Quality in Design - Medical Device Design: Innovation from Concept to Market - page 127

which for three variables becomes

3! − 2! = 4

These interactions are X1.X2, X1.X3, X2.X3, and X1.X2.X3.

Hence our table is modified as shown in Table 7.8 .

The analysis of the results uses Equations (7.2) again - but we need no more experiments!
Our new analysis table is shown in Table 7.9 .

From Table 7.9 we can see that the dominant effect is created by all three parameters in
combination. However, we do not know if this is a statistically significant variation, or if it is
just due to simple random variance. More often than not the variations found are simply due
to random variations (and these in turn are due to tolerances). There is little we can do with
these, but the information does help us to decide where to tighten tolerances and where it is
possible to slacken them.

Table 7.8: Inclusion of Interactions into Analysis Table

Random
Run Number

Experiment X1 X2 X3 T P Tm Result

(Q)

7 1 + 1 + 1 + 1 Max Max Max + 1 + 1 + 1 + 1 1.37

6 2 + 1 + 1 − 1 Max Max Min + 1 − 1 + 1 − 1 1.42

4 3 + 1 − 1 + 1 Max Min Max − 1 + 1 − 1 − 1 1.11

5 4 + 1 − 1 − 1 Max Min Min − 1 − 1 + 1 + 1 1.40

3 5 − 1 + 1 + 1 Min Max Max − 1 − 1 + 1 − 1 0.92

8 6 − 1 + 1 − 1 Min Max Min − 1 + 1 − 1 + 1 1.84

2 7 − 1 − 1 + 1 Min Min Max + 1 − 1 − 1 + 1 1.00

1 8 − 1 − 1 − 1 Min Min Min + 1 + 1 + 1 − 1 1.37

Table 7.9: Effects of Parameters (Including Interactions) Ranked in Order of E Ascending

Max Min E

X3 1.0979 1.5063 − 0.4084

X1X2X3 1.2037 1.4004 − 0.1967

X1X3 1.3139 1.4196 − 0.1057

X1X2 1.3139 1.2903 0.0236

X1 1.3236 1.2806 0.0431

X2 1.2764 1.2178 0.0586

X2X3 1.3416 1.2625 0.0791