood math models and analytical results. The simple math models guide designers to consider alternatives at all levels of detail and makes choices between these alternatives more explicit. On the other hand, TRIZ use very abstract terms to express its theory and method, and it lacks math models and quantitative methodology to support its applications. For a new practitioner, it is very hard to follow its principles and others techniques.


  1. Axiomatic design perspectives on functional, physical and process hierarchies in the design of a system offer a powerful analytical tool to design problem. Two axioms and several corollaries and theorems serve as guidelines for problem solving, and easy understanding math models provide quantitative criteria to evaluate design alternatives. However, Axiomatic design lacks the vast knowledge base to support the application of its theory, so the creative process of conceptualizing and devising a solution is not very clear.
  2. TRIZ models a practical problem to be either a contradiction, or a substance-field model, or a simple function requirement, which serve the first step to problem solving. The second step is to apply its knowledge base tools to search for possible ideas, which guide designer to the suitable design solution. Since TRIZ concentrates its study on the individual part of a technical system, it is very useful in dealing with one functional requirement situation, but in multi-objective situation or multi-level system structure its limitations are obvious. TRIZ consists of both analytical and knowledge base tools, however, its knowledge base tools are used much more frequently in practical design world.
  3. The basic foundations of TRIZ and Axiomatic Design methodology are compatible. Several case studies in this paper show that in the framework of axiomatic design, integration of TRIZ knowledge base tools with axiomatic design analytical methods aids to come up with design concepts and make the design process clear. On the base of TRIZ methodology, hierarchical idea for a design process in axiomatic design enhances TRIZ problem solving abilities, especially in the complicated system situation.


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  4. G.S Altshuller, “And Suddenly the Inventor Appeared”. Technical Innovation Center, Inc. 1996
  5. Victor R. Fey and Eugene I. Rivin, “The Science of Innovation-A Managerial Overview of the TRIZ Methodology”, TRIZ Group,1997.
  6. Mann, D.L., “Axiomatic Design and TRIZ: Compatibility and Contradictions” ,TRIZ Journal, June and July 1999
  7. Boris Zlotin and Alla Zusman, “Mapping Innovation Knowledge” April 1999, Triz-Journal.
  8. Alla Zusman and John Terninko, “TRIZ/Ideation Methodology for Customer Driven Innovation”, Ideation International Inc. 1996.
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  10. Invention Machine Lab 2.12.
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