Faults

A fault is an unintentional deviation in a circuit model. A defect created in the production of a circuit can lead to a fault which impacts circuit behaviour.

Definition bq

We use fault models to abstract physical defects for testing digital circuits.

Fault Coverage

We can use fault coverage as a quantitative measure of test set quality:
$\text{Fault Coverage}=\frac{\text{\# of detected faults}}{\text{\# of total faults}}$

Fault coverage follows diminishing returns as number of test vectors increase. The acceptable threshold depends on the company and product.

Quote bq

Testing can be used to show the presence of faults but not to show their absence. No circuit can be “guaranteed defect free”.

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Untestable Faults

A fault is untestable if there is no test vector for that fault.
$f\oplus f^{p/d}=0\text{(for all possible test vectors)}$

Untestable faults only occur in networks with redundancy.

Redundancy

A redundant line is a line that can be replaced with a constant logic level (0 or 1) without changing the function realised by the network.

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Multiple Output Circuits

For a multiple output circuit with $m$ outputs, the set of all possible test vectors for a fault $p/d$ is given by:
$F^{p/d}=F_1^{p/d}+F_2^{p/d}+\cdots +F_m^{p/d}$

Each function $F_n^{p/d}$ is the complete set of tests for fault $p/d$ at terminal $f_n$.

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Fault Location Test Sets

Diagnosis of a fault is harder than detection. To locate a fault, it needs to be distinguished from all other possible faults that may occur.

Concept bq

Two faults are distinguishable if there exists a fault detection test for one of the faults that is not a test for the other.

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