ROBUST DESIGN FOR SOFTWARE DEVELOPMENT - Software Design for Six-Sigma: A Roadmap for Excellence - page 484

ˆ ˆ ˆ ˆ

y

y y = = β β + + β β M M + + ε ε ˆ ˆ

2 2 0 0 1 1 2 2 2 2

ε ) ε )

ε ) ε )

3 3

2 2

ε ) ε )

ε ) ε )

3 3

1 1

) ) ) )

) )

y y = = β β + + β β M M

i i 0 0 1 1 i i

M M

M1 M2 M3 M4

FIGURE 18.12 Best-fit line of a dynamic robust design DOE.

robust design levels are as follows: factor A at level 2, factor C at level 1 and
factor D at level 2, or simply A2C1D2.
Identify control factors levels that have no significant effect on the func-
tional response mean or variation. In these cases, tolerances can be relaxed
and cost reduced. This is the case for Factor B of Figure 18.11.
Step 2: Select factor levels to adjust mean performance. This is the robustness
optimization step 2. This is more suited for dynamic characteristic robust-
ness formulation, with sensitivity defined as Beta ( β ). In a robust design, the

individual values for are calculated using the same data from each experi-

mental run as in Figure 18.10. The purpose of determining the Beta values
is to characterize the ability of control factors to change the average value
of the functional requirement ( y ) across a specified dynamic signal range as
in Figure 18.12. The resulting Beta performance of a functional requirement
( y ) is illustrated by the slope of a best-fit line in the form of y

β

= β 0 + β 1 M ,

where β 0 is the intercept of the functional requirement data

that is compared with the slope of an ideal function line. A best-fit line is
obtained by minimizing the squared sum of error (

β 1 is the slope and

ε )terms.

In dynamic systems, a control factor's importance for decreasing sensitivity is
determined by comparing the gain in SN ratio from level to level for each factor,
comparing relative performance gains between each control factor, and then selecting
which ones produce the largest gains.
That is, the same analysis and selection process is used to determine control factors
that can best used to adjust the mean functional requirement. These factors may be
the same ones that have been chosen based on SN improvement, or they may be
factors that do not affect the optimization of SN. Most analyses of robust design
experiments amount to a standard ANOVA 12 of the respective SN ratios, ignoring
two-way or higher order interactions. However, when estimating error variances, one
customarily pools together main effects of negligible size. It should be noted at this

12 See Appendix 18.A.