# Linked Coupling Faults Detection by Multirun March Tests
## 5 Experimental Investigations  
The first experiment was provided according to the following conditions:  
1. Memory size: 1024 one-bit cells;
2. _LCF_1 consisting of two single _CFins_: \(CFin(a_{i},a_{j})=\langle\uparrow,\updownarrow\rangle\) and \(CFin(a_{j},a_{k})=\langle\uparrow,\updownarrow\rangle\) in cells \(a_{i},a_{j}\), and \(a_{k}\) with addresses \(i<j<k\);
3. Address sequence: random;
4. Number of one-run march test (\(f=1\)) executions for the average value of \(FC_{Test}(f)\) calculation: 100,000.  
The results for the one-run memory testing in Table 1 satisfy the theoretical estimation (6) for march tests. The results in Table 1 originate from computer simulations conducted using custom tools developed by the authors. These simulations involved generating _LCF_1s in random memory cells and then executing the relevant test to detect the faults. For each test, 100,000 simulations were conducted, and the result of the test was recorded each time. Finally, the average fault coverage (\(FC\)) was calculated based on these simulations. The number of simulations was limited to 100,000 because it was observed that further increasing the number of simulations did not significantly affect the obtained average result.  
The next experiment confirms the validity of the relation (6) for multirun memory testing (\(f>1\)) by applying the March C- test. The results of this experiment for the same \(LCF1\) are provided in Figure 5. The results demonstrate the high efficiency of detecting \(LCF1\)s using multirun memory tests.  
The efficiency of multirun memory testing for detecting linked coupling faults was validated for various \(LCF\) and memory tests. The experiment conditions are similar to the previous ones, except for the \(LCF\) fault configurations. The critical element of the multirun testing for this experiment is a random address sequence applied at each test iteration.  
It should be noted that the proposed approach is applicable for detecting previously undetectable memory linked coupling faults using march tests. March tests exhibit computational complexity that linearly depends on the memory size \(N\) in bits. The approach shares comparable computational complexity with classical march tests and also linearly depends on the memory size. For instance, the March LR test has a complexity of \(22N\), but it does not enable the detection of undetectable linked coupling faults. Conversely, based on the proposed approach, the MATS+ application (\(5N\)), in a multirun scenario (four runs), facilitates the detection of \(89.57\%\) of the undetectable linked coupling faults (see Table 2). The complexity of this procedure is estimated as \(4\times 5N=20N\).  
Tables 2 and 3 list the high efficiency of detecting complex faults with multirun tests. With an increase in the number of iterations, the test efficiency levels off. As listed in Tables 2 and 3, after four iterations, test MATS+ has the same effectiveness as the more complex test March C- designed as a \(CF\) detection test.  
A similar dependence is also observed for the case of multirun tests based on a variable initial memory state (random backgrounds) of the tested memory. The same faults were analyzed as in the previous experiment, and the March C- and simplest one-phase tests \(\{\Uparrow(ra,w\overline{a})\}\) were used. The results for both cases are presented in Tables 4 and 5.  
As presented in Tables 4 and 5, multirun testing with a random background technique results in the same \(FC_{Test}(f)\) for both simple tests like \"one march element\" (\(\{\Uparrow(ra,w\overline{a})\}\)) and complex tests, such as March C-.  
\begin{table}
\begin{tabular}{c c c c} \hline
**MATS++** & **March C-** & **March LA** & **March Y** \\ \hline
33.21\% & 33.45\% & 33.15\% & 32.92\% \\ \hline \end{tabular}
\end{table}
Table 1: Fault coverage \(FC_{Test}(f)\) of \(LCF1\) for one-run march tests.  
Figure 5: Fault coverage \(FC_{Test}(f)\) of \(LCF1\) for multirun March C- test (address sequences: random, and background: zeros).