(1.2)
December 3 , 1996 Version
Copyright c Nam P. Suh 1996
Chapter 1 Introduction to Axiomatic
Design
Table of Contents for Chapter 1
1.1 Current State of Design Practice
1.2 Who are the designers? How do we design? What is design?
Example 1.1 Refrigerator Door Design
1.3 What is the ultimate goal of axiomatic design?
1.4 What is the difference between this book and the first book on the subject?
1.5 Historical Perspective on Axiomatic Design
1.6 Axiomatic Approach vs. Algorithmic Approach
1.7 Axiomatic Design Framework
1.7.1 The Concept of Domains
1.7.2 Definitions
1.7.3 Mapping from Customer Need to Determination of Functional Requirements
1.7.4 The First Axiom: The Independence Axiom
Example 1.2 Beverage Can
1.7.5 Case Studies Involving Decoupling of Coupled Designs
Example 1.3 Newcomen Steam Engine vs. Watt's Engine
Example 1.4 Shaping of Hydraulic Tubes
1.7.6 Decompostion, Zigzagging and Hierarchy
Example 1.5 Refrigerator Design
1.7.7 Requirements for Concurrent Engineering
1.7.8 The Second Axiom: The Information Axiom
Example 1.6 Cutting a Rod to a Length
Example 1.7 Cutting the Rod with Hack Saw
Example 1.8 Buying a House
1.7.9 Reduction of the Information Content -- Robust Design
1.6.9.a Elimination of Bias
1.6.9.b Reduction of Variance
Example 1.9 Cover (hub cap) for Automobile Wheels
1.7.10 Designing with Incomplete Information
1.8 Common Mistakes Made by Designers
Example 1.10 Hood Lock and Release Mechanism
1.9 Comparison of Axiomatic Design with Various Methodologies
1.10 Concluding Remarks
References
Appendices
1. Corollaries
2. Theorems
Homework
Chapter 1 Introduction to Axiomatic
Design
1.1 Current State of Design Practice
It has been a mere 300 years since the industrial
revolution began. Yet, science and technology have developed
to an amazing level at an ever accelerating rate. For example,
humans already have walked on the face of the moon; are sending
space probes to other planets; can reduce the human physiology
into basic building blocks of DNA molecules; build memory chips
that can store, in a single chip, the entire base of scientific
knowledge that was available a hundred years ago; and design and
manufacture equipment that make microscopic electronic components
built on integrated circuit (IC) chips that are themselves smaller
than the tip of a finger. Humankind also has designed and manufactured
weapon systems that can hone in on a target within several feet
after traveling thousands of miles and unleash destructive power
that was unimaginable even 60 years ago. These are incredible
scientific and technological breakthroughs that have shaped the
history of humankind. The next hundred years will bring about
even bigger changes than the last hundred years -- so much so
that it is difficult to even imagine what the world will be like.
Will human beings be wise enough to harness the power of science
and technology for the benefit of humankind?
Notwithstanding these achievements, all
of which required the ability to design equipment, products, software,
processes, organizations and systems, it is easy to see around
us many technological and societal problems that have been created
due to poor design practice. Some are major problems that have
been well publicized, but there are many "small" problems
that simply inconvenience or aggravate the consumer. All of them
-- large and small -- can be dangerous, cost money, or limit the
usefulness of products or delay the introduction of new products.
A large number of products are being recalled; the warranty
cost of some products is a large fraction of the selling price;
poorly designed equipment requires maintenance and wastes valuable
time; and some failures result in loss of property and even lives.
While some of these failures are caused by a lack of scientific
knowledge, a majority of these problems arise because of poor
design of the product, process, systems, software, and systems.
Furthermore, many development projects of many companies result
in major delays, cost over-runs, and in some cases, a complete
failure.
One reason so many design mistakes are being
made today is that design is being done through empiricism or
on a trial-and-error basis. This problem is not confined to any
one country or any one company. It exists everywhere. Universities
throughout the world have not given their engineering students
generalized, codified, and systematic knowledge on design. Rather,
design has been treated as a subject that is not amenable to scientific
treatment. Consequently, design has depended on intuitive and
innate reasoning rather than rigorous scientific study. One of
the biggest challenges of the design field is to overcome this
acceptance of the design as a subject in arts rather than arts
and science. Fortunately, the field of design does not have to
remain at this stage of empiricism. Just as many fields of technology
have gone through similar stages of development, the field of
design, too, will evolve into a true disciplines with scientific
bases. This book, which follows The Principles of Design,
presents an expanded treatise on a scientific foundation for
design.
1.2 What is design? Who are
the Designers? How do we design?
Are you a designer? Is the mayor
of Boston a designer? If not, should the mayor be one? Who performs
design activities in your organization?
Design has been defined in a variety of
different ways depending on the specific context and/or the field
of interest. Mechanical engineers often design products, and,
therefore, when they say design, they typically refer to
product design. Manufacturing engineers, on the other hand, think
of design in terms of new manufacturing processes and systems
(i.e., factories and manufacturing cells). To electrical engineers,
design means developing analog or digital circuits, communications
systems, and computer hardware, while system architects perceive
design in terms of technical or organizational systems where many
parts must work together to yield a system that achieves the intended
goals.
Although some software engineers think that
their primary job is to write computer codes, they cannot produce
good software unless they first design the architecture of the
software before coding. Similarly, managers design organizations
to achieve organizational goals. Then, there are interior designers
who select and arrange furniture and other decorative items to
create the right mood for a house or a building. Even the mayor
of Boston must design an effective and efficient government and
strategic plans to achieve his vision for the city.
All of these are design activities, although
the contents of these activities and the knowledge required to
achieve the design goal are field specific. While these fields
appear to be distinct since each field utilizes different databases
and different design practices, they share many design characteristics.
What is common in all these activities is that they must do the
following:
1. Know their "customers' needs"
2. Define the problem they must solve to satisfy the needs.
3.Conceptualize the solution through synthesis, which involves the task of satisfying several different functional requirements using a set of inputs such as product design parameters within given constraints.
4. Perform analysis to optimize the proposed solution.
5.Check the resulting design solution
to see if it meets the original customer needs.
Design is an interplay between what we
want to achieve and how we want to satisfy them.
Therefore, a rigorous design approach must begin with an explicit
statement of "what we want to achieve" and end
with a clear description of "how we will satisfy the
whats". Once we understand the customer's needs,
this understanding must be transformed into a minimum set of specifications
(which will be defined later as functional requirements (FRs))
that adequately describe "what we want to achieve" to
satisfy the customer's needs.
Often designers find that the precise description
of "what we want to achieve" is a difficult task. Many
designers deliberately leave them implicit rather than explicit
and then, start working on design solutions even before they have
clearly defined their design goals. They measure their success
by comparing their design with the implicit design goals they
had in mind. They spend a great deal of time to improve and iterate
the design until the design solution and "what they had in
mind" converge, which is a time consuming process at best.
To be efficient and to generate the design that meets the perceived
needs, we must specifically state the design goals in terms of
"what we want to achieve" and begin the design process.
Iterations between "what" and "how" are
necessary, but each iteration loop must redefine "what"
clearly.
Example 1.1 Refrigerator Door Design
Consider the refrigerator door design shown
in Fig. a.
Is it a good design?
Each time this question is asked, we get
many different kinds of answers. Some say the door is not a good
design, since it is inconvenient for people who are right handed.
Some say it is a good design. However, the question posed cannot
be answered without asking: "what are the design goals (i.e.,
functional requirements) for the door design?"
If the purpose of the door is to provide
access to what is inside the refrigerator, then the door performs
that function. Therefore, the design for door is a good design.
On the other hand, if the functional requirements of the door
are the following two: (1) provide access to the food in the refrigerator
and (2) minimize the energy consumption, then the door is a poor
design since each time the door is opened to take the food out,
cold air in the refrigerator is replaced by hot outside air, requiring
the use of additional energy. The door should have been designed
differently to satisfy these two different functional requirements.
How would you design the door?
The important lesson of the above example
is that you must think in terms of functions the product
(or software, system, process, organization) must perform. One
must learn to think functionally in designing products,
processes, software, organization, business plans, and policies.
How do you design?
Many engineers design their products, processes,
and systems iteratively, empirically, and intuitively based on
years of experience or cleverness or creativity, involving much
trial-and-error. This practice is haphazardous and overly time
consuming. These intuitive designers/engineers may not be able
to describe explicitely the thought processes they have gone through
to develop their design solutions. Therefore, these designers
may not be able to reapply the same successful logic to another
design task without the repetition of an extensive trial-and-error
process. Certainly, these designers, although they may be very
successful practitioner, will not make good teachers since they
cannot state and communicate their knowledge and skills explicitely.
Historically, these masters transferred their knowledge to the
next generation through apprenticeship.
This situation must change from two different
points of view: design education and design practice. Design
knowledge must be generalized, codified, and systematized so that
anyone can be taught to be a good designer, which is the essence
of education. In academic disciplines such as the field of design,
the role of universities is to condense the time required to learn
a subject through the transmission of codified and generalized
knowledge so as to be more effective in learning and teaching.
We must also shorten the lead time it takes to develop good design
solutions by making correct decisions quickly and the first time
around. To achieve this goal, the designer's experience must
be augmented by teaching designers the underlying principles,
theories and methodologies so that even inexperienced persons
can quickly become good designers. Although experience is important
since design cannot be done without the knowledge and the information
one gains through experience, the experiential knowledge is not
always reliable, especially when the context of application changes.
They cannot be generalized and therefore, can be very limiting
in its applicability and in pedagogic value.
How does human creativity affect
the design process?
The word "creativity" has been
used to describe the human activity that results in ingenious
or unpredictable or unforeseen results (e.g., new products, processes,
and systems) that satisfy the needs of society or human aspirations.
In this context, creative "solutions" are discovered
or derived led by inspiration and/or perspiration, often without
ever defining specifically what one sets out to create. This
creative "spark" or "revelation" may occur
since our brain is a huge information storage and processing device
that can store data and synthesize solutions through the use of
associative memory, pattern recognition, digestion and recombination
of diverse facts, and permutations of events, when the brain receives
an impulse.
Sometimes, the word "creativity"
has been used in a mysterious sense whenever we do not understand
the process or the logic involved in a given intellectual endeavor
(e.g., arts and music), and yet, the result of the effort is intellectually
or emotionally or esthetically appealing and acceptable. A subject
is always mysterious when it relies on an implicit thought process
that cannot be explicitly stated and explained for others to understand
and that can only be learned through experience, apprenticeship
or trial-and-error. Design has been one of these mysteries, but
we must overcome this intellectual and mental barrier.
Design will always benefit when "inspiration"
or "creativity", and/or "imagination" play
a role, but we must augment this process by amplifying human capability
systematically through fundamental understanding of the nature
and human minds and by development of basic knowledge. Design
must become a principle-based subject. The subject of design
should attain the same level of intellectual understanding like
such fields as thermodynamics and mechanics. The knowledge from
design and other fields should converge and form a continuum of
knowledge with few discontinuities, rather than remaining as disparate
islands of knowledge that may characterize the current situation.
Indeed, the understanding of the design process is one of the
challenging intellectual quests. The ultimate beneficiaries of
structured design knowledge will be humankind, society, industry,
and the world.
1.3 What is the ultimate goal
of Axiomatic Design?
Can the field of design be scientific?
The ultimate goal of Axiomatic Design is
to establish a science base for design and to improve design activities
by providing the designer with a theoretical foundation based
on logical and rational thought processes and tools. The goal
of axiomatic design is manifold: to make human designers more
creative, reduce the random search process, minimize the iterative
trial-and-error process, determine the best designs among those
proposed, and endow the computer with creative power through the
creation of the science base for the design field.
In addition to the intellectual reasons
given for developing the science base for design, there are also
more practical reasons. Industrial competitiveness demands that
industrial firms have strong technical capability in design. They
are under pressure to shorten the lead time for introduction
of new products, lower their manufacturing cost, improve quality
and reliability of their products, and satisfy the required functions
most effectively. The greatest impact on all these industrial
needs rest on the quality and timeliness of developing design
solutions. Although human knowledge (i.e., a form of data base),
imagination (which requires an effective use of the data base
in human brain), experience (which results in accumulation of
facts, paradigms and database), and hard work will continue to
be an indispensable part of industrial effort, significant progress
cannot be made without the science base. Current design process
is too resource intensive and ineffective.
Since computers are becoming ever more powerful
and cheaper in terms of memory, faster in number crunching, and
smaller in physical size, designers should make use of computers
as an information storage device and as a design enhancement tool
to augment human capability through codification and generalization
of the design knowledge. The ultimate outcome of design research
may be a thinking design machine (TDB) that should be able to
let computers design products (Suh and Sekimoto, 1990). Today
computers are used in the design field, but they are used primarily
for graphic representation, solid modeling, product modeling,
and optimization of design solutions.
The modern Renaissance period
of design field is here!
The field of design is undergoing an intellectual
Renaissance -- from the notion that design can be learned only
from experience to the idea that it may be amenable to a systematic
and scientific treatment to enhance the creativity and the experiential
elements of the design knowledge. This intellectual Renaissance
is possible because good design decisions are not as random as
they appears to be but are a result of systematic reasoning, the
essence of which can be captured and generalized to enhance the
design process.
1.4 What is the difference between
this book and the first book on the subject?
The purpose of this book is to augment the
first monograph on axiomatic design, the Principles of Design
(Suh, 1990). The goal of this book is to present a variety of
applications of the principles of axiomatic design to aid the
learning process. To achieve this goal, cases studies are presented.
The case studies deal with product development, manufacturing
process design, quality control, software design, business plan
development, and organizational design. Many of the case studies
presented in this book are the contributions of many researchers
and engineers in industry, who applied the axiomatic design principles
to a variety of problems. Some of the case studies have been
modified not to reveal the proprietary information of some industrial
firms. In both the Principles of Design and this book,
general principles are given first followed by specific examples
and case studies.
1.5 Historical Perspective on
Axiomatic Design
Is there anything unique about
Axiomatic Design?
Axioms are truths that cannot be derived
but for which there are no counter-examples or exceptions. Many
fields of science and technology owe their advances to the development
and existence of axioms. They have gone through the transition
from experience based practices to the use of scientific theories
and methodologies that are based on axioms. In that sense, axiomatic
design is not unique.
Perhaps the oldest example of the use of
axioms may be Euclid's geometry, which were created to meet the
needs to measure the distance. These axioms have had powerful
effects on creating the modern mathematical base for manufacturing,
navigation and nearly all fields of science and technology. These
axioms cannot be derived but they are valid as long as there are
no counter-examples and exceptions.
The field of thermodynamics is also based
on axioms. The thermodynamic axioms have provided the basic foundation
for development of many other scientific fields. They have defined
such important concepts as energy and entropy. The scientific
field of thermodynamics was born as a result of many people attempting
to generalize how "good steam engines" work. Before
the field of thermodynamics emerged, many people might have said
that the steam engine was too complicated to explain and that
it could be designed only by experienced ingenious designers and
through trial-and-error processes. Indeed, that might be the
reason the Newcomen engine, which was invented in 1705, had been
used for 64 years to pump the water out of mines before James
Watt realized the shortcomings of the Newcomen engine and invented
the Watt engine in 1769. The invention of Watt's steam engine
eventually lead to the Industrial Revolution.
Similarly, before Newton explained the Kepler's
laws with his law for the gravitational force between masses and
his more general laws of motion, the motion of planets and other
objects had been a mystery. Clearly, Newton's laws were axioms
since they could not be derived or proven except that there were
no exceptions or counter examples until Einstein advanced the
theory of relativity, which has placed a bound on Newton's laws.
Newton's laws have established the concept of force. Even, Einstein's
theory of relativity is also based on an axiom that the speed
of light does not depend on the choice of the coordinate system.
How does technology influence
science? It seems that axioms have played a key role when technology
led to the development of science. Is that true?
It is well known how scientific discoveries
have led to the development of various technologies. The modern
biotechnology revolution owes its existence to the discovery of
the DNA structure by Crick and Watson (Watson, 1969). However,
the converse is also true but less well known; technology often
has preceded and led to the establishment of scientific fields.
Thermodynamics is a well known example. Another is the information
theory, which was created through an attempt to systematize the
telecommunications technology. Information theory now finds applications
in many fields of science. Axiomatic design is an example of
how technology of design has led to the science of design.
How were the design axioms created?
Design axioms were created by identifying
the common elements that are present in all good designs. This
was done by asking "how did I make such a big improvement
in a process?", " how did I create the process?",
"What are the common elements in good designs?" Once
the common elements could be stated, they were reduced down to
two axioms through a logical reasoning process. The historical
account of how the design axioms were developed in the mid 1970's
is given in the Principles of Design (Suh, 1990).
1.6 Axiomatic Approach vs. Algorithmic
Approach
Is there any other way of approaching
the subject of design?
There are two ways to deal with design:
axiomatic and algorithmic. In algorithmic design, we try to identify
or prescribe the design process, so in the end, the process would
lead to a design embodiment that satisfies the design goals.
Generally, the algorithmic approach is founded on the notion that
the best way of advancing the design field is to understand the
design process by following the best design practice. For example,
design for assembly (DFA) and design for manufacturability (DFM)
techniques are algorithmic methods. It is difficult to come up
with design algorithms for all situations, especially at the highest
conceptual level. Algorithms are generally useful at the level
of detail design, i.e., design for assembly, because they are
manageable.
Algorithmic methods can be divided into
several categories: pattern recognition, associative memory, analogy,
experientially based prescription, extrapolation, interpolation,
selection based on probability, etc. Some of these techniques
can be effective if the design has to satisfy only one functional
requirement, but when many functional requirements must be satisfied
at the same time, they are less effective. Axioms provide the
boundaries within which these algorithms are valid, in addition
to providing the general principles.
The axiomatic approach to any subject begins
with a different premise: that there are generalizable principles
that govern the underlying behavior of the system being investigated.
Axiomatic approach is based on the abstraction of the
good design decisions and processes. As stated earlier, axioms
are general principles or self-evident truths that cannot be derived
or proven to be true except that there are no counter-examples
or exceptions. Axioms generate new abstract concepts such as force,
energy, and entropy that are results of Newton's laws and thermodynamic
laws.
Axiomatic approach to design is powerful
and will have many ramifications because of the generalizability
of axioms, based on which corollaries and theorems can be derived.
These theorems and corollaries can be used as design rules that
precisely prescribe the bounds of their validity because they
are based on axioms. Design axioms apply to may different kinds
of problems and issues as shown in this book.
What is the relationship between
design process and design axioms?
In many fields of learning, both the process
of how something is done and the abstraction that can generalize
the underlying principles are equally important. For example,
when we teach small children or babies the notion of numbers,
we do it by counting our fingers -- by counting from thumb to
pinkie, for example. This is done to teach the process
of counting, which has the flavor of being algorithmic. However,
if we keep starting the process of counting using our thumb and
ending up with the pinkie, the child may think that thumb is called
"one". Therefore, we use toes and other objects to
teach the notion of numbers through abstraction of the counting
process. In design, we also need to do both. We need to teach
both the process and the abstracted concept of what is a good
design and how to develop good designs.
1.7 Axiomatic Design Framework
1.7.1 The Concept of Domains
The design world is made of four
domains. What are domains?
Design involves an interplay between "what
we want to achieve" and "how we choose to satisfy the
need (i.e., what)". To systematize the thought process involved
in this interplay, the concept of domains that create demarcation
lines between various design activities is a foundation of axiomatic
design. The world of design is made up of four domains:
the customer domain, the functional domain, the physical
domain, and the process domain. The domain structure
is illustrated schematically in Fig. 1.1. The domain on the left
relative to the domain on the right represents "what we want
to achieve,î whereas the domain on the right represents
the design solution of "how we propose to satisfy the requirements
specified in the left domain.î
Fig. 1.1: Four Domains of the Design World.
{x} are characteristic vectors of each domain
The customer domain is characterized by
customer needs or the attributes the customer is looking for in
a product or process or systems or materials. In the functional
domain, the customer needs are specified in terms of functional
requirements (FRs) and constraints (Cs). In order to satisfy
the specified FRs, we conceive design parameters, DPs, in the
physical domain. Finally, to produce the product specified in
terms of DPs, in the process domain we develop a process that
is characterized by process variables, PVs. For example, a customer
in semiconductor industry needs to coat the surface of a silicon
wafer with photoresist. This is done in the customer domain.
Based on this need, the engineer in an equipment company establishes
the functional requirements (FRs) in terms of thickness and uniformity
and also the constraints (Cs) in terms of tolerable level of contaminant
particles, production rate, and cost. This is done in the functional
domain. Then, the designer of equipment, based on experimental
data and past experience, must conceive a design solution and
identify the important design parameters (DPs) in the physical
domain. The designer might choose to spray the photoresist and
control thickness by spinning the disk at high speed to make use
of centrifugal force. Then, the manufacturing engineer in the
process domain must conceive the means of manufacturing the equipment,
specifying the process variables that can provide the DPs.
In mechanical engineering we often think
of design in terms of product design and often, hardware design.
However, engineers also deal with other equally important designs
such as software design, design of manufacturing processes and
system, and organizations. All designers go through the same
thought process, although some believe that their design is unique
and different from everyone else's. In materials science, the
design goal is develop materials with certain properties (i.e.,
FRs). This is done through the design of microstructures (i.e.,
DPs) to satisfy these FRs, and through the development of material
processing methods (i.e., PVs) to create the desired microstructures.
In business, after business goals {FRs} are established, the
next task is to design business structure and organizations {DPs}
to meet the business goals, and find human and financial resources
{PVs} to staff and operate the business. Similarly, universities
must define the mission of their institutions (i.e., FRs), design
their organizations effectively to have an efficient educational
and research enterprise (i.e., DPs), and must deal with human
and financial resource issues (i.e., PVs). In the case of the
U. S. Government, President of the United States must define the
right set of {FRs}, design the right government organization and
programs {DPs}, and secure the resources necessary to get the
job done {PVs}, subject to the constrains imposed by the Constitution
and Congress. In all organizational design the process domain
represents the resources: human and financial.
Table 1.1 shows how all these seemingly
different design tasks in many different fields can be described
in terms of the four design domains. In the case of the product
design, the customer domain consists of the customer requirements
or attributes the customer is looking for in a product; the functional
domain consists of functional requirements, often defined as engineering
specifications and constraints; the physical domain is the domain
in which the key design parameters {DPs} are chosen to satisfy
the {FRs}; and the process domain specifies the manufacturing
methods that can produce the {DPs}. As an example, the design
issues in the organizational design of an academic department
are illustrated in terms of the design domains in Table 1.2.
| Domains Character Vectors | Customer D. {CAs} | Functional D. {FRs} | Physical D. {DPs}
| Process D. {PVs} |
| (a) Manufacturing | Attributes which consumers desire | Functional requirements specified for the product | Physical variables which can satisfy the functional requirements | Process variables that can control design parameters (DP)s |
| (b) Materials | Desired performance | Required Properties | Micro-structure | Processes |
| (c) Software
| Attributes desired in the software | Output
Spec of Prog codes | Input Variables or Algorithms
Modules Prog. codes | Sub-routines
machine codes compilers modules |
| (d) Organization
| Customer satisfaction | Functions of the organization | Programs or Offices | People and other resources that can support the programs |
| (e) Systems
| Attributes desired of the overall system | Functional requirements of the system | Machines or components, sub-components | Resources (human, financial, materials, etc.) |
Table 1.1: Characteristics of the four domains
of the design world for various designs: manufacturing, materials,
software, organizations, and systems.
Customer Domain CA1: Customer Satisfaction | Functional Domain FR1: Quality | Physical Domain DP1: Programs | Process Domain PV1: People - Academic |
| CA11 Undergraduates
CA12 Graduates CA13 Research Sponsors CA14 Public (Society at Large) | FR11 Provide quality undergrad. education
FR12 Provide quality graduate education FR13 Set the trend in quality research FR14 Participation in public activities | DP11 Undergraduate curriculum
DP12 Graduate curriculum DP13 Important res. topics DP14 Opportunities | PV11 Strong involvement of faculty
PV12 Academically strong grad studs. PV13 Strong faculty
PV14 Active support of external |
CA2: Cash Flow | FR2: Good Management of Resources | DP2: Administrative Mechanisms | PV2: Administrative People |
| CA21 Teaching Support
CA22 Research support CA23 Capital Investment
CA24 Human Resource | FR21 Use the general fund effectively
FR22 Generate external research support FR23 Generate gifts FR24 Create chairs, support, etc. | DP21 Budget & Plans
DP22 Financial support for fund DP23 Fund raising mechanisms
DP24 "Attention" to faculty | PV21 Budget officer
PV22 Support staff for research fund PV23 Dept. Head & Faculty PV24 Dept. Head & Associate Head |
CA3: Profit (i.e., net gain) | FR3: Productivity (intellectual & financial) | DP3: Means | PV3: Methods |
| CA31 Better teaching paradigms
CA32 Research infrastructure
CA33 New Inventions &
CA34 Better tools (i.e.,
CA35 Outstanding grads: | FR31 Create relevant pedagogical tools
FR32 Develo labs & centers
FR33 Promote scholarly & creative activities: Patents, monographs, prizes & FR34 Secre equipment & facilities FR35 Promote effective mentorship | DP31 Textbooks, videotapes
DP32 (Better) research organizations
DP33 Active support, promotion, & DP34 Investment in capital goods
DP35 Stronger faculty/student | PV31 Support & Reward Mech.
PV32 Establish interdisciplinary PV33 Staff support PV34 Fund raising
PV35 Formation of "research teams" |
CA4: Growth, Intellectual & Physical | FR4: "Innovation" | DP4: Environment (i.e., culture) | PV4: "Resource" |
| CA41 Define ME of the 21st Cent.
CA42 Define Eng. of 21st
CA43 Shape the society of the
CA44 Strengthen the human | FR41 Create new pedagog tools & disc.
FR42 Pioneer new engineering tools, methods, & books FR43 Solve societal problems
FR44 Entice minorities & women into | DP41 Creative, experimental approach DP42 Active interaction w/industry
DP43 Active interaction w. industry, DP44 Special Programs | PV41 Faculty time & financial support PV42 "Manufacturing Institute" PV43 External Participation PV44 Financial resource |
All designs fit into these four domains.
Therefore, all design activities, be it product design or software
design, can be generalized in terms of the same principles. Because
of this logical structure of the design world, the generalized
design principles can be applied to all design applications and
we can consider all the design issues that arise in four domains
systematically and if necessary, concurrently.
1.7.2 Definitions
Is it important that we adhere
to certain definitions of key words?
Before proceeding any further discussion
of axiomatic design, it is important for us to summarize the definition
of a few key words discussed in the preceding section, since axioms
are valid only within the bounds established by the definitions
of these key terms. Just as the words like heat and work have
unique meaning in thermodynamics, which are different from their
daily usage, so is the case with key words used in axiomatic design.
The definitions are as follows:
Axiom: Self-evident truth or fundamental
truth for which there are no counter examples or exceptions.
It can not be derived from other laws of nature or principles.
Corollary: Inference derived from axioms
or propositions that follow from axioms or other propositions
that have been proven.
Functional Requirement: A minimum set of
independent requirements that completely characterizes the functional
needs of the product (or software, organizations, systems, etc.)
in the functional domain. By definition, each FR is independent
from each other at the time FRs established.
Constraint: Constraints are bounds on acceptable
solutions. There are two kinds of constraints: input constraints
and system constraints. Input constraints are imposed as part
of the design specifications. System constraints are constraints
imposed by the system in which the design solution must function.
Design parameter: Design parameters are
the key physical (or other equivalent terms in case of software
design, etc.) variables in the physical domain that characterize
the design that satisfies the specified FRs.
Process variable: Process variables are
the key process (or other equivalent term in the case of software
design, etc.) variables in the process domain that characterize
the process that can generate the specified DPs.
Most of the key words listed are associated
with the Independence Axiom. Additional definitions of key words
associated with the Information Axiom will be given in a later
section. The significance of these definitions should become
clearer through the examples given throughout this book.
1.7.3 Mapping from Customer Needs
to Determination of Functional Requirements
The attributes desired in a product by customers
(CAs) or customer needs are sometimes difficult to define or vaguely
defined. Nevertheless we have to do the best we can to understand
the customer needs by working with customers to define their needs.
Then these needs (or the attributes the customer is looking for
in a product) must be translated to functional requirements FRs.
This must be done a "solution neutral environment".
That means FRs must be defined without ever thinking about something
that has been already designed or what the design solution should
be. If FRs are defined based on an existing design, then we will
simply be specifying the FRs of that product and the result of
the design endeavor will be likely to be similar to the existing
product, forestalling creative thinking.
To aid the process of defining FRs, QFD
(Quality Function Deployment) has been used. In QFD the customer
needs and the possible functional requirements are correlated
and important FRs are determined. Experience plays an important
role in defining FRs, since qualitative judgment plays a major
role in assessing the customer needs. QFD may be an effective
tool for an existing product that needs to be improved, but to
develop a completely new original design, the FRs must be defined
in a solution neutral environment.
Industrial firms often use "marketing
requirement specification" (MRS) as the product specification
document. They are often very thick, for which the primary inputs
are provided by the marketing people. Often the document is a
random mixture of CAs, FRs, Cs, DPs, and PVs. When the marketing
group specifies DPs, and PVs, the design process becomes complicated
since they lose freedom to come up with the best design solutions.
They should limit their inputs to CAs, FRs, and Cs.
1.7.4 The First Axiom: The Independence
Axiom
During the mapping process (for example,
going from the functional domain to the physical domain), we must
make correct design decisions using the Independence Axiom. When
several designs that satisfy the Independence Axiom are available,
the Information Axiom can be used to select the best design. When
only one FR is to be satisfied, the Independence Axiom is always
satisfied and therefore, the Information Axiom is the only axiom
the one FR design must satisfy, which is the subject of Chapter
2.
So what are the design axioms?
How many axioms are there?
The basic postulate of the axiomatic approach
to design is that there are fundamental axioms that govern the
design process. Two axioms were identified by examining the common
elements that are always present in good designs, be it a product,
process, or systems design. They were also identified by examining
actions taken during the design stage that resulted in dramatic
improvements. The history of how the design axioms were created
is given by Suh (1990).
As many case studies presented in this book
show, the performance, robustness, reliability, and functions
of products, processes, software, systems, and organizations are
significantly improved, when these axioms are satisfied. Conversely,
machines and processes that were not working well can be analyzed
to determine the causes of their dysfunction or malfunction and
to solve the problems based on the design axioms.
The first axiom is called the Independence
Axiom. It states that the independence of Functional Requirements
(FRs) must be always maintained, where FRs are defined as the
minimum number of independent functional requirements that
characterize the design goals. The second axiom is called the
Information Axiom, and it states that among those designs
that satisfy the Independence Axiom, the design that has the highest
probability of success is the best design. Based on these design
axioms, we can derive theorems and corollaries. The axioms are
formally states as
Axiom 1: The Independence Axiom
Maintain the independence of the functional
requirements (FRs).
Axiom 2: The Information Axiom
Minimize the information content of
the design.
As stated earlier, the functional requirements,
FRs, are defined as the minimum set of independent requirements
that the design must satisfy. A set of functional requirements
{FRs} are the description of design goals. The Independence Axiom
states that when there are two or more functional requirements
(note: review the refrigerator door example involving two requirements
discussed in Example 1.1), the design solution must be such that
each one of the functional requirements can be satisfied without
affecting the other functional requirement. That means we have
to choose a correct set of DPs to be able to satisfy the functional
requirements and maintain their independence.
The Independence Axiom is often misunderstood.
Many people confuse between the functional independence with
the physical independence. The Independence Axiom requires that
the functions of the design be independent from each other, not
the physical parts. This is illustrated using the beverage can
as an example.
Example 1.2 Beverage Can Design
Consider an aluminum beverage can that contains
carbonated drinks. How many functional requirements must the
can satisfy? How many physical parts does it have? What are
the design parameters (DPs)? How many DPs are there?
Solution
According to an expert working at one of
the aluminum can manufacturer, it appears that there are 12 FRs
for the can. It has to contain the pressure, withstand a moderate
impact when the can is dropped from a certain height, stack on
top of each other, provide easy access to the liquid in the can,
minimize the use of aluminum, printable on the surface, and others.
However, the aluminum can consists of only three pieces: the
body, the lid, and the opener tab. What the Independence Axiom
requires is that the 12 FRs be independent from each other, not
that there be 12 physical pieces making up the can!
Where are the DPs? According to Theorem
4, there must be at least 12 DPs. Most of the DPs are associated
with the geometry of the can. Thickness of the can body, the
curvatures at the bottom of the can, the reduced diameter of the
can at the top to reduce the material used to make the top lid,
the corrugated geometry of the opening tab to increase the stiffness,
the small extrusion on the lid to attach the tab, etc. There
are 12 DPs in the can design and the Independence Axiom is satisfied
by the can, according to the engineer who improved the can design
after taking the axiomatic design course at MIT.
After we define the FRs, we must
conceptualize a solution. When and how does it take place during
the design process?
After the FRs are established, the next
step in the design process is the conceptualization process, which
occurs during the mapping process going from the functional domain
to the physical domain.
To go from "what" to "how"
(for example, from the functional domain to the physical domain)
requires mapping which involves creative conceptual work.
Once the overall design concept is generated by mapping, we
must identify the design parameters (DPs) and complete the mapping
process. During this process, we must think of all different
ways of fulfilling each of the FRs by identifying plausible DPs.
Sometimes it is convenient to think about a specific DP to satisfy
a specific FR, repeating the process until the design is completed.
One can use a database of all kinds (generated through brainstorming,
morphological techniques, etc.), analogy from other examples (apparently
Thomas Edison's favorite means of invention), extrapolation and
interpolation, laws of nature, order of magnitude analysis, reverse
engineering (copying somebody else's good idea by examining an
existing product), and others. It is relatively easy to identify
a DP for a given FR, but when there are many FRs we must satisfy,
the design task becomes difficult and many designers make mistakes
by violating the Independence Axiom. This is the subject of Chapter
3 which is on multi-FR design.
If it is a mapping process, shouldn't
we be able to write design equations?
The mapping process between the domains
can be mathematically expressed in terms of the characteristic
vectors that define the design goals and design solutions. At
a given level of design hierarchy, the set of functional requirements
that define the specific design goals constitutes a vector {FRs}
in the functional domain. Similarly, the set of design parameters
in the physical domain that are the "Howís" for
the FRs also constitutes a vector {DPs}. The relationship between
these two vectors can be written as
{FRs}=[A] {DPs}
(1.1)
where [A] is a matrix defined as the Design
Matrix that characterizes the product design. Equation (1.1)
may be written in terms of its elements as FRi = Aij DPj. Equation
(1.1) is a design equation for design of a product. The design
matrix is of the following form for a symmetrical matrix (i.e.,
i=j):
(1.2)
where
Aij = 
Equation (1.1) may be written as
FR1 = A11 DP1 + A12 DP2 + A13 DP3
FR2 = A21 DP1 + A22 DP2 + A23 DP3 (1.3)
FR3 = A31 DP1 + A32 DP2 + A33 DP3
For a linear design, Aij are constants,
whereas for nonlinear design Aij are functions of DPs. There
are two special cases of the design matrix: diagonal matrix where
all Aij's except those i=j are equal to zero, and triangular matrix
where either upper or lower triangular elements are equal to zero
as shown below.
(1.4)
(1.5)
For the design of processes involving mapping
from the physical domain to the process domain, the design equation
may be written as:
{DPs}=[B] {PVs} (1.6)
[B] is the design matrix that defines the
characteristics of the process design.
How do we know whether or not
the Independence Axiom is satisfied?
To satisfy the Independence Axiom, the design
matrix must be either diagonal or triangular. When the design
matrix [A] is diagonal, each of the FRs can be satisfied independently
by means of one DP. Such a design is called an uncoupled
design. When the matrix is triangular, the independence of FRs
can be guaranteed if and only if the DPs are changed in a proper
sequence. Such a design is called a decoupled or quasi-coupled
design. Therefore, when several functional requirements must
be satisfied, we must develop designs that will enable us to create
a diagonal or triangular design matrix.
The design matrix [A] or [B] can be made
of matrix elements which are constants or functions. If the matrix
is made of constants, it represents a linear design. If it is
a relational matrix where its elements are functions of DPs, the
design matrix may represent a nonlinear design.
The design matrix is a second order tensor
just as stress, strain, and moment of inertia are also second
order tensors. However, there is one big difference between the
design matrix and these other second order tensors. These other
tensors can be changed through coordinate transformation to convert
any matrix into a diagonal matrix. The diagonal elements of the
diagonal matrix are invariant such as principal stresses in the
case of stress tensor. However, the coordinate transformation
technique cannot be applied to design equations to find the invariant
(i.e., the diagonal matrix), since the design matrix [A] typically
involves physical things that are not amenable to coordinate transformation.
In other words, mathematically we can always transform any design
matrix into a diagonal matrix, but the diagonal elements may not
have any physical significance.
What are constraints?
The design goals are often subject to constraints,
Cs. Constraints provide the bounds on the acceptable design solutions
and differ from the FRs in that they do not have be independent.
Some constraints are specified by the designer. Many constraints
are also imposed by the environment within which the design must
function. These are system constraints. Often it is best to
treat cost as a constraint, but price can be treated as a functional
requirement. Cost is affected by all design changes and therefore,
cost cannot be made independent of other FRs in an uncoupled design.
If it is decided that cost must be a functional requirement,
then the best we can do is to develop a decoupled design, which
also satisfies the Independence Axiom. With cost as a constraint,
the design is acceptable as long as the cost does not exceed a
set limit.
Since we are dealing with axioms,
shouldn't there be corollaries and theorems?
As will be discussed further in Chapter
3, we can derive many corollaries and theorems based on these
two axioms. For example, Theorem 1 states that to satisfy
the independence of a given set of FRs, the number of DPs must
be at least equal to the number of FRs. Theorem 4 states
that in an ideal design, the number of DPs is equal to the
number of FRs. When the number of DPs is less than
that of FRs, the design is always coupled. Many theorems and
corollaries can be used as design rules for specific cases. In
Appendix 1-A, the theorems and corollaries are given.
How do we create a design hierarchy
through zigzagging?
A previous discussion pointed out that FRs
and DPs (as well as PVs, the characteristic vector for the process
domain) can be decomposed into a hierarchy. However, contrary
to the conventional wisdom on decomposition, they cannot be decomposed
by remaining in one domain. One must zigzag between the domains
to be able to decompose the FRs, DPs, and PVs. Through this zigzagging
we create hierarchies for FRs, DPs, and PVs in each design domain.
For example, if one of the FRs for a vehicle is "move forward,î
we cannot decompose it without deciding first in the physical
domain "how we propose to go forward." If we choose
a horse and buggy as a means of moving forward, the next layer
of FRs will be different from when an automobile is chosen as
the DP to satisfy the FR. In other words, to create a FR, DP,
and PV hierarchies, we must map into the domain on the right
("how domain") first from the domain on the left ("what
domain"), and then come back to the domain on the left ("what
domain") to generate the next level FRs, etc. The decomposition
and the design hierarchies will be discussed further in Sec. 1.6.6.
1.7.5 Case Studies Involving Decoupling
of Coupled Designs
Two examples of coupled designs which were
improved by decoupling are given in this section. One is a historical
case, which led to the Industrial Revolution, and the other was
example was motivated by the case study worked out by engineers
of an aircraft company as part of their exercise in learning axiomatic
design. These engineers at the aircraft company solved a long
standing problem, simplifying the manufacturing process and eliminating
many problems associated with the original process.
Example 1.3 Newcomen Steam Engine vs.
Watt's Engine
Figure a
shows the Newcomen engine, which was invented in 1705. This engine
was used to pump water out from mines. Recently, this design
was examined in terms of the Independence Axiom by Thomas [1995].
The engine works by injecting steam into
a cylinder to push a piston outward and by condensing the steam
to create a vacuum inside the cylinder and pull the piston inward
during which work is done to pump the water out of the mine.
The steam is condensed by injecting cold water. During the subsequent
cycle, the steam is injected into the cylinder that raises the
temperature of the cylinder and drives the condensed water out
of the cylinder before the steam can fully expand. The functional
requirements are: FR1= expand the piston by using steam and FR2=
create a vacuum in the cylinder to pump the water out of the mine.
The design parameters are: DP1= injection of steam and DP2= cooling
of the cylinder to condense the steam. The design equation may
be written as:
(a)
DP1 affects both FR1 and FR2 since the steam
has to heat the cylinder and the piston before the injected steam
can expand in the cylinder. Similarly, DP2 affects both FR1 and
FR2, because when the steam is condensed by circulating cold water
around the cylinder, the cylinder and the piston have to be cooled
before the steam inside the cylinder can be condensed. Therefore,
the design matrix is neither diagonal nor triangular. The Newcomen
engine is a coupled design. The performance of the engine is
low with long cycle times, because the injection of the steam
(i.e., DP1) and the cooling of the cylinder (i.e., DP2) affect
both FR1 and FR2 through the thermal inertia of the cylinder and
the piston. It is a coupled design.
This coupled design can be uncoupled by
creating a separate condenser elsewhere in which the steam ejected
from the cylinder can be condensed. This is the invention James
Watts made in 1769, 64 years after the invention of the Newcomen
engine. The design equation for this first version of the Watts
engine may be expressed as:
(b)
The James Watts engine was a successful
engine because it was an uncoupled design. In Watt's engine,
the functional requirements can be independently satisfied.
The engine was further improved by Watts and others, making it
from the single-stroke to double-stroke, etc. It is interesting
to note that James Watts' first patent application was based on
the idea of separating function of steam injection from the condensation
function that had taken place in the same cylinder to save the
steam. James Watt came out with an uncoupled design without the
benefit of the Independence Axiom. The hope is that the explicit
statement of the design axioms will enable an ordinary engineer
to do what James Watt did in a much shorter period of time. Indeed,
many inventions made by engineers after learning axiomatic design
demonstrate that to be the case.
Some one hundred years after the invention
of the steam engine, because of the importance of the steam engine
as a motive source for power, the science of thermodynamics was
established. It was done through the generalization of the experience
gained working with effective steam engines, which is now known
as the second law of thermodynamics. It is interesting to note
that we may now invoke either the second law of thermodynamics
or the First Design Axiom (i.e., the Independence Axiom) to come
up with the solution James Watts came out empirically. After
the advent of the second law of thermodynamics, the first law
of thermodynamics was established. Since then, thermodynamics
has impacted all scientific and technological endeavors of humankind.
Example 1.4 Shaping of Hydraulic Tubes
Tubes must be bent to complex shapes in
many applications (e.g., aircraft) without changing the circular
cross-sectional shape of the tube. This is a particularly difficult
job when the tube is made of titanium because it has a hexagonal
close packed (hcp) structure and its mechanical properties are
non-isotropic and it cannot be bent repeatedly.
When an aircraft company tried to bend titanium
tube into complex shapes, it found that the round cross-sectional
shape could not be maintained. To prevent this distortion of
the cross-sectional shape, they inserted a wire with spacer disks
(whose diameter was equal to the inside diameter of the tube)
into the tube. The spacer disks were symmetrically mounted on
the wire through a hole at the center of the disks. When they
removed the wire with disks from the tube, they found that the
disks scratched the inner surface of the tube. Therefore, they
applied a lubricant, which made the removal of the wire easier.
Then, they had clean out the lubricant from the inside the tube
with a solvent, which in turn, created a solvent disposal problem.
The engineer, who took the axiomatic design
course specially offered at his company, solved the tube bending
problem as part of his term project for the course. The solution
was so successful that the company made his solution proprietary
to his company. Therefore, the solution presented here has been
obtained independently to illustrate the design procedure.
To design a machine and a process that can
achieve the task, the functional requirements can be formally
stated as:
FR1= bend the titanium tube to prescribed curvatures
FR2= maintain the circular cross-section
of the bent tube
Theorem 4 states that in an ideal design
the number of DPs is equal to the number of FRs. To come up with
an acceptable solution, we must look for a design with two DPs
according to this theorem.
The mechanical concept that can do the job
is schematically shown in Fig. a
for a two-dimensional bending case. It consists of a set of matching
rollers with semi-circular grooves on their periphery. These
"bending" rollers can counter-rotate at different speeds
and move relative to each other to control the bending as shown
in Fig. a.
A second set of "feed" rollers, which counter-rotate
at the same speed, feed the straight tube feedstock into the bending
rollers. The centers of these two bending rollers are fixed with
respect to each other and the contact point of the bending rollers
can rotate about a fixed point. As the tubes are bent around
the rollers, the cross-sectional shape will tend to change to
a non-circular shape. The deformation of the cross-section is
prevented by the semi-circular cam profile machined on the periphery
of the bending rollers. [It may be necessary to make the groove
profile slightly oval shaped at the top and bottom of the groove
to prevent buckling from the compression side.] The DPs for this
design are:
DP1= Differential rotation of the bending rollers to bend the tube
DP2= The profile of the grooves on the periphery
of the bending rollers
The kinematics of the roller motion needs
to be determined. To bend the tube, one of the bending rollers
must rotate faster than the other. In this case, the tube will
be bent around the slower roller. The forward speed of the tube
is determined by the average speed of the two bending rollers.
The motion of these rollers can be controlled digitally using
stepping motors.
The design is an uncoupled design, since
each of these DPs only affect one FR. Is this the best design?
The only way this question can be answered is to develop alternate
designs that satisfy the FRs and constraints (Cs), and the Independence
Axiom. Then, we need to compute the information content of the
proposed designs to select the best among the proposed designs.
If the design done so far is acceptable,
we need to decompose the FRs to form the next level FRs (e.g.,
FR11 and FR12 for FR1, based on the DP1 chosen) and then map them
into the physical domain to determine the next level DPs. This
process can go on until the design is completed. However, it
will not be done here. How would you decompose FR1 and DP1?
Another design solution that can achieve
the desired goal might be to fill the tube with incompressible
material, such as a low-melting point metal that can be solidified
in the tube before bending the tube. After bending, the metal
can be molten and removed from the tube. Is this a better solution
than the use of the grooved rollers?
1.7.6 Decomposition, Zigzagging and Hierarchy
In the preceding examples the design was
completed when we mapped from the Functional Domain to the Physical
Domain. It was the highest level conceptual design. For example,
in the case of the Watt engine, we have not designed the details
of the condenser, etc. Therefore, we need to decompose the highest
level FRs into lower level FRs, and similarly, the highest DPs
to level DPs. Similarly, to complete the design of the tube bending
machine, the details of mechanisms, groove shape, and the servocontrol
mechanisms must be developed by decomposing the highest level
FRs and DPs of the conceptual design. In fact, this decomposition
process must proceed layer by layer until the design can be implemented.
Through this decomposition process, we establish
hierarchies of FR, DP, and PV, which is a representation of the
architecture of the design. [This is further discussed in Chapter
4 in relation to software design.]
As stated in Sect. 1.6.4, we must zigzag
between the domains in order to decomposed these characteristic
vectors. That is, we start out in the "what" domain
and go to "how" domain. This is illustrated in Fig.
1.2. From FR in the functional domain, we go to DP in the physical
domain. Then, we come back to the functional domain to create
FR1 and FR2 that collectively satisfy the highest level FR and
the corresponding DP. Then we go to the physical domain to find
DP1 and DP2, which satisfy FR1 and FR2, respectively. This process
continues until the FR can be satisfied without further decomposition.
This process is pursued until all the branches reach the final
state.
In many organizations, attempts are made
to decompose functional requirements or specifications without
zigzagging and by remaining only in the functional domain. Since
decomposition cannot be done this way, they think of an existing
design and end up re-specifying the design that already exists.
For example, suppose you want to design a vehicle that goes
forward, stops, and turns. This vehicle has to satisfy these
three FRs. We cannot decompose these FRs, unless we first design
the vehicle at the highest conceptual level. If we decided to
use an electric motor as a DP to satisfy the FR of moving forward,
the next lower level FRs would be different than if we had decided
to use gas turbines. Therefore, when we define the FRs in a solution
neutral environment, we have to "zig" to the physical
domain, and after proper DPs are chosen, we have "zag"
to the functional domain for further decomposition. Those organizations
that created a division for specification of FRs could not have
gotten satisfactory performance out of the division.
This process of mapping and zigzagging must
continue until the design is completed. The result of this zigzagging
is the creation of hierarchical tree for both FRs and DPs. This
will be illustrated in the following example.
Example 1.5 Refrigerator Design
Historically humankind has had the need
to preserve food. Now consumers want an electrical appliance
that can preserve food for an extended time. The typical solution
is to freeze food for long-term preservation and to keep some
food at a cold temperature without freezing for short-term preservation.
These needs can be formally stated in terms of two functional
requirements:
FR1=freeze food for long-term preservation
FR2=maintain food at cold temperature for
short-term preservation
To satisfy these two FRs, a refrigerator
with two compartments is designed. Two DPs for this refrigerator
may be stated as:
DP1=the freezer section
DP2=the chiller (i.e., refrigerator) section.
To satisfy FR1 and FR2, the freezer section
should only affect the food to be frozen and the chiller (i.e.,
refrigerator) section should only affect the food to be chilled
without freezing. In this case, the design matrix will be diagonal.
However, the conventional freezer/refrigerator design uses one
compressor and one fan which turn on when the temperature of the
freezer section is higher than the set temperature and the chiller
section is cooled by controlling the opening of the vent as shown
in Figs. a
and b
(see Lee, et al., 1994). Therefore, the chiller section temperature
cannot be controlled independently from the freezer section.
It is a coupled design. Let us see how we can improve this design.
Having chosen the DP1, we can now decompose
FR1 as:
FR11=control temperature of the freezer section in the range of -18 C
FR12=maintain the uniform temperature throughout the freezer section at the preset temperature
FR13=control humidity to relative humidity
of 50%
Similarly, based on the choice of DP2 made,
FR2 may be decomposed as:
FR21=control the temperature of the chilled section in the range of 2 to 3 C
FR22=maintain a uniform temperature throughout
the chilled section at a preset temperature to within 1 C
To satisfy the second level FRs, i.e., FR11,
etc., we have to conceive a design and identify DPs that can satisfy
the FRs at this level of decomposition. Just as FR1 and FR2 were
independent from each other through the choice of proper DP1 and
DP2, we must now assure that FRs at this second level are independent
from each other.
Suppose that the requirements of the freezer
section will be satisfied by pumping in chilled air into the freezer
section, circulate the chilled air uniformly throughout the freezer
section, and monitor the returning air for temperature and moisture
in such a way that the temperature is controlled independently
from the moisture content of the air. Then, the second level
DPs may be chosen as:
DP11=Turn on and off the compressor when
the air temperature is higher and lower than the set temperature,
respectively.
DP12=Blow the air into the freezer section
and circulate it uniformly throughout the freezer section
at all times
DP13=Condense the moisture in the returned
air when its dew point is exceeded
Then, the design equation may be written
as:
(a)
Equation (a) indicates that the design is a decoupled design.
We can now design the chilled section where
the food has to be kept in the range of 2 to 3 C. Here again,
we may also circulate the chilled air throughout the chilled section
and turn on the compressor when the temperature of the returned
air is out of the preset range. This would result in a decoupled
design as well. One of the design questions to be answered here
is whether the same compressor and the same fan can be used to
satisfy the set {FR11, FR12, FR13} from the set {FR21, FR22} to
minimize the information content without compromising their independence.
Most commercial refrigerators use only one compressor and one
fan to achieve these goals (see Figs. a
and b).
Many of these are coupled designs.
One can propose various specific design
alternatives and evaluate the options in terms of the Independence
Axiom. If a design allows the satisfaction of these FRs independently,
then the design is acceptable for the set of specified FRs. Otherwise,
the designer must compromise the FRs by eliminating some of the
FRs or by giving much larger tolerance for temperature control,
moisture control, etc., to satisfy the Independence Axiom if the
design is slightly coupled and the off-diagonal terms are relatively
small.
Recently, one company has improved the preservation
of food in their chilled section by adding one additional fan
so as to control the temperature of the chilled section more effectively
as shown in Figs. c
and d
(Lee, et al., 1994). This could be done since the evaporator
was sufficiently cold and had large thermal inertia to cool the
air being pumped into the chiller section even during the period
the compressor was not turned on. To have a uniform temperature
distribution they added extra vents to insure good circulation
of air. In this design, DP21 is the fan for the chiller section
and the DP22 is the vent. The temperature in the chiller section
was much more uniform (Fig. e)
and temporal fluctuation was much less than those of coupled designs
(Fig. f).
The design matrix for the {FR21, FR22}-{DP21, DP22} relationship
is diagonal as shown in the design equation:
(b)
The new design with the extra fan satisfies
the specified functional requirements much better as shown in
Figs. e
and f.
Because it is a better design since it satisfies the Independence
Axiom, food stored in the refrigeration (i.e., the chiller section)
stays fresh longer.
The designers of this new refrigerator found
that this design saves electricity because air can be defrosted
due to the air flow into the chiller section when the compressor
is not operating. This new design also enables the use of quick
refrigeration mode in the chilled section by turning on the fan
of the chiller section as soon as food is put into the chiller
section. To cool 100 g of water from 25 C to 10 C, it took only
37 minutes vs. 58 minutes in a conventional refrigerator as shown
in Fig. g
(Lee, et al., 1994).
This idea of using two fans and uniformly
positioned ducts may or may not be the best solution if the FRs
can be satisfied independently using only one fan according to
Corollary 3. If there is an alternate design that can satisfy
the Independence Axiom, we have to consider the Information Axiom
to choose the better of the two designs. Only the detailed calculation
of the information axiom can determine the best design option
if one can conceive of designs that use only one fan and yet satisfy
the Independence Axiom.
If the design effort produces several designs
that are acceptable in terms of the Independence Axiom, we will
have to choose the best design among those proposed. This is
done by invoking the Information Axiom. As explained in a later
section extensively it is done by comparing the design range with
the system range. The design range is the temperature tolerance
specified by the designer and the system range represents how
a given design (i.e., product or system) can meet the specified
functional requirement. The best design is the one that has the
minimum information content since it has the highest probability
of success.
When does the analysis come into
picture during the design process?
In the preceding three examples, the design
matrix was formulated in terms of X and 0. In some cases, it may
be sufficient to complete the design with simply X's and 0's.
In many cases, we may take further steps to optimize the design.
After the conceptual design is done in terms of X and 0, we need
to model the design more precisely to optimize the design. Through
modeling we can replace X's with constants in the case of a linear
design or functions that involve DPs.
1.7.7 Requirements for Concurrent
Engineering
So far we have not discussed the mapping
from the physical domain to the process domain, i.e., product
design. After certain DPs are chosen, we have to map from the
physical domain to the process domain (i.e., process design) by
choosing the process variables, PVs. This process design mapping
must also satisfy the Independence Axiom. Sometimes we may simply
use existing processes or invent new processes. When the existing
processes must be used to minimize capital investment in new equipment,
the existing process variables must be used and thus act as constraints
in choosing DPs. In developing a product both the product design
and the process design (or selection) must be at the same time.
This is sometimes called "concurrent engineering"
or "simultaneous design".
For concurrent engineering to be possible,
both the product design represented by Eq. (1.1) and the process
design represented by Eq. (1.6) must satisfy the Independence
Axiom. That means, the product design matrix [A] and the process
design matrix [B] must be diagonal or triangular so that the product
of these matrices [C]=[A][B] must be diagonal or triangular.
[Note: each element Cik
= SjCij
Cjk
summed over j.] Table 1.3 shows the characteristic of the matrix
[C] depending on the kinds of the matrices [A] and [B] are. For
example, to get an uncoupled concurrent design, both matrices
must be diagonal. If one is diagonal and the other is triangular
the resulting product of matrices is triangular. If both [A]
and [B] are triangular, they must be the same kind, either both
upper triangular denoted by [UT] or low triangular [LT]. If
one is [LT] and the other is [UT], the product is a full matrix
[X]. Therefore, when [A] and [B] are triangular matrices, both
of them must be either upper triangular or lower triangular for
the manufacturing process to satisfy the independence for functional
requirements. This is stated as Theorem 9 (Design for Manufacturability).
| [A] | [B] | [C] = [A] {B] | |
| 1. Both diagonal | [\] | [\] | [\] |
| 2. Diag x Full | [\] | [X] | [X] |
| 3. Diag x triang. | [\] | [LT] | [LT] |
| 4. Tria. x Triang | [LT] | [LT] | [LT] |
| 5. Tria. x Triang | [LT] | [UT] | [X] |
| 6. Full x Full | [X] | [X] | [X] |
Table 1.3 The characteristic of concurrent
engineering matrix [C]. Note that only (1), (3), and (4)
are acceptable designs from the concurrent engineering point
of view.
Many examples of concurrent engineering
will be given in later chapters. Examples are also given in Suh
(1990)
1.7.8 The Second Axiom: The Information
Axiom
In the preceding sections, the Independence
Axiom was discussed and its implications were presented. In this
section, we well now discuss how we can choose the best design.
Even for the same task defined by a given set of FRs, it is most
likely that every designer will come up with different designs,
all of which are acceptable in terms of the Independence Axiom.
Indeed there can be a large number of designs that can satisfy
a given set of FRs. However, one of these designs is likely to
be superior to others. The Information Axiom provides a quantitative
means of measuring the merits of a given design, which can be
used to select the best among those acceptable. In addition,
the Information Axiom provides the theoretical basis for design
optimization and also robust design.
There can be many designs which are equally
acceptable from the functional point of view. However one of
these designs may be superior to others in terms of probability
of success in achieving the design goals as expressed by the functional
requirements. The Information Axiom state that the one with the
highest probability of success is the best design. Specifically,
the Information Axiom may be stated as:
Axiom 2: The Information Axiom
Minimize the information content
Information content I is defined in terms
of the probability of satisfying a given FRs. If the probability
of success of satisfying a given FR is p, the information I associated
with the probability is defended as
I = - log2
p (1.7)
The information is given in units of bits.
The logarithmic function is chosen so that the information content
will be additive when there are many functional requirements that
must be satisfied at the same time.
In the general case of n FRs for an uncoupled
design, I may be expressed as
(1.8)
where pi is the probability of DPi satisfying
FRi and log is either the logarithm based on 2 (with the unit
of bits) or the natural logarithm (with the unit of nats). Since
there are n FRs, the total information content is the sum of all
these probabilities. The Information Axiom states that the design
that has the smallest I is the best design, since it requires
the least amount of information to achieve the design goals.
When all probabilities are equal to one, the information content
is zero, and conversely, the information required is infinite
when one or more probabilities are equal to zero. That is, if
probability is low, we must supply more information to satisfy
the functional requirements.
The definition given in Eq. (1.7) is the
same as that used in information theory, which is also related
to the negative entropy. However, there are important differences
between the information used in information theory and axiomatic
design. The major difference is that in information theory and
thermodynamics, the total probability of an ensemble of events
is always equal to zero, because there are a finite number of
events that can be anticipated in information theory and natural
sciences. In the case of axiomatic design, since there is an
infinite number of different designs, the sum of probabilities
(i.e., total probability) is not equal to zero.
A design is called complex when its
probability of success is low, that is, when the information content
required to achieve the FRs is high. This occurs when the tolerances
for FRs of a product (or DPs in the process design) are small,
requiring high accuracy. This situation also arises when there
are many parts since as the number of parts increases, it also
increases the possibility that some of the components do not meet
the specified requirements. In this sense, the quantitative measure
for complexity is the information content. According to Eq. (1.8),
complex systems may require more information to make the systems
function. A physically large system is not necessarily complex
if the information content is low. Even a small system can be
complex if the probability of its success is low. Therefore,
the notion of complexity is tied to the tolerance for the FRs:
the tighter the tolerance, the more difficult it becomes to satisfy
the FRs.
Example 1.6 Cutting a Rod to a Length
Suppose we need to cut Rod A to 1 +/- 0.000001
meter and Rod B to 1 +/- 0.1 meter. Which has higher probability
of success?
Solution
The answer depends on the cutting equipment
available for the job! However, most engineers with some practical
experience would say that the one that has to be cut within one
micron would be more difficult, because the probability of success
associated with the smaller tolerance is lower than that associated
with the larger tolerance using typical equipment. Therefore,
the job with the lower probability of success is more complex
than the one with higher probability.
In the real world, the probability of success
is governed by the intersection of the tolerance defined by the
designer to satisfy the FRs and the tolerance (or the ability)
of the system to produce the part within the specified tolerance.
For example, if the design specification for cutting a rod is
1 meter plus or minus one micron and the available tool (i.e.,
system) for cutting the rod consists of only a hacksaw, the probability
of success will be extremely low. In fact, the information required
to achieve the goal would approach infinity as long as the only
system available to cut the rod is the hacksaw. Therefore, this
may be called a complex design. On the other hand, if the rod
needs to be cut within an accuracy of 10 cm, the hacksaw may be
more than adequate and therefore, the information required is
zero. In this case, the design is simple.
The probability of success can be computed
by specifying the Design Range (dr) for the FR and
by determining the System Range (sr) that the proposed
design can provide to satisfy the FR. Figure 1.3 illustrates
these two ranges graphically. The vertical axis (the ordinate)
is for the probability density and the horizontal axis (the abscissa)
is for either FR or DP, depending on the mapping domains involved.
When the mapping is between the functional domain and the physical
domain as in product design, the abscissa is for FR, whereas for
the mapping between the physical domain and the process domain
as in process design, the abscissa is for DP. In Fig. 1.3, the
System Range is plotted as a probability density versus the specified
FR. The overlap between the design range and system range is
called the common range (cr), and this is the only region
where the functional requirements are satisfied. Consequently,
the area under the Common Range divided by the area under the
System Range is equal to the designís probability of success
of achieving the specified goal. Then, the information content
may be expressed as [Suh, 1996]:
(1.9)
where Asr denotes the area under the System Range and Acr is the area of the Common Range. Furthermore, since Asr = 1.0 in most cases and there are n FRs to satisfy, the information content may be expressed as
n
I = S log (1/Acr)i (1.10)
i
Fig. 1.3: Design Range, System Range, and
Common Range in a plot of the probability density function (pdf)
of a functional requirement. The deviation from the mean is equal
to the square root of the variance.
Example 1.7 Cutting of the Rod with
a Hack Saw
Let us revisit the example cited in Example
1.6. We want to cut the rods as specified earlier, but now we
know the equipment available for the job. It is an ordinary hack
saw available in a machine shop. The system range is shown below.
The plot of the system range and the design
range shows that in the case of cutting Rod B, the system range
is completely inside the design range and therefore, the common
range and the system range are the same. Therefore, the probability
of success is 1 and the information required to fulfill the functional
requirement is zero as oer Eq. (1.9). On the other hand, Rod
A has such a tight tolerance requirement that the common range
is almost zero, making the information required approach infinity.
In normal machine shops the information
required is supplied by experienced machinists or tool makers
by carefully measuring the length and making careful cuts, even
lapping the part. Since machinists' expertise or skills are limited,
the information supplied cannot compensate for the lack of system
capability.
Often design decisions must be made when
there are many FRs that must be satisfied at the same time. The
Information Axiom provides a powerful criterion for making such
decisions without the use of arbitrary weighting factors used
in other decision making theories. In Eq. (1.8), each information
content term corresponding to each FR is simply summed up with
all other terms without multiplying it with a weighting factor
for two reasons. First, if we sum up the information terms,
each of which has been modified by multiplying with a weighting
factor, the total information content does no longer represent
the total probability (Homework 1.1). Second, the intention of
the designer and the importance assigned to each FR by the designer
are represented by the design range. If it is a critical FR that
must be satisfied within a tight tolerance, the designer would
give a narrow design range. The following example illustrates
the point.
Example 1.8 Buying a House
Professor Sandra Wade of Boston College
is planning to buy a new house. She and her husband decided that
there are the following four important functional requirements
the house must satisfy:
FR1 = Commuting time for Prof. Wade must be in the range of 15 to 30 minutes.
FR2 = The quality of the high school must be good, i.e., more than 65 % of the high school graduates must go to reputable colleges.
FR3 = The quality of air must be good, i.e., the air quality must be good over 340 days a year.
FR4 = The price of the house must be reasonable,
i.e., a four bed room house with 3,000 square feet of heated
space must be less than $650,000.
They looked around towns A, B, C and collected
following data:
| Town | FR1=Comm. time [min] | FR2=Quality of school [%] | FR3=Quality of air [days] | FR4=Price [$] |
| A | 20 to 40 | 50 to 70 | 300 to 320 | 450k to 550k |
| B | 20 to 30 | 50 to 75 | 340 to 350 | $450k to 650k |
| C | 25 to 45 | 50 to 80 | 350 and up | $600k to 800k |
Which is the town that meets the requirements
of the Wade family the best? You may assume uniform probability
distributions for all FRs.
Solution
The FRs specifies the design range. The
system range is given by the table above which the Wades collected
from realtors about Towns A, B, and C. Using these design and
system ranges, the information contents for each FR and each town
can be computed using Eq. (1.8). Figures a
and b
illustrates the overlap (i.e., common range) between the design
range and the system range for FR1 and FR2 of Town A.
The information content of Town A is infinite
since it cannot satisfy FR3, i.e., the design range and the system
range do not overlap at all. The information contents of Towns
B and C are computed using Eq. (1.8) as follows:
| Town | I1 [bits] | I2 [bits] | I3 [bits] | I4 [bits] | S I [bits] |
| A | 1.0 | 2.0 | Infinite | 0 | Infinite |
| B | 0 | 1.32 | 0 | 0 | 1.32 |
| C | 2.0 | 1.0 | 0 | 2.0 | 5.0 |
The information associated with buying a
house in Town B is 2.32, whereas for Town C, it is 5.0. In Town
A, Professor Wade is not likely to find a house that satisfies
her needs, unless she is willing to change her specifications.
The best town for Professor Wade to buy her house is Town B.
After having done this analysis, she may
change her mind about the importance of the quality of school.
In that case, she may respecify the functional requirement on
the school quality, FR2. For example, she may require that the
town must send 80% of its graduates to colleges or that 30% of
its graduates must have a combined SAT (scholastic aptitude test)
score of 1400 or better. She can give the importance of each
FR by changing the design range without using a weighting factor.
When there is only one FR, the independence
axiom is always satisfied. In the one-FR case, the only task
left is the optimization of a given design based on the Information
Axiom. Various optimization techniques have been advanced to
deal with optimization problems involving one objective function.
However, when there are more than two FRs, some of these optimization
techniques do not work. In order to satisfy a design with more
than one FR, we must first develop a design that is either uncoupled
or decoupled. If the design is uncoupled, it can be seen that
each FR can be satisfied and the optimum points can be found,
since there is one DP that controls the FR. If the design is
decoupled, the optimization technique must follow a set sequence.
The second axiom on information provides a metric that enables
us to measure the information content and thus be able to judge
a superior design.
1.7.9 Reduction of the Information
Content -- Robust Design
The ultimate goal of design is to reduce
the additional information required to make the system function
as designed to zero, i.e., minimize the information content as
per the Information Axiom. To achieve this goal, the design must
satisfiy the Independence Axiom. Then, the variance of the system
range can be made small and the bias can be eliminated so that
the system range lies inside the design range, reducing the information
content to zero (see Fig. 1.3). A design that can accommodate
large variations in design parameters and process variables and
yet satisfy the functional requirements is called a robust design.
There are four different ways of achieving
the goal of reducing the bias and the variance of a design and
develop a robust design, provided that the design satisfies
the Independence Axiom.
1.7.9. a Elimination of Bias
In Fig. 1.3, the target value of FR is shown
at the middle of the design range. The distance between the target
value and the peak of the system range is called bias.
In order to have an acceptable design, the bias associated with
each FR should be very small or zero. That is, the peak of the
system range should be inside the design range and overlap the
target value.
How can we eliminate the bias?
What are the pre-requisites for eliminating the bias?
In one-FR design, the bias can be changed
by changing the appropriate DP, since FR is a function of DPs
and since we do not have to worry about its effect on other FRs.
Therefore, it is easy to eliminate the bias when there is only
one FR.
When there are more than one FRs to be satisfied,
we may not be able to eliminate the bias unless the design satisfy
the Independence Axiom. If the design is coupled, each time a
DP is changed to eliminate the bias for a given FR, the bias for
other FRs changes also, making the design uncontrollable. If
the design is uncoupled design, the design matrix is diagonal
and the bias associated with each FR can be changed independently
as if the design is an one-FR design. When the design is decoupled
design, the bias for all FRs can be eliminated by following the
sequence dictated by the triangular matrix.
1.7.9. b Reduction of Variance
What is variance? What causes
variance? How do we control it? How is it related to the redundant
design?
Variance is the distribution of the difference
between the target value and the actual outcome. The variance
is caused by a number of factors such as noise, coupling, environment,
and random variations in design parameters. Therefore, in most
situations, the variance must be minimized. The variation can
be reduced in a few specific situations discussed in this section.
In a multi-FR design, the pre-requisite for variance reduction
is the satisfaction of the First Axiom -- the Independence Axiom.
1. Reduction of the Information Content
through Reduction of "Stiffness"
Suppose there is only one FR which is related
to DP as
FR1 = A11. DP1 (1.11)
In a linear design, the allowable tolerance
for DP1, given the specified tolerance for FR1, depends on the
magnitude of A11, i.e., the "stiffness". As shown in
Fig. 1.4, the smaller the "stiffness" A11, the larger
is the allowable tolerance of DP1. However, there is a lower
bound for the stiffness, which is discussed in Chapter 2.
Fig. 1.4 For a given tolerance DFR
specified, the allowable variance of DP1 increases with decrease
in the stiffness, A11. To have a robust design that can tolerate
large variations in the design parameters, the stiffness should
be reduced.
Example 1.9 Cover ("hub cap")
for Automobile Wheels
Consider a cover (otherwise known as "hub
cap") for wheels of passenger automobiles. Sheet metal is
pressed to make a decorative cover to hide nuts that hold the
rim of the wheel assembly on to the car. The design is simple.
Holes are punched in the rim of the wheel and metallic clip springs
are welded on the wheel cover. To attach the cover on the rim,
the springs welded on the cover are pushed into the holes in the
rim, which deflect and snap in the holes. The interference between
the spring and the hole keeps the cover attached to the rim.
To prevent the rim from falling off the rim when the car goes
over a bump and at the same time to make the mounting of the rim
easy when fires are replaced by drivers, tests showed that the
force for retention and installation must be 34 N +/- 4 N. That
is, the design range is from 30N to 38 N. However, due to slight
misplacement of the spring during welding and the wear of punching
dies during the fabrication of the rim, it was found that the
force is not always in this range. Figure
a shows the force distribution.
According to the Information Axiom, the
system range of the existing design is broader than the design
range and therefore some of the rims are outside of the design
range and thus, not acceptable from quality control point of view.
Since this design involves only one FR, it is easy to change
the bias and bring the center of the system range into the design
range.
To reduce the system range associated with
the variance so that the system range is inside the design range,
we need to use springs with softer stiffness as shown in Fig.
b. The
design with the stiffer spring requires tighter control of the
interference between the hole and the spring in comparison to
the softer spring. Therefore, when the stiffer spring was used,
the welding operation, the wear of dies, and positioning of the
spring clip during welding had to be controlled within a such
tight tolerance that the production operation could not consistently
manufacture to the specification. By simply using softer spring
clips, the production problem was eliminated without any additional
changes in the manufacturing operation.
2. Reduction of the Information Content
through the Design of a System that is Immune to Variations
When the stiffness shown in Fig. 1.4 is
zero, the system will be completely insensitive to variations
in DP. If the goal is to vary the FR by changing DP, the stiffness
must be large enough to allow the control of FR, although from
the robustness point of view low stiffness is desired. When there
are many DPs that affect a given FR, design should be done such
that the FR will be "immune" to variations of all these
other DPs except one specific DP chosen to control the FR. In
the case of non-linear design, we should search for such a design
window where this condition is satisfied.
The variance is defined as the square of
the standard deviation. It is equal to the mean squared deviation
of the n variables xi
from its mean x, S(xi
- x)2/n.
From a statistical point of view, it is the basic measure of
the distribution of the output. The true variances of infinite
populations are additive. Therefore, if a number of DPs with
different variances are affecting the FRs, the total variance
of the FR is equal to the sue of the separate variances when these
DPs are statistically independent.
Often the variation in the system range
may be due to many factors that affect the FR. Consider the one
FR design problem. The designer might have created a redundant
design as follows:
FR = f(DPa, DPb, DPc)
or
FR = Aa. DPa + Ab. DPb + Ac. DPc (1.12)
where Aa, Ab and Ac are coefficients and
DPs are design parameters that affect the FR. In this case, the
variance can be introduced by any uncontrolled variations in the
coefficients Aa, Ab, Ac, and DPs. The variance can be reduced
by making the design such that FR is not sensitive to (or immune
to) DPb and DPc changes, which can be done if Ab and Ac are small
or if DPb and DPc are fixed so that they remain constant. In
this case, since FR is a function of only DPa, FR can be controlled
by changing DPa. In this case, the only source of variance is
the random variation of Aa, dAa.
Now consider the case of multi-FR design
given by
(1.13)
In this ideal design with a diagonal and
symmetric matrix, the variance will be minimized if the random
variations dA11,
dA22 and
dA33 can
be eliminated. It should be noted that any error in DPs will
contribute to the variance and the bias. Therefore, the coefficients
A11, A22 and A33 should be small, but large enough to exceed the
required signal-to-noise ratio. This subject will be discussed
more extensively in Chapter 3, Section 5, on "designing-in
quality".
3. Reduction of the Information Content
By Fixing the Values of Extra DPs
When the design is a redundant design, the
variance can be reduced by identifying the key DPs and preventing
the extra DPs from variations, i.e., fixing the values of these
extra DPs.
Consider a multi-FR design given by
(1.14)
Equation (1.14) represents a redundant design.
The task is now to reduce the information content of the redundant
design represented by Eq. (1.14). The first thing we have to
do is to seek means of making the design represented by Eq. (1.14)
to be an ideal, uncoupled design shown by Eq. (1.13). This can
be done in two different ways: DP4, DP5, and DP6 can be fixed
so that they do not act as design parameters or making the coefficients
associated with these DPs equal to zero. Fixing DP4, DP5, and
DP6 will also minimize the variance due to any variations of these
three DPs. The variance can also be eliminated by making A14,
A15, A25, A26, A34 and A36 to be zero so that FRs will be immune
to the changes in DP4, DP5, and DP6. If the design matrix were
different than the one shown above, other appropriate design elements
should be made zero or other appropriate DPs must be fixed to
eliminate the variance of FRs.
4. Reduction of the Information Content
by Increasing the Design Range
In some special cases, the design range
can be increased without jeopardizing the design goals. The system
range may then be inside the design range. This can be illustrated
using Example 1.8 (Buying a House).
Example 1.10 Reevaluation of the Decision
on Purchase of a House
Professor Wade had to eliminate the possibility
of buying a house because the design range (i.e., FR) for air
quality could not be satisfied by Town A. The design range called
for acceptable air quality for at least 340 days a year, but the
town had good air quality only for between 300 and 320 days a
year. Therefore, the design range and the system range did not
overlap at all.
After having evaluated the effect of air
quality on health, Professor Wade decided that her original design
range on air quality was too stringent. Therefore, she has changed
FR3 to be: the air quality must be good over 300 days a year.
The design range has been expanded by lowering the minimum number
of acceptable days to 300 days. Now the information associated
with air quality for Town A is zero since the system range is
completely inside the design range. Unfortunately, even then,
Town B looks like a better town to look for a house.
1.7.10 Designing with Incomplete
Information
During the design of products, processes,
software, systems and organizations, we encounter situations where
the necessary knowledge about the proposed design is insufficient
and thus design must be executed in the absence of complete information.
The basic questions are: "Under what circumstances can
design decisions be made in the absence of sufficient information?"
and "what kinds of information are the most essential information
in making design decisions?" These questions will be explored
in this section.
Throughout the design process, the designer
collects, manipulates, creates, classification, transforms, and
transmits information. Information in design assumes a variety
of different forms. It is in the form of knowledge, database,
causality, paradigms, etc. The information necessary in design
must be distinguished from the information content we need
to minimize as per the Information Axiom.
Information is not as specific as
the information content defined by Eqs. (1.7) and (1.8),
which was specifically defined as a function of the probability
of satisfying the functional requirement in terms of design range
and system range. For example, in mapping from the customer attributes
(CAs) of the customer domain to the the functional requirements
(FRs) of the functional domain, information needed is in the form
of customer preference, potential FRs, and the relationship between
the CAs and the FRs. Similarly, information is needed when FRs
are mapped into the physical domain and when the design parameters
(DPs) are mapped into the process domain.
The information we need is indicated by
the design equations. The information on the characteristic vectors,
i.e., what they are, etc., are needed. Given an FR, the most
appropriate DP must be chosen, the possibility of which increases
with the size of the library of DPs that satisfy the FR. Similarly,
given a DP, the more PVs we have, the larger will be the options
we have. Once DPs and PVs are chosen, information on all the
elements of the design matrix, which define the relationship between
"what we want to achieve" and "how we want to achieve",
must be available.
One of the central issues in the design
process is: "What are the minimum information that is necessary
and sufficient in making design decisions given a set of {DPs}
for a given set of {FRs}. The necessary information depends on
whether or not the proposed design satisfies the Independence
Axiom. In the case of a coupled design, which violates the Independence
Axiom, all the information associated with all the elements of
the design matrix is required. That is, design cannot be done
rationally without complete information in the case of coupled
designs. Similarly, even in the case of uncoupled design that
satisfies the Independence Axiom, the information is required
for all the diagonal elements of the design matrix. The information
required for the uncoupled case is less than the coupled design
case, since there are no off diagonal element. In the case of
decoupled design, information on the off-diagonal elements may
not be required to satisfy the given set of {FRs} with a given
set of {DPs}.
Information Required for an Uncoupled
Design
Consider an ideal design that consists of
three FRs. For an uncoupled design, which is the simplest case,
the design equation may be written as
(1.15)
A11, A22 and A33 relate FRs to DPs. They
are constants in the case of linear design, whereas in the case
of nonlinear design, A11 is a function of DP1, etc. To proceed
with this design, we must know the diagonal elements. Therefore,
the minimum information required is the information associated
with the on-diagonal (i.e., diagonal) elements.
Information Required for a Decoupled
Design
Again consider the three FR case, but this
time the design is a decoupled design given by the following design
equation:
(1.16)
As in the case of the uncoupled design given
by Eq. (1.15), we need to know the diagonal elements Aii. It
will be also desirable to know the off-diagonal elements Aij.
However, even in the absence of complete information on off-diagonal
elements, we can proceed with the design even if the diagonal
elements are known and if the magnitudes of the off-diagonal elements
are smaller than those of the diagonal elements, i.e., Aii>Aij.
This can be done since the value of FR1 can be set first and
then, the value of FR2 can be set by varying the value of DP2,
regardless of the value of A21. When DP2 is chosen, we must be
certain that it does not affect FR1, but it is not necessary that
any information on A21 is available, if DP2 has the dominant effect
on FR2, i.e., A22>A21. Similarly, as long as DP3 should not
affect FR1 and FR2, the design can be completed, even if we do
not have any information on A31 and A32. This is the only case
when design can proceed in the absence of complete information.
This is stated as Theorem 17.
Suppose that the upper triangular elements
are not quite equal to zero but have very small values a12, a13,
and a23 as shown in Eq. (1.17):
(1.17)
The magnitudes of these elements |aij| are
much smaller than |Aji|, i.e, |aij|<<|Aji|. In this case,
FR1 will be affected by large state changes of DP2 and DP3 and
may not be negligible since
WFR1=A11 WDP1+a12
WDP2 +a13
WDP3
(1.18)
where W
signifies a large change in the value of DPs due to the change
in the state. In this case, the effect of the state change must
be compensated for if the required tolerances of FRs are smaller
than the variances caused by the state change.
1.8 Common Mistakes Made by Designers
1. Coupling Due to Insufficient Number
of DPs (Theorem 1)
Designers do not recognize a coupled design
and try to make it work by a brute force approach. Coupled designs
are created by having more FRs than DPs or more DPs than PVs.
In an ideal design, the number of FRs and the number of DPs are
the same (Theorem 4).
2. Not Recognizing a Decoupled Design
Although a decoupled design satisfies the
Independence Axiom, one must first recognize that one has a decoupled
design and change the DPs or PVs according to a proper sequence.
Many designers do not know that they have a decoupled design
and randomly change DPs to make things work. Consequently, the
design appears to be dysfunctional.
3. Having more DPs than the number
of FRs
When we have more DPs than FRs, we have
a redundant design. In this case, it is important to fix the
extra DPs and create an uncoupled or decoupled design if the design
can be reduced to these designs that satisfy the Independence
Axiom. Otherwise, the redundant design is a coupled design.
5. Not creating a robust design --
not minimizing the information contentt through elimination of
bias and reduction of variance
Products can easily go out of tolerance
and develop operational problems when the design is not robust.
Robust design can accommodate large variations in DPs or PVs,
and yet satisfy the FRs. This can be done by reducing "stiffness",
bias and variance as discussed in Sect. 1.7.9 and Chapter 3, Section
5.
6. Concentrating on Symptoms rather
than Cause --Importance of Establishing and Concentrating on FR.
Surprisingly a large number of designer,
engineers, and managers begin the design process without first
determining functional requirements (FRs). In the absence of
well established FRs, the designer will go through a random process
of ideation and will not be able to communicate to and work with
others during the design process. When a complete new product,
process, software, or system is to be designed, FRs must be established
in a solution neutral environment.
When an existing product is analyzed for
its malfunctions, most people concentrate on symptoms rather than
concentrating on functions. If a product satisfies its functional
requirements well, those symptoms which impede the performance
of functions would not have appeared. Therefore, it is imperative
that the analysis begin by asking what FRs must be satisfied by
the product and examine how well goals are achieved. For example,
an automobile manufacturer found that its hood lock and release
mechanism was making strong undesirable sound each time it is
activated by opening the hood. Engineers were given the task
of eliminating the sound. What should they do? They immediately
began concentrating on how the sound is created and investigating
various means of eliminating the sound rather than examining the
relationship between the functional requirements and the design
parameters (DPs). Once they understand the design matrix, they
can develop means of satisfying the FRs without making the noise.
Example 1.11 Hood Lock and Release Mechanism
An automobile company found that the lock
and release mechanism of a trunk lid shown in Fig. a
makes very undesirable sound. To eliminate the noise, it was
suggested that the current design be improved. Analyze the current
design. Design an improved lock and release mechanism for the
trunk lid.
A Possible Solution:
If the functional requirements are properly
satisfied, the noise would not have been generated. Therefore,
it would be a mistake to concentrate on the noise problem from
the beginning. We have to ask what the functional requirements
are and investigate how the lock and release mechanisms should
be designed to satisfy these FRs through mapping, zigzagging,
and decomposition. This process should reveal the source of noise
and the means of reducing the noise. Once an uncoupled or decoupled
design is developed, the selected design should be optimized to
create a robust design.
The design task is to hold a pin attached
to the hood in the lock when the hood is closed and to release
the pin to an open position when the hood is to be opened. Therefore,
the highest level FRs are:
FR1 = Hold the pin (attached to the hood) in the locked position
FR2 = Release the pin from the lock position
to an open position
Having decided on the FRs, we have to map
them in the physical domain by conceiving a design idea that can
provide a solution for these high level FRs. At this stage, we
may choose the corresponding DPs as
DP1 = Mechanical locking mechanism
DP2 = Release mechanism
Although DP1 and DP2 are created without
any detailed mechanisms in mind, the original design shown in
Fig. a
is consistent with this choice of DPs at this highest level.
As we decompose these DPs to lower level DPs, many different mechanisms
may be conceived.
For these high level DPs, the design matrix
may be expressed as
[DM] = 
This is an uncoupled design! This is the
best design at this level of decision making.
FR1 may be decomposed to generate the next
level FRs as
FR11 = Locate the pin (attached to the hood) at the locked position
FR12 = Lock the pin
Having established FR11 and FR12, we have
to conceive a design solution at this second level. The following
DPs are chosen:
DP11= A cam plate that provides dead stop position
DP12 = Rotating cam plate with a slot for
the pin and a cam profile to engage a spring loaded ratchet mechanism
(to keep the ratchet spring loaded against the cam surface)
It turns out that the original design shown
in Fig. a
has these two features, and thus, satisfies the functional requirements
at this level. The design matrix for the second level FRs, FR11
and FR12, and their corresponding DPs is
[DM] = 
Again the design is an uncoupled design!
FR2 may now be decomposed to generate the
next level FRs, FR21, etc. The second level FRs are established
as
FR21 = Release the pin
FR22 = Put the pin and the rotating disk
at the normally open position
The corresponding second level DPs of DP2
may be determined as
DP21 = Ratchet removing mechanism
DP22 = Spring force at the hinge of the
hood to pull the pin and rotate the rotating locking disk
out of the locked positions (let's put a "spring"
on hood hinge)
The design matrix is:
DM = |X 0|
|0 X|
The original design shown in Fig.e a
differs from this proposed design in that it relies on the heavy
spring to unlock and push the hood upward. To provide enough
energy to accelerate the hood upward, a heavy spring was used.
Then, a stopper had to be placed on the lock plate to stop the
cam. In the proposed design, the equilibrium position of the
hood is the ìnormally openî position due to the spring
placed on the hinge of the hood. This original design can also
be modified to be consistent with this new design characterized
by DP21 and DP22 by replacing the heavy spring with a light spring
to keep the cam plate in place and by placing a spring at the
hinge of the hood. This will clearly will eliminate the strong
sound that emanates when the latch is opened.
The decomposed FRs and DPs of FR22 and DP22
are, respectively:
FR221 = Put the rotating disk at "normally open" position
FR222 = Put the pin at its "normally
open" position
The original design shown in Fig. a couples FR221 and FR222 since the heavy spring does both of these jobs, i.e., only one DP. A new proposed design can be as follows:
DP221 = Soft spring of the latch (that replaced the heavy spring)
DP222 = Equilibrium position determined
by the spring force on the hood hinge and the weight of
the hood
The design matrix is
[DM] = 
This design is a completely uncoupled design.
It should be noted that we could have chosen
a different DP22. Then, FR221 and FR222 would be quite different
than the ones listed above. For example, had we chosen a mechanism
that does not use a spring at the hood hinge but rather use a
spring mounted on the latch mechanism just like the original design
shown in Fig. a,
the third level FRs may be stated as
FR221 = Accelerate the pin (and hood) out of its closed position
FR222 = Decelerate the pin and the disk and stop at the open position
FR223 = Put the rotating disk at "normally
open" position.
Now we have to chose the appropriate design
concept and the design parameters for this third level FRs. (Homework
1.5)
In the case of the original design shown
in Fig. a,
FR22 was decomposed in a different way. In this original design,
the FRs were:
FR221 = Accelerate the pin (and hood) out of its closed position
FR222 = Put the cam plate at "normally
open" position
The corresponding DPs are:
DP221 = Heavy spring/cam plate
CP222 = Stopper
The design matrix is:
[DM] = 
The original design is a decoupled design,
but noise is made because of the conversion of the mechanical
energy to sound energy by the stopper.
1.9 Comparison of Axiomatic Design
with Various Methodologies
Often questions are asked as to how axiomatic design differs from other design methodologies. When they ask these questions, they have many different methodologies in mind, including statistical process control (SPC) techniques, the Taguchi methodology (Taguchi, 1987), and the Altshuller inventive problem solving methodology (Altshuller, 1996). The following comments are offered as general comments:
1. Axiomatic design deals with principles
and methodologies rather than simply algorithms or methodologies.
Based on the two axioms, it derives theorems and corollaries,
and also develops methodologies based on functional analysis and
information minimization which lead to robust design.
2. Axiomatic design is applicable to all
designs: products, processes, systems, software, organizations,
materials, and business plan.
3. All methodologies, including the Taguchi
method, must satisfy the design axioms for them to be valid.
For example, the Taguchi method is valid only on designs that
satisfies the Independence Axiom. So far, there seems to be no
contradiction between Altshuller's methodologies and the design
axioms.
4. The Taguchi method does instruct how
to make design decisions. It is a method of checking and improving
a finished design.
5. Both axiomatic design and the Taguchi
method lead to robust design for designs that satisfy the Independence
Axiom.
6. Robust design cannot be done by applying
the Taguchi method if it violates the Independence Axiom. (See
the example involving design of an automatic transmission given
in Chapter 3.)
7. Although many efforts are being made
in industry to improve a bad design using optimization techniques,
the design that violates the Independence Axiom cannot be improved.
Optimization of bad designs lead to optimized bad designs.
1.10 Concluding Remarks
The field of design covered in this book
is a broad field that not only transcends specific engineering
fields but also encompasses such fields as management and business.
In this chapter, the need to establish the science base for the
design field so as to facilitate the educational process and to
improve design skills of multitudes of people engaged in design
is presented. This chapter then covers the basic concepts and
methodologies of axiomatic design, including the concepts of domains,
mapping, the two design axioms (the Independence Axiom and the
Information Axiom), decomposition, hierarchy, and zigzagging.
Several key terms such as functional requirement
(FR), design parameter (DP), and process variable (PV) are carefully
defined, since the strict adherence to definitions is important
in any axiomatic field. Self-consistent and logical reasoning
cannot be used in axiomatic design in the absence of clear definition
and the acceptance of these definitions in applying the basic
principles.
It is shown that mapping between the domains
generates design equations and design matrices. The design equation
models the design. The design matrix characterizes the relationship
between the characteristic vectors of the domains and forms the
basis for functional analysis of design. The design matrix provides
the basis for identifying acceptable designs. Uncoupled and decoupled
designs are shown to satisfy the Independence Axiom and thus,
acceptable. Coupled designs do not satisfy the Independence
Axiom and thus, unacceptable.
The second axiom, the Information Axiom,
deals with information, probability of satisfying the FRs, and
complexity. Information content is defined in terms of the probability
of success and the notion of additional information that must
be supplied to be able to satisfy the functional requirement.
Complexity is related to information content, since it is more
difficult to meet the design objectives (i.e., FRs) when the probability
of success is low. The computation of information content in design
is facilitated using the notion of the system range and the design
range.
References
1. Altshuller, G., And Suddenly the Inventor
Appeared, Technical Innovation Center, Worcester, MA, 1996
2. Lee, Janghee, Cho, Kwang-Yun, and Lee,
Kitae, "a New Control System of a Household Refrigerator-Freezer",
Presented at the International Refrigeration Conference at Purdue
University, 1994
3. Suh, N. P., The Principles of Design,
Oxford University Press, 1990
4. Suh, N. P. and S. Sekimoto, "Design
of Thinking Design Machine", Annals of CIRP, Vol
1, 1990
5. Suh, N. P., "Axiomatic Design of
Mechanical Systems", Special 50th Anniversary Combined
Issue of the Jouranal of Mechanical Design and the Journal of
Vibration and Acoustics, Transactions of the ASME, Volume
117, pp 1-10, June 1995
6. Suh, N. P., "Design and Operation
of Large Systems", Journal of Manufacturing Systems, Vol.
14, No.3, pp 203-213, 1995
7. Taguchi, G., Systems of Engineering
Design: Engineering Methods to Optimize Quality and Minimize Cost,
American Supply Institute, 1987.
8. Thomas J., ìThe Archstand Theory
of Design for Informationî, Ph.D. Thesis, Massachusetts
Institute of Technical, Department of Civil Engineering, February
1995.
9. Watson, J. D., The Double Helix,,
Athenaeum, New York, 1969
Appendices
Some of these theorems are derived in this
book as well as in the references given. For those theorems not
derived in this book, the readers may consult the original references.
1. Corollaries (From Ref. 3)
Corollary 1 (Decoupling of Coupled Designs)
Decouple or separate parts or aspects of
a solution if FRs are coupled or become interdependent in the
designs proposed.
Corollary 2 (Minimization of FRs)
Minimize the number of FRs and constraints.
Corollary 3 (Integration of Physical Parts)
Integrate design features in a single physical
part if FRs can be independently satisfied in the proposed solution.
Corollary 4 (Use of Standardization)
Use standardized or interchangeable parts
if the use of these parts is consistent with FRs and constraints.
Corollary 5 (Use of Symmetry)
Use symmetrical shapes and/or components
if they are consistent with the FRs and constraints.
Corollary 6 (Largest Tolerance)
Specify the largest allowable tolerance
in stating FRs.
Corollary 7 (Uncoupled Design with Less Information)
Seek an uncoupled design that requires
less information than coupled designs in satisfying a set of FRs.
Corollary 8 (Effective Reangularity of a Scalar)
The effective reangularity R for
a scalar coupling ìmatrixî or element is unity.
2. Theorems of general design (Most of
these theorems are from Ref. 3)
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 results, or the FRs cannot
be satisfied.
Theorem 2 (Decoupling of Coupled Design)
When a design is coupled due to the greater
number of FRs than DPs (i.e., m. > n), it may
be decoupled by the 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 x n elements constitutes a triangular
matrix.
Theorem 3 (Redundant Design)
When there are more DPs than FRs, the design
is either a redundant design or a coupled design.
Theorem 4 (Ideal Design)
In an ideal design, the number of DPs is
equal to the number of FRs.
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 with a
new one, or by selection of a completely different set of FRs,
the design solution given by the original DPs cannot satisfy the
new set of FRs. Consequently, a new design solution must be sought.
Theorem 6 (Path Independence of Uncoupled Design)
The information content of an uncoupled
design is independent of the sequence by which the DPs are changed
to satisfy the given set of FRS.
Theorem 7 (Path Dependency of Coupled and Decoupled Design)
The information contents of coupled and
decoupled designs depend on the sequence by which the DPs are
changed to satisfy the given set of FRs.
Theorem 8 (Independence and Tolerance)
A design is an uncoupled design when the
designer-specified tolerance is greater than
in which case the nondiagonal elements of
the design matrix can be neglected from design consideration.
Theorem 9 (Design for Manufacturability)
For a product to be manufacturable, the
design matrix for the product, [A] (which relates the FR
vector for the product to the DP vector of the product)
times the design matrix for the manufacturing process, [B]
(which relates the DP vector to the PV vector of
the manufacturing process) must yield either a diagonal or triangular
matrix. Consequently, when any one of these design matrices,
that is, either [A] or [B], represents a coupled
design, the product cannot be manufactured. When they are triangular
matrices, both of them must be either upper triangular or lower
triangular for the manufacturing process to satisfy the independence
for functional requirements.
Theorem 10 (Modularity of Independence Measures)
Suppose that a design matrix [DM]
can be partitioned into square submatrices that are nonzero only
along the main diagonal. Then the reangularity and semangularity
for [DM] are equal to the product of their corresponding
measures for each of the non-zero submatrices.
Theorem 10a (R and S for Decoupled Design)
When the semangularity and reangularity
are the same, the design is a coupled design.
Theorem 11 (Invariance)
Reangularity and semangularity for a design
matrix [DM] are invariant under alternative orderings of
the FR and DP variables, as long as orderings preserve the association
of each FR with its corresponding DP.
Theorem 12 (Sum of Information)
The sum of information for a set of events
is also information, provided that proper conditional probabilities
are used when the events are not statistically independent.
Theorem 13 (Information Content of the Total System)
If each DP is probabilistically independent
of other DPs, the information content of the total system is the
sum of the information of all individual events associated with
the set of FRs that must be satisfied.
Theorem 14 (Information Content of Coupled versus Uncoupled Designs)
When the state of FRs is changed from one
state to another in the functional domain, the information required
for the change is greater for a coupled process than for an uncoupled
process.
Theorem 15 (Design-Manufacturing Interface)
When the manufacturing system compromises
the independence of the FRs of the product, either the design
of the product must be modified, or a new manufacturing process
must be designed and/or used to maintain the independence of the
FRs of the products.
Theorem 16 (Equality of Information Content)
All information contents that are relevant
to the design task are equally important regardless of their physical
origin, and no weighting factor should be applied to them.
Theorem 17 (Design in the absence of complete Information)
Design can proceed even in the absence of
complete information only in the case of decoupled design if the
missing information is related to the off-diagonal elements.
3. Theorems for Design of Large Systems
(From Ref. 6)
Theorem 18 (Importance of High Level Decisions)
The quality of design depends on the selection
of FRs and the mapping from domains to domains. Wrong decisions
made at the highest levels of design domains cannot be rectified
through the lower level design decisions.
Theorem 19 (The Best Design for Large Systems)
The best design among the proposed designs
for a large system that satisfy n FRs and the Independence
Axiom can be chosen if the complete set of the subsets of {FRs}
that the large system must satisfy over its life is known a
priori.
Theorem 20 (The Need for Better Design for Large Systems)
When the complete set of the subsets of
{FRs} that a given large system must satisfy over its life is
not known a priori, there is no guarantee that a specific
design will always have the minimum information content for all
possible subsets and thus, there is no guarantee that the same
design is the best at all times, even if there are designs
that satisfy the FRs and the Independence Axiom.
Theorem 21 (Improving the Probability of Success)
The probability of choosing the best design
for a large system increases as the known subsets of {FRs} that
the system must satisfy approach the complete set that the system
is likely to encounter during its life.
Theorem 22 (Infinite Adaptability versus Completeness)
The large system with an infinite adaptability
(or flexibility) may not represent the best design when the large
system is used in a situation where the complete set of the subsets
of {FRs} that the system must satisfy is known a priori.
Theorem 23 (Complexity of Large Systems)
A large system is not necessarily complex if it has a high probability of satisfying the {FRs} specified for the system.
Theorem 24 (Quality of Design)
The quality of design of a large system
is determined by the quality of the database, the proper selection
of FRs, and the mapping process.
4. Theorems for Design and Operation
of Large Organizations (Mostly from Ref. 6)
Theorem 25 (Efficient Business Organization)
In designing large organizations with a
finite resource, the most efficient organizational design is the
one that specifically allows reconfiguration by changing the organizational
structure and by having a flexible personnel policy when a new
set of FRs must be satisfied.
Theorem 26 (Large System with Several Sub-Units)
When a large system (e.g., organization)
consists of several sub-units, each unit must satisfy independent
subsets of {FRs} so as to eliminate the possibility of creating
a resource intensive system or coupled design for the entire system.
Theorem 27 (Homogeneity of organizational structure)
The organizational structure at a given
level of the hierarchy must be either all functional or product-oriented
to prevent the duplication of the effort and coupling.
Homework
1.1 Prove that if each information content
term of the right hand side of Eq. (1.3) is multiplied by a weighting
factor ki,
the total information content will not be equal to information.
1.2 Consider the design of a hot and cold
water tab. The functional requirements are the flow rate and
the temperatures of the water. If we have a faucet that has a
valve for hot water and another valve for cold water, it is a
coupled design since the temperature and flow rate cannot be controlled
independently. We can design an uncoupled faucet that has a knob
for temperature control only and another knob for the flow rate
control only. Design such an uncoupled faucet by decomposing
the FRs and DPs.
1.3 Professor Smith of the University of
Edmington raised the following question about the water faucet
design: If we take the coupled design (i.e., the design with
two valves, one for cold water and the other for hot water) and
then put a servo control mechanism, we may be able to control
the flow rate and the temperature independently. Therefore, Professor
Smith says that a coupled design is as good as the uncoupled design.
What would your answer be to Professor Smith's
question? Analyze the design proposed by Professor Smith by establishing
FRs and DPs, by creating a design hierarchy through zigzagging,
and by constructing the design matrices at each level. Is Professor
Smith's design a couple design or an uncoupled design or a decoupled
design?
1.4 In some design situations, we may find
that we have to make design decisions in the absence of sufficient
information. In terms of the Independence Axiom and the Information
Axiom, explain when and how we can make design decisions even
when we do not have sufficient information. What kinds of information
can we do without and what kinds of information we must have in
design? Illustrate your argument using a design task with three
FRs as an example.
1.5 For the latch mechanism discussed in Example 1.11, develop a design solution and state DP221, DP222, and DP223. Sketch the latch mechanism designed by you.