ROBUST DESIGN FOR SOFTWARE DEVELOPMENT - Software Design for Six-Sigma: A Roadmap for Excellence - page 475

18.4.2 Smaller-the-Better Loss Function

Functions like “reduce audible noise” would like to have zero as their target value.
The loss function in this category and its expected values are given in (18.6) and
(18.7), respectively.

Ky 2 L ( y , T ) = (18.6)

K σ

y

2
y

2

E [ L ( y , T )] = + µ (18.7)

In this development as well as in the next sections, the average loss can be estimated
from a parameter design or even a tolerance design experiment by substituting the
experiment variance S 2

y and

and average y as estimates for σ µ y into Equations

(18.6) and (18.7).
Recall the example of two settings in Figure 18.3. It was obvious that setting 1
was more robust (i.e., produced less variation in the functional requirement [y] than
setting 2 by capitalizing on nonlinearity as well as on lower quality loss similar to the
scenario on the right of Figure 18.4). Setting 1 (DP * ) robustness is even more evident
in the flatter quadratic quality loss function.
Because quality loss is a quadratic function of the deviation from a nominal value,
the goal of the DFSS project should be to minimize the squared deviations or variance
of a requirement around nominal (ideal) specifications, rather than the number of units
within specification limits (as is done in traditional statistical process control (SPC)
procedures).
Several topics recently have been published on these methods, for example, Phadke
(1989), Ross (1988), and—within the context of product DFSS—Yang and El-Haik
(2008), El-Haik (2005), and El-Haik (2008) to name a few, and it is recommended
that the reader refer to these topics for further specialized discussions. Introductory
overviews of Taguchi's ideas about quality and quality improvement also can be
found in Kackar (1985).

18.5 ROBUST DESIGN CONCEPT #3: SIGNAL, NOISE, AND
CONTROL FACTORS

Software that is designed with Six Sigma quality always should respond in exactly
the same manner to the signals provided by the customer. When you press the ON
button of a television remote control you expect the television to switch on. In a
DFSS-designed television, the starting process always would proceed in exactly the
same manner; for example, after three seconds of the remote pressing action, the
television comes to life. If, in response to the same signal (pressing the ON button)
there is random variability in this process, then you have less-than-ideal quality. For
example, because of such uncontrollable factors such as speaker conditions, weather
conditions, battery voltage level, television wear, and so on, the television sometimes