Probabilistic Testability Analysis

1
Probabilistic Testability Analysis

• Aditya Newalkar

2
Characteristics of a testability analysis program

• Goal is not to generate test vectors themselves
  but to aid the generation of test vectors
• Linear complexity
• Predicts test coverage
• Handles the reconvergent fanouts

3
Our goals

• Find the probabilistic testability of all the
  stuck at faults
• Find 10 of the hardest to detect faults

4
Strategy

• The 1-observability of (signal) A at (output) F
  is a measure of how many patterns can detect a
  single stuck-at-0 fault of A at F, and vice versa
  for 0-observability Brg89.
• P(D/0) P(D1)0-observability of signal D
• Find the 0-observability and 1-controllability of
  all the signals,
• Take the product to find the probability of s-a-0
  fault.
• P(D/1) P(D0)1-observability of signal D

5
Reconvergent fanouts

• Signals are no longer independent
• Testability measures cannot be calculated
  independently
• Causes significant error in the measurement

6
Graph model of netlist

• Netlist is viewed as a directed simple graph
• Each gate is a node
• Each net is an arc (directed edge)
• The gate node is connected to one output node
  (SRC node)
• The gate node is connected to two or more input
  nodes (DEST nodes)
• SRC nodes are connected to DEST nodes of the
  next gate
• The direction of the arc is always SRC to
  DEST

7
Algorithm for calculating Controllability

• While indegreeOf(P) gt 0
• InPinControlArrayi controllability of
  incoming edges of P
• i
• End While
• If (P Primary Input) then
• Return 0.5
• If (P LogicGateType) then
• Calculate controllability of the output from the
  array InPinControlArray
• Return controllability
• Else
• Add all the controllability values in the array
  InPinControlArray
• Return controllability
• End if

8
Result and Discussion
C17 74181
Coverage 99 99
Hardest Fault (s-a-0) 6 E20
Hardest Fault (s-a-1) 7 A6
Minimum 1-Observability 0.1875 0.001519
Minimum 0-Observability 0.03125 0.007813