# Linked Coupling Faults Detection by Multirun March Tests
## 4 Multirun March Tests for LCF Detection  
Multi-cell faults such as pattern-sensitive faults (_PSFs_) or linked coupling faults (_LCFs_) are triggered when specific bit patterns occur in the cells affected by these faults or when a certain value change occurs in one of the cells. Due to the limitations of march tests, a single run of such a test can only generate a limited number of patterns in the selected memory cells. Increasing the number of generated patterns in memory cells cannot be achieved by simply increasing the test's complexity. One effective solution for achieving high fault coverage for multi-cell faults, as demonstrated in [24; 25; 26; 27; 28; 29; 30], is multirun testing. This testing concept involves executing the same test procedure multiple times, each time with different initial conditions (different initial memory backgrounds and/or address sequences). Executing the same march test under varying initial conditions generatesdifferent bit patterns in memory cells, thereby enabling the detection of a wider range of potential multi-cell faults, including various types of linked coupling faults.  
The low coverage of _LCF_s by classic one-run march tests is explained by the sequential procedure for accessing memory cells and the unchanged test implementation scenario [23]. Analyzing the example of six formal descriptions (5) of the _LCF_1 in Figure 2 reveals that only two of the six scenarios guarantee the detection of this fault. Accordingly, the fault can be detected only by changing the scenarios and repeatedly applying the test. In this case, the scenario is the address sequence of the march test that detects the entire set of single coupling faults. Multiple (multirun) memory testing was considered within the exhaustive, pseudo-exhaustive, and transparent memory testing frameworks [3,23]. In all cases, it was necessary to repeat the march test for various scenarios determined by the degrees of freedom inherent in march tests [20]. March memory tests detect complex faults by applying them repeatedly for various address sequences or initial memory cell states [31]. An essential result of multirun memory testing is detecting all possible faulty states. However, achieving 100% coverage may require a sufficient number (multiplicity) of test applications.  
For the variable address sequence that defines the scenario for _LCF_(\(a_{i},a_{j},a_{k},\ldots,a_{z}\)), a time sequence always exists for accessing cells \(a_{i},a_{j},a_{k},\ldots,a_{z}\), satisfying the conditions of Statement 2. An example is _LCF_1 (5), where two of the six sequences of cell addresses \(a_{i},a_{j}\), and \(a_{k}\) are detectable for this fault. In the general case, for any faulty memory state, a set of address sequences exists for which this memory state is detected by a single test. Accordingly, in a random address sequence selection procedure, the ratio \(p\), representing the number of address sequences for which a fault is detectable, to the total number of sequences, expressed as a percentage, determines the fault coverage, \(FC\), when detecting this fault using a one-run memory test with randomly selected address sequences. The value of \(p=FC/100\%\) can be understood as the probability of fault detection, while the probability of this fault remaining undetectable is \(1-p\). For an \(f\)-run memory test with a random address sequence selection procedure, the probability of this fault being undetectable is \((1-p)^{f}\) and the detection probability is estimated as \(1-(1-p)^{f}\). Assuming that a single application of the march test allows for detecting the _LCF_ failure with \(FC_{Test}\), its \(f\)-time use with arbitrary (random) address sequences allows for reaching the value \(FC_{Test}(f)\) determined as follows (6) [23]:  
\[FC_{Test}(f)=\left(1-\left(1-\frac{FC_{Test}}{100\%}\right)^{f}\right)\times 1 00\%;\ f=1,2,3,\ldots \tag{6}\]  
As \(f\) increases, the value of the fault coverage \(FC_{Test}(f)\) tends to 100%. For the _LCF_1 failure, considering (5), \(FC_{Test}=(2/6)\times 100\%=33.33\%\).