UNIT 2 : Fault modeling Module 2.3 Fault redundancy and Fault collapsing TOPIC : Fault collapsing due to fault equivalence and fault dominance

Fault collapsing

 The number of faults that need to be simulated can be decreased by exploiting two relations between a pair of faults f i and f j : a) Fault equivalence b) Fault dominance

Collapsed Ratio

   Many of the faults are removed due to fault equivalence and fault dominance.

Collapsed ratio is the ratio of remaining faults and total number of faults.

Collapsed ratio : (Total Faults – Fault removed) / Total fault.

Fault equivalence

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Definition :

Two faults of a Boolean circuit are called equivalent iff they transform the circuit such that the two faulty circuits have identical output functions. Equivalent faults are also called indistinguishable and have exactly the same set of tests.

Example: An input line s-a-0 and output line s-a-0 in an AND gate.

Fault equivalence

 Two faults fi and fj in a circuit are said to be equivalent if the corresponding faulty versions of the circuit are identical. In other words all tests that detect fi also detect fj.

 Number of fault sites in a gate-level circuit = PI(primary inputs) + #gates + # (fanout branches)  An n-input Boolean gate requires only (n+1) instead of (2n+2) single stuck-at faults to be modeled because of equivalent fault collapsing.

Fault equivalence : example

Stuck-at-0 at output of AND gate is equivalent to stuck-at-0 at the input pins.

So, while testing we can remove the 2 stuck at-0 fault at the input pins, since these two fault will be tested by equivalent fault stuck at-0 at the output pin.

Equivalent fault collapsing for Boolean gates

Fault equivalence : circuit

Fault deleted due to equivalent fault collapsing Collapsed ratio : 16/30 = 0.533

Fault dominance

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Definition : If all tests of fault F1 detect another fault F2, then F2 is said to dominate F1. The two faults are also called “conditionally” equivalent with respect to the test set of F1. When two faults F1 and F2 dominate each other, then they are equivalent.

Fault dominance

  Let T, be the set of all tests that detect a fault g. We say that a fault f dominates the fault g iff f and g are functionally equivalent under T. In other words, iff dominates g, then any test t that detects g.

Fault dominance : Example

A 3-input AND gate.

 fi -> s-a-1 fault in one input of the gate   fj -> s-a-1 in the gate output ◦ Tests for fi -> 011 ◦ Tests for fj -> 000, 001, 010, 011, 100, 101, 110 Thus, fj dominates fi .

Fault dominance : circuit example Collapsed ratio : 12/30 = 0.40