ROBUST DESIGN FOR SOFTWARE DEVELOPMENT - Software Design for Six-Sigma: A Roadmap for Excellence - page 483

Control Factors A B C D
Level 1 0.62 1.82 3.15 0.10

Level 2 3.14 1.50 0.12 2 .17

Gain (meas. in dB) 2.52 0.32 3 .03 2.07

FIGURE 18.11 Signal-to-noise ration response table example.

The factors of concern are identified in an inner array, or control factor array, which
specifies the factorial levels. The outer array, or noise factor array, specifies the noise
factors or the range of variation the software possibly will be exposed to in its life
cycle. This experimental setup allows the identification of the control factor values
or levels that will produce the best performing, most reliable, or most satisfactory
software across the expected range of noise factors.

18.8 ROBUSTNESS CONCEPT #6: PARAMETER DESIGN ANALYSIS

After the experiments are conducted and the signal-to-noise ratio is determined for
each run, a mean signal-to-noise ratio value is calculated for each factor level. This
data is analyzed statistically using analysis of variance (ANOVA) techniques (El-Haik
& Roy, 2005). 10 Very simply, a control factor with a large difference in the signal
noise ratio from one factor setting to another indicates that the factor is a significant
contributor to the achievement of the software performance response. When there
is little difference in the signal-to-noise ratio from one factor setting to another, it
indicates that the factor is insignificant with respect to the response. With the resulting
understanding from the experiments and subsequent analysis, the design team can:

Identify control factors levels that maximize output response in the direction
of goodness and minimize the effect of noise, thereby achieving a more robust
design.
Perform the two-step robustness optimization 11 :
Step 1: Choose factor levels to reduce variability by improving the SN ratio.
This is robustness optimization step 1. The level for each control factor with
the highest SN ratio is selected as the parameter's best target value. All
these best levels will be selected to produce the “robust design levels” or the
“optimum levels” of design combination. A response table summarizing SN
gain usually is used similar to Figure 18.11. Control factor level effects are
calculated by averaging SN ratios that correspond to the individual control
factor levels as depicted by the orthogonal array diagram. In this example, the

10 See Appendix 18.A.
11 Notice that the robustness two-step optimization can be viewed as a two-response optimization of the
functional requirement ( y ) as follows: Step 1 targets optimizing the variation (

σ y ), and step 2 targets

shifting the mean ( µ y ) to target T y . For more than two functional requirements, the optimization problem

is called multiresponse optimization.