Biomedical Engineering Reference
In-Depth Information
0.9
0.8
0.7
0.6
Untested array, p = 0.05
Array after structural testing, p = 0.05
Untested array, p = 0.01
Array after structural testing, p = 0.01
0.5
0.4
0.3
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Malfunction Probability, q
Figure 4.41
Failure rate for synthesized design without testing and with structural testing.
Next, the synthesis method from [15] is used to map the protein array on
the defect-free regions of the array. We also use the functional test to detect
and locate malfunctions in the array. These malfunctions are then bypassed
during the synthesis of the chip for the protein array. As a baseline, we also
carry out the synthesis for an array to which neither the structural test nor
functional test have been applied.
First, we determine the failure rate
R
, 0 ≤
R
≤ 1, for the three scenarios
when the protein assay is mapped to an array with defects and malfunc-
tions. When functional testing is carried out, the failure rate due to target
defects and malfunctions is zero because all of them are detected by the
test procedure. If no testing is carried out, the failure rate is as high as 0.85;
that is, the protein assay fails for as many as 85% of the 200 simulated chips.
If structural testing is used, the failure rate is lower, but it is still signifi-
cant—as high as 0.75.
Figure 4.41 shows that as the malfunction probability increases, the failure
rate
R
becomes considerable even when structural testing is used. Moreover,
the benefits of structural testing are less evident for the smaller value of the
defect probability, that is,
p
= 0.01. Therefore, functional testing is needed to
augment droplet-transportation-based structural testing for digital micro-
fluidic arrays. A counterintuitive finding from Figure 4.41 is that the failure
rate is lower for
p
= 0.05 compared to
p
= 0.01. This occurs because large
p
implies that there is a low likelihood of a defect-free cell. Hence, structural
testing is likely to catch such defects.
The detection of more defects and malfunctions using functional testing
leads to a corresponding increase in the assay completion time. This happens
because fault detection and fault location leave fewer unit cells available for
the protein assay, and the synthesis procedure employs less parallelism in
the execution of the microfluidic operation. Figure 4.42 shows the assay com-
pletion time for the three scenarios that we are considering for the protein
