ROBUST DESIGN FOR SOFTWARE DEVELOPMENT - Software Design for Six-Sigma: A Roadmap for Excellence - page 479

18.6 ROBUSTNESS CONCEPT #4: SIGNAL-TO-NOISE RATIOS

A conclusion of the previous sections is that quality can be quantified in terms of
the respective software response to noise and signal factors. The ideal software only
will respond to the customer signals and will be unaffected by random noise factors.
Therefore, the goal of the DFSS project can be stated as attempting to maximize
the SN ratio for the respective software. The SN ratios described in the following
paragraphs have been proposed by Taguchi (1987).

Smaller-is-better . For cases in which the DFSS team wants to minimize the
occurrences of some undesirable software responses, you would compute the
following SN ratio:

1
N

N

y i SN =− 10 log 10 (18.8)

n = 1

The constant, N , represents the number of observations (that has y i as their
response) measured in an experiment or in a sample. Experiments are conducted,
and the y measurements are collected. Note how this SN ratio is an expression
of the assumed quadratic nature of the loss function.
Nominal-the-best . Here, the DFSS team has a fixed signal value (nominal value),
and the variance around this value can be considered the result of noise factors:

10 log 10 µ

2

SN =− (18.9)

σ

2

This signal-to-noise ratio could be used whenever ideal quality is equated
with a particular nominal value. The effect of the signal factors is zero because
the target date is the only intended or desired state of the process.
Larger-is-better . Examples of this type of software requirement are therapy
software yield, purity, and so on. The following SN ratio should be used:

1
N

N

1
y i

=−

SN 10 log 10 (18.10)

n = 1

Fraction defective ( p ). This SN ratio is useful for minimizing a requirement's
defects (i.e., values outside the specification limits or minimizing the percent of
software error states, for example).

10 log 10

p

SN = (18.11)

1 − p

where p is the proportion defective.