AXIOMATIC DESIGN IN SOFTWARE DESIGN FOR SIX SIGMA (DFSS) - Software Design for Six-Sigma: A Roadmap for Excellence - page 335

TABLE 13.1 Software Functional Requirements (FRs) Examples

Functional Requirement
Category Example

Operational requirement Outline of what the product will do for the user.

Performance requirement Speed or duration of product use.

Security requirements Steps taken to prevent improper or unauthorized use.

Maintainability
requirements

Ability for product to be changed.

Reliability requirements The statement of how this product prevents failure

attributed to system defects.

Availability requirements Ability for product to be used in its intended manner.

Database requirements Requirements for managing, storing, retrieving, and

securing data from use.

Documentation
requirements

Supporting portions of products to enable user
references.

Additional requirements Can include many categories not covered in other

sections.

where FR

} mx1 is the vector of independent functional requirements with m elements,

{

} px1 is the vector of design parameters with p elements. Examples of FRs and
DPs are listed in Tables 3 13.1 & 13.2.
The shape and dimension of matrix A is used to classify the design into one of
the following categories: uncoupled , decoupled , coupled , and redundant .Forthe
first two categories, the number of functional requirements, m , equals the number of
design parameters, p . In a redundant design, we have m

DP

{

<

p . A design that completely
complies with the independence axiom is called an uncoupled (independent) design.
The resultant design matrix in this case, A , is a square diagonal matrix, where m = p

and A ij = j and 0 elsewhere as in (13.1). An uncoupled design is

an ideal (i.e., square matrix) design with many attractive attributes. First, it enjoys the
path independence property that enables the traditional quality methods objectives
of reducing functional variability and mean adjustment to target through only one
parameter per functional requirement, its respective DP. Second, the complexity of the
design is additive (assuming statistical independence) and can be reduced through
axiomatic treatments of the individual DPs that ought to be conducted separately.
This additivity property is assured because complexity may be measured by design
information content, which in turn is a probabilistic function. Third, cost and other
constraints are more manageable (i.e., less binding) and are met with significant ease,
including high degrees of freedom for controllability and adjustability.
A violation of the independence axiom occurs when an FR is mapped to a DP,
that is, coupled with another FR. A design that satisfies axiom 1, however, with path
dependence 4 (or sequence), is called a decoupled design as in (13.2). In a decoupled
design, matrix A is a square triangular (lower or upper, sparse or otherwise). In an

X = 0 when i =

3 Zrymiak, D. @ http://www.isixsigma.com/library/content/c030709a.asp
4 See Theorem 7 in Section 2.5 as well as Section 1.3.