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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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