7/25/2019 Falut Collapsing

1/12

TOPIC : Fault collapsing due to faultequivalence and fault dominance

UNIT 2 : Fault modeling

Module 2.3 Fault edundanc! and Faultcollapsing

7/25/2019 Falut Collapsing

2/12

Fault collapsing

T"e num#e of faults t"at need to#e simulated can #e deceased#! e$ploiting t%o elations

#et%een a pai of faults fiand f&:a' Fault equivalence

#' Fault dominance

7/25/2019 Falut Collapsing

3/12

Collapsed (atio

Man! of t"e faults ae emoveddue to fault equivalence and faultdominance.

Collapsed atio is t"e atio ofemaining faults and totalnum#e of faults.

Collapsed atio :)Total Faults * Fault emoved' +

Total fault.

7/25/2019 Falut Collapsing

4/12

Fault equivalence

Defnition :

Two faults of a Boolean circuit arecalled equivalent i they transform

the circuit such that the two faultycircuits have identical outputfunctions. Equivalent faults arealso called indistinguishable and

have exactly the same set of tests.,$ample: -n input line sa/ and output

line sa/ in an -N0 gate.

7/25/2019 Falut Collapsing

5/12

Fault equivalence

T%o faults 1 and f& in a cicuit ae said to #eequivalent if t"e coesponding fault! vesionsof t"e cicuit ae identical. In ot"e %ods alltests t"at detect 1 also detect f&.

Num#e of fault sites in a gatelevel cicuit PI)pima! inputs' 4gates 4 )fanout#anc"es'

-n ninput 5oolean gate equies onl! )n6'instead of )2n2' single stuc7at faults to #emodeled #ecause of equivalent fault collapsing.

7/25/2019 Falut Collapsing

6/12

Fault equivalence :e$ample

8tuc7at/ at output of -N0 gate isequivalent to stuc7at/ at t"e input

pins.

8o9 %"ile testing %e can emovet"e 2 stuc7at/ fault at t"e input

pins9 since t"ese t%o fault %ill #e

7/25/2019 Falut Collapsing

7/12

,quivalent fault collapsing fo5oolean gates

7/25/2019 Falut Collapsing

8/12

Fault equivalence : cicuit

Fault deleted due to equivalent faultcollapsing

Collapsed atio : 6+3/ /.;33

7/25/2019 Falut Collapsing

9/12

Fault dominance

Denition !f all tests of fault"# detect another fault "$%then "$ is said to dominate

"#. The two faults are alsocalled &conditionally'equivalent with respect to

the test set of "#. (hen twofaults "# and "$ dominateeach other% then they areequivalent.

7/25/2019 Falut Collapsing

10/12

Fault dominance

f and g aefunctionall! equivalent unde T.

In ot"e %ods9 i> dominates g9 t"enan! test t t"at detects g.

7/25/2019 Falut Collapsing

11/12

Fault dominance :,$ampleA 3-input AND gate.1 ? sa6 fault in one input of t"e

gate

f& ? sa6 in t"e gate output Tests fo 1 ? /66

Tests fo f& ? ///9 //69 /6/9 /669 6//96/69 66/

T"us9 f& dominates 1 .

7/25/2019 Falut Collapsing

12/12

Fault dominance : cicuite$ample

Collapsed atio : 62+3/ /.@/