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uncertainty may lead to an inaccurate interpretation and, therefore, to vul-
nerable or unwanted design. There are many classifications for a customer's
linguistic inexactness. In general, two major sources of imprecision in human
knowledge—linguistic inexactness and stochastic uncertainty (Zimmerman,
1985)—usually are encountered. Stochastic uncertainty is well handled by the
probability theory. Imprecision can develop arise from a variety of sources:
incomplete knowledge, ambiguous definitions, inherent stochastic character-
istics, measurement problems, and so on.
This brief introduction to linguistic inexactness is warranted to enable de-
sign teams to appreciate the task on hand, assess their understanding of the
voice of the customer, and seek clarification where needed. The ignorance of
such facts may cause several failures to the design project and their efforts
altogether. The most severe failure among them is the possibility of propagat-
ing inexactness into the design activities, including analysis and synthesis of
wrong requirements.
Design parameters (DPs) are the elements of the design solution in the physical
domain that are chosen to satisfy the specified FRs. In general terms, standard
and reusable DPs (grouped into design modules within the physical structure)
often are used and usually have a higher probability of success, thus improving
the quality and reliability of the design.
Constraints (Cs) are bounds on acceptable solutions.
Process variables (PVs) are the elements of the process domain that characterize
the process that satisfies the specified DPs.
The design team will conceive a detailed description of what functional require-
ments the design entity needs to perform to satisfy customer needs, a description of
the physical entity that will realize those functions (the DPs), and a description of
how this object will be produced (the PVs).
The mapping equation
FR
=
f(DP)
or, in matrix notation
FR
=
[A]
mxp
{
}
mx1
DP
}
px1
,
is used to reflect the relationship between the domain, array
FR
,
and
{
{
}
the codomain array
DP
in the physical mapping, where the array
FR
}
mx1
is
{
}
{
a vector with
m
requirements,
}
px1
is the vector of design parameters with
p
characteristics, and
A
is the design matrix. Per axiom 1, the ideal case is to have a one-
to-one mapping so that a specific DP can be adjusted to satisfy its corresponding FR
without affecting the other requirements. However, perfect deployment of the design
axioms may be infeasible because of technological and cost limitations. Under these
circumstances, different degrees of conceptual vulnerabilities are established in the
measures (criteria) related to the unsatisfied axiom. For example, a degree of
coupling
may be created because of axiom 1 violation, and this design may function adequately
for some time in the use environment; however, a conceptually weak system may have
limited opportunity for continuous success even with the aggressive implementation
of an operational vulnerability improvement phase.
When matrix
A
is a square diagonal matrix, the design is called
uncoupled
(i.e.,
each FR can be adjusted or changed independent of the other FRs). An uncoupled
DP
{
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