Biomedical Engineering Reference
In-Depth Information
4.3 Performance Evaluation
In this section, we evaluate the performance of the proposed testing and
diagnosis method. We first carry out complexity analysis of parallel scan-
like testing and compare it with results obtained from the Euler-path-based
method [36]. Next we use probabilistic analysis to evaluate the improvement
in diagnostic resolution obtained using the proposed technique for locating
multiple defects.
4.3.1 Complexity Analysis
We first calculate the complexity of parallel scan-like testing. For simplicity,
we only discuss the off-line test of a target array that contains a single defect.
The parallel scan-like test method is based on three stages: peripheral test,
column test, and row test.
To test an
N
×
N
target array, the peripheral test is first carried out, and this
stage takes 4
N
steps. Each step is defined as a droplet manipulation from
one electrode to another, which takes 1 s for a typical actuation frequency
of 1 Hz. Next, column and row tests are carried out, and each takes
N
steps.
Thus, the total test procedure includes 8
N
steps, that is,
O
(
N
). Fault diagnosis
is based on 1-D binary partitioning; therefore, it is also
O
(
N
). Compared to
the Euler-path-based method, which has
O
(
N
2
) complexity, the times needed
for both testing and diagnosis are significantly reduced.
To make a more practical comparison, we apply the proposed parallel scan-
like test method and the Euler-path-based method to the off-line testing of
microfluidic arrays with sizes varying from 10 × 10 to 50 × 50 electrodes. Note
that the complexity for both the proposed method and the Euler-path-based
method is independent of defect location. Thus, for each size, a sample array
with a randomly injected faulty cell is generated as a target array. To get the
precise test time, we calculate the time needed to route the droplet from the
source to the pseudosource and from the pseudosink to the sink reservoir,
and add it to the test time derived using the previous complexity analysis.
The results are shown in Figure 4.16.
As predicted by the complexity analysis, the test time for the Euler-path-
based testing increases quadratically with the array size, while the parallel
scan-like test time increases only linearly. A significant improvement can be
seen for large arrays.
4.3.2 Probabilistic Analysis
Next, we calculate the probability of the occurrence of incorrectly classified
defects, that is, the probability that an electrode is a candidate defect site
when it is not defective. Assume that each electrode fails independently with
probability
p
. The probability that an electrode is defect free is, therefore,
