This is part 1 of a 2-part
article. Part 2 appeared in September,
2000. Compatiability Analysis and Case Studies of Axiomatic Design and TRIZ.
Department of Industrial and
Manufacturing Engineering
Wayne State University
Detroit, MI 48201, USA
ABSTRACT
This is our first research paper in comparisons of TRIZ
and Axiomatic Design. In this paper, Axiomatic Design (AD) and TRIZ are briefly
reviewed and their possible relationships are analyzed and listed.
INTRODUCTION
It is self-evident that decisions made during design stage
of product and process development profoundly affect the product quality and
productivity. 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 and The Theory of Inventive
Problem Solving (TRIZ) have been developed to aid design decision making and
related problem solving.
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 of 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 Russian), so they have been
evolved independent and separate from many of the design strategies developed
outside Russia.
REVIEW OF AXIOMATIC DESIGN
The
design process usually consists of several steps as follows [1] [3] [8].
·
Establish
design objectives to satisfy a given set of customer attributes
·
Generate
ideas to create plausible solutions
·
Analyze
the solution alternatives that best satisfies the design objectives
·
Implement
the selected design
Decisions
made during the each step of design process will profoundly affect product
quality and manufacturing productivity. To aid design decision making,
Axiomatic Design theory has been developed in the last decade. The Axiomatic
Design approach to the execution of the above activities is based on the
following key concepts:
(1)
There
exist four domains in the design world, customer domain, functional domain,
physical domain and process domain. 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 four distinct domains.
(2)
Solution
alternatives are created by mapping the requirements specified in one domain to
a set of characteristic parameters in an adjacent domain. 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.
(3)
The
mapping process can be mathematically expressed in terms of the characteristic
vectors that define the design goals and design solution.
(4)
The
output of each domain evolves from abstract concepts to detailed information in
a top-down or hierarchical manner. Hierarchical decomposition in one domain
cannot be performed independently of the other domains, i.e., decomposition
follows zigzagging mapping between adjacent domains.
(5)
Two
design axioms provide a rational basis for evaluation of proposed solution
alternatives and the subsequence selection of the best alternative. The two
axioms can be stated as follows:
Axiom 1 (independence axiom): maintain the independence of the FRs.
Axiom 2 (information axiom): minimize the information content of the design.
The first axiom is the independent axiom, and it
focus on the nature of the mapping between “what is required” (FRs) and “how to
achieve it” (DPs). 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. 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. Defining {FR} as a vector of functional
requirements and {DP} as a corresponding vector of design parameters, and {PV}
as vector of process variables, the mapping between the functional and physical
domains, between physical and process domains can be expressed mathematically
in equation (1) and (2).
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. When 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. When there are many FR&DP,
two quantitative measures, reangularity and semangularity in equation (3) and
(4), are used to determine the independence of the functional requirements [1].
A design’s information content
is calculated according to the following logarithmic expression.
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. 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).
(6)
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 the decomposition of the FRs. Iterations between FR-to-DP
mapping and the functional decomposition suggest a zigzagging between the
functional and physical domains.
REVIEW OF TRIZ
TRIZ is Russian acronym for The Theory of Inventive
Problem Solving that originated from extensive studies of technical and patent
information. 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, the
conclusion was that 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: the problem itself and the system
in which the problem exists. Successful innovative experience shows that both
problem analysis and system transformations are important to problem solving.
Accordingly, TRIZ methodology includes the analytical tools for problem analysis,
the knowledge base tools for system changing and their theoretical foundations.
Figure 4 illustrates the basic structure of TRIZ.
Theoretical Foundations
The
Patterns of Evolution of Technological System are the theoretical foundation of
TRIZ methodology. 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 pattern consists
of several sub-patterns or lines [9].
(1)
Stages
of evolution of a technological system
(2)
Evolution
toward increase ideality
(3)
Non-uniform
development of system elements
(4)
Evolution
toward increase dynamism and controllability
(5)
Increased
complexity followed by simplification
(6)
Matching
and mismatching elements
(7)
Evolution
toward micro-level and increased use of fields
(8)
Evolution
toward decrease human involvement
Patterns
and their lines serve as “soft equation” or “function” describing the system
“life curve” in the evolution space. Based on them, the further configurations
of a system can be reliably “calculated or forecasted” if the current system
configuration is given.
TRIZ Analytical Tools
TRIZ analytical tools, which include ARIZ, substance 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 building 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. However,
“real world” problems do not always appear as contradictions. 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 method, whereby,
given an unclear technical problem, the inherent contradictions are revealed,
formulated and resolved. Figure 6 is the structure of ARIZ [5].
Knowledge Base Tools
TRIZ knowledge base tools include 40 Inventive Principles,
76 Standard Solutions and Effect Database. 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].
Forty Inventive Principles are used to guide the TRIZ
practitioner in developing useful “concepts of solution” for inventive
situation. 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
1250 contradictions.
Seventy-six Standard Solutions were
developed for solving standard problems based on the Patterns of Evolution of
Technological Systems. These Standard Solutions are separated into five 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.
Effect Knowledge Base is probably the most
easy to use tool in TRIZ. Very early in his research, Altshuller recognized
that given a difficult problem, the ideality and ease of implementation of a
particular solution could 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, one has to select a
appropriate function the system wants to perform (based on the required
function analysis), then the knowledge base provides many alternatives for delivering
the function.
COMPARISONS OF AD
RULES AND TRIZ PROBLEM SOLVING TOOLS
The following table summarizes the possible relations
between Axiomatic Design rules and TRIZ problem solving tools.
Axiomatic Design
|
TRIZ
|
|
Corollary 1 (Decoupling of Coupled Design)
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 ensured by decoupling
if a proposed design couples the functional requirements. Decoupling does 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.
|
Contradiction in an engineering system
in TRIZ is similar to the functional coupling in AD theory. Overcoming
contradiction means the removal of functional coupling in AD.
There
are two types of contradictions: technological contradiction and physical
contradiction. 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 Principles are often required to remove
contradiction, though restatement of the problem may sometimes help to
overcome contradiction.
|
|
Corollary 2 (Minimization of FRs)
Minimize
the number of functional requirements and constraints.
Corollary
2 states that as the number of functional requirements and constraints
increases, the system become more complex and thus the information content is
increased. So, this Corollary recommends the designer strive for maximum
simplicity in overall design or the utmost simplicity in physical and
functional characteristics.
|
Ideal
Final Result (IFR) philosophy corresponds to the Corollary 2 in AD.
IFR
states that a system is a “fee” for realization of the required function and
IFR will be realized if the system does not exist, but the required function
is performed. IFR helps an engineer to focus on concepts that minimize
requirements in substance, energy and complexity of engineering product and
process.
|
|
Corollary 3 (Integration of Physical Parts)
Integration
design features into a single physical process, device or system when FRs can
be independently satisfied in the proposed solution.
Corollary
3 states that the number of physical components should be reduced through
integration of parts without coupling functional requirements. However, mere
physical integration is not desirable if it results in an increase of
information content or in a coupling of functional requirements.
|
Evolution Pattern 5, Increased Complexity
followed by Simplification, corresponds to Corollary 3.
This
pattern states that technological systems tend to develop first toward
increased complexity (i.e., increased quantity and quality of system
functions) and then toward simplification (where the same or better
performance is provided by a less complex system).
Line
Mo-Bi-Poly reflects that Mono-function products evolve into bi-function or
poly-function products through integration of physical embodiments. It is
obvious that this integration should not result in a technical contradiction,
that is a coupling.
|
|
Corollary 4 (Use of Standardization)
Use
standardization or interchangeable parts if the use of these parts is
consistent with FRs and constraints.
The
corollary states a well-known design rule: use standard parts, methods,
operations and routine, manufacture, and assembly. Special parts should be minimized to decrease cost.
Interchangeable parts allow for the reduction of inventory, as well as the
simplification of manufacturing and service operations, i.e., they reduce the
information content.
|
No
Patterns, principles or tools correspond to this corollary. TRIZ focus its
studies on inventive problem solving, so it pays less attention to the
standardization and interchangeability of physical components.
|
|
Corollary 5 (Use of Symmetry)
Use
symmetrical shapes and/or arrangements if they are consistent with the FRs
and constraints.
It
is self-evident that symmetrical parts are easier to manufacture and easier
to orient in assembly. Not only should the shape be symmetrical wherever
possible, but hole location and other features should be placed symmetrically
to minimize the information required during manufacture and use. Symmetrical
parts promote symmetry in the manufacturing process.
|
Principle 4, Asymmetry (one of 40 Inventive
Principles) in TRIZ is in opposition to Corollary 5 in Axiomatic Design.
The
reason why TRIZ and AD offer opposite principles is that AD theory states the
general rules of engineering design, but TRIZ methodology concentrates its
studies on the inventive problem solving techniques. These techniques were
derived from the patent database, which relates to novel methods and unique
ideas.
|
|
Corollary 6 (Largest Tolerance)
Specify
the largest allowable tolerance in stating functional requirements.
This
corollary is a consequence of both Axiom 1 and Axiom 2. Since it becomes
increasingly difficult to manufacture a product as the tolerance is reduced,
more information is required to produce parts with tight tolerances. On the
other hand, if the tolerance is too large, then the error in assembly may
accumulate such that FR cannot be satisfied. Therefore, the tolerance should
be made as large as possible, but should remain consistent with the
likelihood of producing functionally acceptable part.
|
No
corresponding tools are found in TRIZ.
Corollary
6 is a general rule of design and it is nothing to do with invention.
|
|
Corollary 7 (Uncoupled Design with less Information)
Seek
an uncoupled design that requires less information than coupled designs in
satisfying a set of FRs.
This
corollary is a consequence of Axiom 1 and 2. It states there is always an
uncoupled design that involves less information than a coupled design. The
implication of this corollary is that if a designer proposes an uncoupled
design which has more information content than a coupled design, then the
designer should return to the “drawing board” to develop another uncoupled or
decoupled design having less information content than the coupled design.
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40 Inventive Principles and Line of Mo-Bi-Poly.
40
Inventive Principles provide the techniques to overcome contradictions.
Evolution
Line “Mo-Bi-Poly” offers guidelines to reduce the complication of a system.
|
|
Theorem 1 (Coupling Due to Insufficient Number of DPs)
When
the number of DPs is less than the number of
FRs, either a coupled design result or the FRs cannot be satisfied.
Theorem 2 (Decoupling of Coupled Design)
When
a design is a coupled due to the greater number of FRs than DPs (m>n), it may be decoupled by the
addition of the design new DPs so as to make the number of FRs and DPs equal
to each other, if a set of the design matrix containing n´n elements constitutes a
triangular matrix.
|
Substance Field Analysis states any properly
functioning system can be modeled with a complete Su-field triangle and any
deviation from a “complete” triangle, for example missing one element,
reflects the existence of a problem.
Building a Su-field Model, one of 76 Standard
Solutions, shares the same idea with Theorem 2 in AD. This Standard Solution
states: if a given object is unreceptive (or barely receptive) to required
changes and the problem description does not include any restriction for
introducing substances or fields, the problem can be solved by completing the
Su-field model to introduce the missing element.
|
|
Theorem 5 (Need for New Design)
When
a given set of FRs is changed by the addition of a new FR, or substitution of
one of the FRs by a new one, or by selection of a completely different set of
FRs, the design solution given by original DPs cannot satisfy the new set of
FRs. Consequently, a new design solution must be sought.
|
Enhancing Su-field Model, Class 2 of 76 Standard
Solutions, corresponds to Theorem 5.
The
addition of a new FR, or substitution of one of the FRs by a new one means
the previous system is an inefficient Su-field model, i.e., the system is not
effective enough. In this case, enhancing Su-field model is required to
improve the system functions.
|
CONCLUSIONS
1.
The
basic premise of the axiomatic approach to design is that there are basic
principles that govern decision making in design, just as the laws of nature
govern the physics and chemistry of nature. Two basic principles, Independence
Axiom and Information Axiom, are derived from the generation of good design
practices. The corollaries and theorems, which
are direct consequences or are derived from the axioms, tend to have the
flavor of design rules.
2.
The
main axiom of TRIZ is that the evolution of technological systems is governed
by objective patterns. These patterns can be employed for conscious development
of technological system and inventive problem solving, replacing the
inefficiencies of blindly searching. These patterns and other TRIZ tools are
revealed by analysis of hundreds and thousands of inventions available in the
world patent database.
3.
Axiomatic
design pays much attention to the functional, physical and process hierarchies
in the design of a system. At each layer of the hierarchy, two axioms are used
to assess design solutions. However, TRIZ abstracts the design problem as
either the contradiction, or the Su-field model, or the required function
realization. Then corresponding knowledge base tools are applied once the
problem is analyzed and modeled. Though approaches to the solutions are of some
differences, many design rules in AD and problem-solving tools in TRIZ are
related and share the same ideas in essence.
REFERENCES
1.
Suh, N.P., “The Principles of Design”, Oxford University Press, 1990
2.
G.S. Altshuller, “Creativity as an Exact
Science”. Gordon and Breach Science Publishers, 1984
3.
Leonard
D.A and Suh N.P “Axiomatic Design and Concurrent Engineering”. Computer-Aided Design,
Vol 26, N 7 July 1994
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.
9.
“Tools
of Classical TRIZ”. Ideation International Inc. 1999.
10.
Invention
Machine Lab 2.12.
11.
Shinya.S
and Kawassaki.U, “A Study of Creative Design Based on the Axiomatic Design
Theory”, DE-Vol.68, Design Theory and Methodology-DTM’94 ASTM 1994
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Nam
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