This paper compares the Theory of Inventive Problem Solving (TRIZ) and Axiomatic Design (AD). Both AD and TRIZ are briefly reviewed and their possible . Abstract: Axiomatic design (AD) and theory of inventive problem solving of the differences and similarities between AD and TRIZ. 2 Review of AD and TRIZ. reviewing the use of axiomatic design (AD) within a TRIZ framework and making based on application similarities and differences found in the literature.

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Editor On 19, Aug This is part 1 of a 2-part article. Part 2 desig in September, Kai Yang and Hongwei Zhang kyang mie. Traditionally, product and process have been designed based on know-how and trail-and-error; however the empiricism of a designer is limited and can lead to costly mistakes.

Axiomatic design is a general methodology that helps designers to structure and understand design problems, thereby facilitating the synthesis and analysis of suitable design requirements, solutions, and processes. This approach also provides a consistent framework from which the metrics axjomatic design alternatives can be quantified.

TRIZ offers a wide-ranging series of tools to help designers and inventors to avoid trial-and-error approach in design process and to solve problem in creative and powerful ways.

The most part of TRIZ tools were created by means of careful research of the world patent database mainly in Russianso they have been evolved independent and separate from many of the design strategies developed outside Russia. The design process usually consists of several steps as follows [1] [3] [8].

Decisions made during the each step of design process will profoundly affect product quality and manufacturing productivity.

### A Comparison of TRIZ and Axiomatic DesignThe Triz Journal

To aid design decision making, Axiomatic Design theory has been ddesign in the last decade. The Axiomatic Design approach to the execution of the above activities is based on the following key concepts: The needs of the customer are identified in customer domain and are stated in the form of required functionality of a product in functional domain.

Design parameters that satisfy the functional requirements are defined in physical domain, and in process domain manufacturing variables define how the product will be produced. The whole design process involves the continuous processing of information between and within comprison distinct domains. The mapping between the customer and functional domains is defined as concept design; the mapping between functional and physical domains is product design; the mapping between the physical and process domains corresponds to process design.

Hierarchical decomposition in one domain cannot be performed independently of the other domains, i. The two axioms can be stated as follows: Axiom 1 independence axiom: Axiom 2 information axiom: It states that a good design maintains the independence of the functional requirements. The second axiom is the information axiom and it establishes information content as a relative measure for evaluating and comparing alternative solutions that satisfy the independence axiom.

The four-domain structure is schematically illustrated in figure 1.

## A Comparison of Triz and Axiomatic Design

During the mapping process, one should not violate the independence axiom described above. In the product design, the creation or synthesis phase of design involves mapping the FRs in the functional domain to design parameters DPs in the physical domain.

Since the complexity of the solution process necessarily increases with the number of FRs, it is important to describe the perceived design needs in terms of a minimum set of independent requirements.

This means that two or more dependent FRs should be replaced by one equivalent FR. In the process design, a set of process variables PVs is created by mapping the DPs in physical domain to the process domain. The PVs specify the manufacturing methods that produce the DPs. The number of plausible solutions for any given set of FRs depends on the imagination and experience of the designer.

Thus, the design axioms are used to determine acceptable design solution. In equation 1 and 2[A] and [B] are called design matrix. To satisfy the Independence Axiom, matrix [A] and [B] must be either diagonal or triangular. Tiz the design matrix, for example [A]is diagonal, each of the FR can be satisfied independently by means of one DP and this design is an uncoupled design.

When the design matrix is triangular, the independence of FRs can guarantee if the DPs are changed in a proper sequence, and this design is a decoupled design.

Where, P is the probability of successfully satisfying the functional requirements. The probability of success is the function of both the design range that the designer is trying to satisfy, and the capability of the proposed solution, which is called the system range.

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A desirable solution corresponds to the region of overlap between the design range and the system range shown in figure 2 for uniform probability function. The region of overlap is called the common range. Then the definition for the information content given by equation 5 can be rewritten as in equation 6. When there are n functional requirements, the total information is given by equation 7.

Figure 3 is a graphic interpretation of the general mapping process between functional and physical domains, and between physical and process domains. The FR-to-DP mapping takes place over a number of levels of abstraction. A given set of FRs must be successfully mapped to a set of DPs in the physical domain prior to comparjson decomposition of the FRs.

Iterations comparispn FR-to-DP mapping and the functional decomposition suggest a zigzagging between the functional and physical domains. Studies of patent collections by Altshuller, the founder of TRIZ, indicated that only one per cent of solutions was truly pioneering inventions, the rest represented the use of previously known idea or concept but in a novel way [2]. Thus, vomparison conclusion was com;arison an idea of a design solution to new problem might be already known.

But where this idea could be found? TRIZ, based on a systematic view of technological world, provides techniques and tools, which help designers to create a new design idea and avoid numerous trails and errors during a problem solving process.

Any problem solving process involves two components: Successful innovative experience shows that both problem analysis z system transformations are important to problem solving. Accordingly, TRIZ methodology includes the comoarison tools for problem analysis, the knowledge base tools for system changing and their theoretical foundations.

Figure 4 illustrates the basic structure of TRIZ. These patterns indicate that there exist basic laws for engineering system development, and understanding them enhances ones ability to the design problem solving. There are eight patterns and each comparispn consists of several sub-patterns or lines [9].

TRIZ analytical tools, which include ARIZ, axiomatci field analysis, contradiction analysis and required function analysis, are used for problem modeling, analysis and transformation. These analytical tools do not use every piece of information about the product where the problem resides.

The way they generalize a specific situation is to represent a problem as either a contradiction, or a substance-field model, or just as a required function realization. ARIZ is such a sophisticated analytical tool that it integrates above three tools and other techniques.

Substance field analysis is a TRIZ analytical tool for cokparison functional model for problems related to existing or new technological systems.

Each system is created to perform a certain function. Typically, a function represents some action toward a certain objects, and this action is performed by another object. This situation can be modeled by a triangle whose corners represent objects and an action or interaction called a field. A substance may be a article or tool and the field may be some form of energy. In general, any properly functioning system can be modeled with a complete triangle as shown in figure 5. Any deviation from the complete Su-field triangle, for example missing elements or occurring inefficient and undesired functions, reflects the existence of a problem.

Contradiction Analysis is a powerful tool of looking problem with the new perspective. In TRIZ standpoint, a challenging problem can be expressed as either a technical contradiction or a physical contradiction. A technical contradiction might be solved by using contradiction table that identifies 39 characteristics most frequently involved in design process. A physical contradiction might be solved by separation principles. Contradiction analysis is the fundamental step to apply 40 inventive principles, one of the knowledge base tools.

Required function analysis refers to select the objective of the system and match it with the function list in the TRIZ Effect Knowledge Base. Required function analysis is the first step to use this knowledge base to look up the recommendations for accomplishing the objective.

ARIZ refers to Algorithm for Inventive Problem Solving, a set of successive logical procedures directed at reinterpretation of a given problem. In TRIZ standpoint, a technological problem becomes an invention one when a contradiction is overcome. Furthermore, Su-field analysis and required function analysis may not be applied directly in some situations.

Thus it is not obvious how or where to apply TRIZ knowledge base tools to aid the problem solving. ARIZ is a step-by-step methodwhereby, given an unclear technical problem, the inherent contradictions are revealed, formulated and resolved.

Figure 6 is the structure of ARIZ [5]. These tools are developed based on the accumulated human innovation experience and the vast patent collection.

The knowledge base tools are different from analytical tools in that they suggest the ways for transforming the system in the process of problem solving while analytical tools help change the problem statement [7].

Each of solution is a recommendation to make a specific change to a system for the purpose of eliminating technical contradictions. Contradiction table recommends which principles should be considered in solving approximately contradictions. Seventy-six Standard Solutions axiomztic developed for solving standard problems based on the Patterns of Evolution of Technological Systems.

These Standard Solutions are separated into dwsign classes according to their objectives; the order of solutions within the classes reflects certain directions in the evolution of technological systems. To use these tools, one identifies based on the model obtained in Su-field analysis the class of a particular problem and then chooses a set of Standard Solution accordingly.

The standard solution is a recommendation as to what kind of system transformation should be made to eliminate the problem. Very early in his research, Altshuller recognized that given a difficult problem, the ideality and ease of implementation of a particular solution z be substantially increased by utilizing various physical, chemical and geometric effects, thus a large vast of database has been developed.

In applying Effect Knowledge Base tool, axiomatix has to select a appropriate function the system wants to perform based on the required function analysisthen the knowledge base provides many alternatives for delivering the function.

Decouple or separate parts or aspects of a solution if FRs are coupled or become interdependent in the proposed design. This corollary states that functional independence must be adiomatic by decoupling if a proposed design couples the functional requirements. Decoupling compaarison not necessarily imply that the system has to be broken into two or more separate physical parts, or that a new element has to be added to the existing manufacturing system design. Functional decoupling may be achieved without physical separation.

However, in many cases, such physical decomposition may be the best way of solving the coupling problem. Overcoming contradiction means the removal of functional coupling in AD. There are two types of contradictions: A technological contradiction is derived from a physical contradiction.

So, certain changes of the physical structure of a technological system guided by Contradiction Table and 40 Inventive Principles or Separation Ad are often required to remove contradiction, though restatement of the problem may sometimes help to overcome contradiction.