Quality in Design - Medical Device Design: Innovation from Concept to Market - page 128

To determine their respective significance we undertake a simple statistical analysis. First we rank
the parameters in order of variation, starting with the most negative and ending with the most
positive. Once ranked we determine the probability of that effect being in that position using

i 05

21

.

P

(7.4) i

k

The value Z is determined from standard tables (see Appendix B, Table B.1 - you should try
to replicate the Z column in Table 7.10 for yourself).

If, in your table, you have items with the same value of E then you must follow the division
rule as seen earlier. So, for example, if X1X2 and X1 had identical values of E, the rank list
would be 1, 2, 3, 4.5, 4.5, 6, 7.

The next part of the analysis is to plot a graph of effect E versus Z, as in Figure 7.5 . Most
of the points lie on the normal straight line (this will be discussed more later). However X3
stands out like a sore thumb - as does X2X3. They are clearly different from the rest.

Note that the normal line goes through zero; this is obtained using a best-fit line and forcing
0-0. The graph indicates a “wrong” best fit which goes through the points, but not through
0-0; a common error made by those doing their first 2 k experiments. The best way of
achieving this is to plot the graph (as an x-y scatter graph) in a spreadsheet program, then
add a linear trend line with the “crosses at zero” option flagged. But be careful, as those with
severe outliers will distort your best-fit line! Figure 7.6 demonstrates this where there are
obvious outliers from the straight line. These are the significant effects; all others are random
aberrations over which you have little control, apart from tightening tolerances.

These two points are outliers whose effects are statistically significant, or whose effects
are due to the change in parameter and not simply due to random variation. Thus the same
argument applies to X3 and X2X3 in Figure 7.5 .

Table 7.10: Normalized Scores for the Parameters' Effects

E Rank P Z

X3 − 0.4084 1 0.07 − 1.465

X1X2X3 − 0.1967 2 0.21 − 0.792

X1X3 − 0.1057 3 0.36 − 0.565

X1X2 0.0236 4 0.50 0

X1 0.0431 5 0.64 0.565

X2 0.0586 6 0.79 0.792

X2X3 0.0791 7 0.93 1.465