AXIOMATIC DESIGN IN SOFTWARE DESIGN FOR SIX SIGMA (DFSS) - Software Design for Six-Sigma: A Roadmap for Excellence - page 341

(equivalent to DPs), and method (equivalent to the relationship between FRi and DPi,
that is module) in a single entity. Object retains certain information on how to perform
certain operations, using the input provided by the data and the method imbedded in
the object. (In terms of axiomatic design, this is equivalent to saying that an object is
[FRi Aij DPj].)

An object-oriented design generally uses four definitions to describe its opera-
tions: identity, classification, polymorphism, and relationship. Identity means that
data—equivalent to DPs—are incorporated into specific objects. Objects are equiva-
lent to an FR—with a specified [FR i =

=

A ij DP j ] relationship—of axiomatic design,
where DPs are data or input and A ij is a method or a relationship. In an axiomatic
design, the design equation explicitly identifies the relationship between FRs and
DPs. Classification means that objects with the same data structure (attributes) and
behavior (operations or methods) are grouped into a class. The object is represented
as an instance of specific class in programming languages. Therefore, all objects
are instances of some classes. A class represents a template for several objects and
describes how these objects are structured internally. Objects of the same class have
the same definition both for their operations and for their information structure.
Sometimes an “object” also is called a tangible entity that exhibits some well-
defined “behavior.” “Behavior” is a special case of FR. The relationship between
“objects” and “behavior” may be compared with the decomposition of FRs in the FR
hierarchy of axiomatic design. “Object” is the “parent FR” relative to “Behavior,”
which is the “child FR.” That is, the highest FR between the two layers of decomposed
FRs is “object,” and the children FRs of the 'object FR' are “behavior.”
The distinction between “super class,” “class,” “object” and “behavior” is neces-
sary in OOT to deal with FRs at successive layers of a system design. In OOT, class
represents an abstraction of objects and, thus, is at the same level as an object in the
FR hierarchy. However, object is one level higher than behavior in the FR hierarchy.
The use of these key words, although necessary in OOT, adds unnecessary complexity
when the results of axiomatic design are to be combined with OOT. Therefore, we
will modify the use of these key words in OOT.
In ADo-oSS, the definitions used in OOT are slightly modified. We will use one
key word “object,” to represent all levels of FRs (i.e., class, object, and behavior).
“Objects with indices” will be used in place of these three key words. For example,
class or object may be called “object i,” which is equivalent to FR i , Behavior will be
denoted as “Object ij” to represent the next level FRs, FR ij .
Conversely, the third level FRs will be denoted as “Object ijk .” Thus, “Object i ,”
“Object ij ,” and “Object ijk ” are equivalent to FR i ,FR ij , and FR ijk , which are FRs at
three successive levels of the FR hierarchy.
To summarize, the equivalence between the terminology of axiomatic design and
thoseofOOTmaybestatedas:
An FR can represent an object.
DP can be data or input for the object, (i.e., FR).
The product of a module of the design matrix and DP can be a method (i.e., FR
=

×

DP).
Different levels of FRs are represented as objects with indices.

A