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Application of Axiomatic
Design
“The ultimate goal of the Axiomatic Design is to establish
a science base for design and to improve design activities
by providing the designer with 1) a theoretical foundation
based on logical and rational thought processes and 2) tools.”
[Suh, 1990] While there are many steps in the engineering
design process, the axiomatic design process focuses on the
generation of requirements and the selection of means for
achievement. One of the central ideas of axiomatic design
is the importance of distinguishing between what (objectives)
is to be achieved and how (means) it will be achieved.
In axiomatic design terminology, the objectives of the design
are expressed as Functional Requirements (FR’s) and the solutions
are expressed as Design Parameters (DP’s). The design process
is one of selecting the best set of DP’s to satisfy the determined
FR’s.
It was found that the strengths of axiomatic design, namely
the emphasis on separating the objectives (the FR’s) from
the means (DP’s) and the structured decomposition process,
made it particularly well suited to achieve the proposed research
objectives. The following paragraphs provide a brief introduction
into the axiomatic design methodology and explain the usage
during the development of the MSDD. For more detail on the
axiomatic design methodology, the reader is directed to the
work of [Suh, 1990].
The Axioms
The functional requirements (FRs) represent the goals
of the design or what we want to achieve. The design parameters
(DPs) express how we want to satisfy the functional
requirements. The FRs and DPs can mathematically be described
as a vector. The relationship between the FRs and the DPs
can be stated as a matrix. This matrix is called the Design
Matrix (DM). Design - as used in the axiomatic
design - is defined as the mapping process from the
functional space to the physical space to satisfy the designer-specified
functional requirements.
Axiomatic design consists of two axioms:
- The independence axiom: Maintain the independence of the
functional requirements.
- The information axiom: Minimize the information content
of the design
The first axiom states that when multiple FR’s exist, the
design solution must be such that each FR can be satisfied
without affecting the other FR’s. When this objective is achieved,
the design matrix will be diagonal, as each DP will affect
only its associated FR with no coupling occurring in the off-diagonal
elements. Such a design is said to be uncoupled. In cases
where independence is not achieved, two possibilities arise.
In one case, the design will be partially coupled, meaning
that the rows and columns of the design matrix can be interchanged
such that the matrix is upper or lower triangular. When off-diagonal
elements exist and the matrix cannot be rearranged to a triangular
state, the design is said to be coupled. An acceptable design
is either uncoupled or partially coupled. A partially coupled
design is said to be path dependent.
The information axiom states simply that simpler designs
are better. Quantifying the complexity or information content
of system designs can be quite challenging, however. The information
axiom was not used in creating the MSDD and thus will not
be discussed further herein.
AD process
The axiomatic design methodology begins with the identification
of customer needs and the conversion of these needs into a
set of one or more high-level functional requirements. The
goal is to develop the minimum set of independently achieved
requirements that completely characterize the desired functions
of the design [Suh, 1990]. Suh describes achieving this result
as a process of first mapping from the customer domain to
the functional domain to state (objectives) functional requirements
(FR’s) in solution-neutral terms. Next, the designers must
determine how the just-determined FR’s will be met
by the (means) design parameters (DP’s). Synthesis of design
parameters is essentially a creative process. At high levels,
the DP’s may be conceptual in nature and may describe a general
system or structure for achieving an FR without yet containing
enough information to be implemented. At lower levels of decomposition,
DP’s typically describe a physical solution in enough detail
for a concept to be implemented. Typically, decomposition
proceeds until all FR’s and DP’s have been decomposed to an
operational level of detail.
In axiomatic design, the FR’s and DP’s are connected by means
of design matrices. That is, a vector of FR’s can be related
to its associated vector of DP’s according to the equation:
{FR’s} = [A]{DP’s}
(1)
The elements of the design matrix, A, indicate the affects
of changes of the DP’s on the FR’s. As an example, consider
the design equation shown below:
(2)
The binary elements of the design matrix, expressed as X’s
and 0’s, indicate the presence or absence of a relationship
between a DP and the associated FR. X’s should always be present
along the diagonal, meaning that each DP affects its associated
FR (e.g., A11=X indicates that DP1 affects
FR1). The X at A21 shows that DP1
also affects FR2. This design matrix information
can also be represented graphically. An arrow from a DP to
an FR indicates the presence of a non-zero, off-diagonal element
in the design matrix. For example, Figure 3 provides the graphical
representation of the design matrix shown in equation 2.
Figure 1: Graphical representation of design
matrix of equation (2). An arrow from a DP to a FR indicates
the presence of a non-zero off diagonal element in the design
matrix.
Axiom 1 analyzes the design matrix to check, if the functional
requirements can be satisfied by the design parameters independently.
Three different kinds of design can be distinguished:
1. uncoupled design
2. decoupled design
3. coupled design.
The designs can be represented mathematically and graphically
as shown in Figure 2. The differences between the three kinds
can be explained by showing the adjustment of the FRs. This
is demonstrated in the lower half of Figure 2.
Figure 2: The mathematical and graphical representation
of the mapping process highlights the three different kinds
of design: uncoupled, decoupled and coupled.
The illustration of the different adjustments for an uncoupled,
decoupled and coupled design highlights why the design must
maintain the independence of the functional requirements.
It eases the adjustment of the functional requirements.
The independence axiom elaborates if the design is an uncoupled,
decoupled or coupled design. A coupled design is not acceptable
and the selection process of DPs must be repeated. A decoupled
design is worse than an uncoupled but still allows the exact
adjustment of the functional requirements. The next step in
the applying axiomatic design process is the decomposition
is illustrated in Figure 3.
Figure 3: The decomposition process of axiomatic design
is also called zig-zagging.
Applying Axiomatic Design
Axiomatic design was used in the development of the MSDD
in the following way:
- state the requirements (FRs)
- determine design solutions (DPs), which can satisfy the
FRs
- determine the dependencies between DPs and FRs by filling
out the design matrix
- decompose further if necessary
The first two steps are straight forward. Filling out the
design matrix (step 3) was a little more difficult. The relationships
between the FR’s and DP’s in the MSDD are more conceptual
in nature and the following questions were developed to formalize
the process for filling in the entries of the design matrix
and to describe the thinking that goes into the determination
of each entry:
- Does the particular choice of DPj affect system
performance in terms of FRi?
- Would failing to implement DPj impede the manufacturing
system’s ability to satisfy FR?
Once a set of DP’s has been determined, the next step is
to decide if further decomposition is necessary. In the case
of the MSDD, decomposition proceeds for as long as it is possible
to do so without limiting the usefulness or range of applicability
of the decomposition. When further decomposition is needed,
the next step is to develop the next level of FR’s. By following
a downward path in the MSDD (shown in Appendix A), one can
see this alternation back and forth between FR’s and DP’s.
In developing lower-level FR’s for the MSDD, the focus was
on breaking down the higher-level FR-DP pairs into component
parts. Questions asked at this stage included:
- What are the components of the parent FR and/or DP?
- What requirements are placed on these components?
Reading from left to right, the MSDD indicates path dependence.
The FR-DP pairs on each level are arranged in such a way that
the pair whose DP influences the most FR’s is on the left
side. We see that quality, then problem resolution, then predictable
output, then throughput time reduction, then labor reduction
are critical to implementing the desired system-design goals
(see MSDD include link to the complete MSDD). As a
result, decisions should be made following the MSDD from left
to right. A summary of the axiomatic design process for decomposition
is shown in Figure 4.
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