Biomedical Engineering Reference
In-Depth Information
1
Without diagonal testing
With single-diagonal testing
With cross-diagonal testing
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.89
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Defect Occurrence Probability
Figure 4.19
Simulation results highlighting the likelihood of an incorrect classification.
min
{
i
,
j
}-1
min
{
i
,
j
}-1
min
{
N
-
i
,
j
}-1
(
i
,
j
)
N
-
max
{
i
,
j
}
(
i
,
j
)
N
-1+
min
{
i
,
j
}-
max
{
i
,
j
}
N
-
max
{
N
-
i
,
j
}
Figure 4.20
Illustration of untestable sites for (a) single-diagonal diagnosis and (b) cross-diagonal diagnosis.
shown in Figure 4.14. Therefore, for a single electrode in row
i
and column
j
,
the probability
P
untest
that it cannot be tested is
P
untest
= (1 − (1 −
p
)
i−1
)(1 − (1 −
p
)
N−i
)(1 − (1 −
p
)
j−1
)(1 − (1 −
p
)
N−j
)
When diagonal testing is carried out, the electrode is untestable only if
there is also a real defect in the same diagonal or diagonals as shown in
Figures 4.20a and 4.20b.
If a single-diagonal diagnosis is carried out as in Figure 4.20a, the prob-
ability
P
untest
of an untestable electrode is
P
untest
= (1 − (1 −
p
)
i−1
)(1 − (1 −
p
)
N−i
)(1 − (1 −
p
)
j−1
)
×
(1 − (1 −
p
)
N−j
)(1 − (1 −
p
)
min{i, j}−1
) ×
(1−(1−
p
)
N−max{i, j}
)
