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Testability Analysis: Understanding Controllability and Observability in ECE 255, Study notes of Spanish Language

University of California - Santa BarbaraSpanish Language

An overview of testability analysis, a method used to evaluate the controllability and observability of circuits. The analysis is simpler than test generation or fault simulation and is based on the difficulty of controlling logical values on nodes from primary inputs (pis) and observing nodal values at primary outputs (pos). The scoap program, which computes numerical measures for combinational and sequential controllability and observability of each node. It also discusses the importance of considering correlation errors and the applications of testability measures in guiding test point selection and search in test generation.

Typology: Study notes

Pre 2010

Uploaded on 08/31/2009

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Testability Analysis ECE 255 1 Testability Analysis ECE 255 2
Testability Analysis
• To give an early warning about the testing problems
that lie ahead.
• It provides guidance in improving the testability
• To be useful, testability analysis should be simpler
than actual test generation or fault simulation
– Topological analysis: only the structure of ckt is
analyzed. No test vectors are generated.
– Linear complexity: The analysis should be linear (
or almost linear) in circuit size.
Testability Analysis ECE 255 3
SCOAP (Sandia Controlability/
Observability Analysis program)
• Goldstein, IEEE Trans. on CAS, 1979
• Assume that the testability of a circuit is related to the
difficulty of controlling the logical values on nodes from
PIs &observing nodal values at POs
• It provides numeric measures of the difficulty
• SCOAP computes six number for each node.
CC0(N) & CC1(N): combinational 0 & 1 controllability
of node N.
SC0(N) & SC1(N): sequential 0 & 1 controllability of node N
CO(N): combinational observability
SO(N): sequential observability
Testability Analysis ECE 255 4
•CC
0 & CC1(N): the number of combinational nodes that
must be assigned values to justify a 0 or a 1 on node N.
SC0& SC1(N): the number of sequential nodes that
must set to justify a 0 or a 1 on node N.
X
1
X
2
Y
CC0(Y) = min[ CC0(X1), CC0(X2)] + 1
CC1(Y) = CC1(X1) + CC1(X2) + 1
SC0(Y) = min[SC0(X1), SC0(X2)]
SC1(Y) = SC1(X1) + SC1(X2)
Testability Analysis ECE 255 5
CC0(Y) = CC0(X1) + CC0(X2) + CC0(X3) + 1
CC1(Y) = min[CC1(X1), CC1(X2), CC1(X3)] + 1
SC0(Y) = SC0(X1) + SC0(X2) + SC0(X3)
SC1(Y) = min[SC1(X1), SC1(X2), SC1(X3)]
• The observabiliy of X1is a function of the output
obsevability and of the cost of holding all other inputs at 0.
CO(X1) = CO(Y) + CC0(X2) + CC0(X3) + 1
&SO(X
1) = SO(Y) + SC0(X2) + SC0(X3)
• Boundary conditions:
(1) CC0= CC1= 1 & SC0= SC1= 0 for all PIs
(2) CO = SO= 0 for all POs
X
1
X
2
Y
X
3
Testability Analysis ECE 255 6
Controllability Examples
pf3

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Testability Analysis ECE 255 1 Testability Analysis ECE 255 2

Testability Analysis

  • To give an early warning about the testing problems that lie ahead.
  • It provides guidance in improving the testability
  • To be useful, testability analysis should be simpler than actual test generation or fault simulation - Topological analysis: only the structure of ckt is analyzed. No test vectors are generated. - Linear complexity: The analysis should be linear ( or almost linear) in circuit size.

Testability Analysis ECE 255 3

SCOAP (Sandia Controlability/

Observability Analysis program)

  • Goldstein, IEEE Trans. on CAS, 1979
  • Assume that the testability of a circuit is related to the difficulty of controlling the logical values on nodes from PIs &observing nodal values at POs
  • It provides numeric measures of the difficulty
  • SCOAP computes six number for each node. CC^0 (N) & CC^1 (N): combinational 0 & 1 controllability of node N. SC^0 (N) & SC^1 (N): sequential 0 & 1 controllability of node N CO(N): combinational observability SO(N): sequential observability Testability Analysis ECE 255 4
  • CC^0 & CC^1 (N): the number of combinational nodes that must be assigned values to justify a 0 or a 1 on node N. SC^0 & SC^1 (N): the number of sequential nodes that must set to justify a 0 or a 1 on node N. X 1 X 2

Y

CC^0 (Y) = min[ CC^0 (X 1 ), CC^0 (X 2 )] + 1 CC^1 (Y) = CC^1 (X 1 ) + CC^1 (X 2 ) + 1 SC^0 (Y) = min[SC^0 (X 1 ), SC^0 (X 2 )] SC^1 (Y) = SC^1 (X 1 ) + SC^1 (X 2 )

Testability Analysis ECE 255 5

CC^0 (Y) = CC^0 (X 1 ) + CC^0 (X 2 ) + CC^0 (X 3 ) + 1

CC^1 (Y) = min[CC 1 (X 1 ), CC^1 (X 2 ), CC^1 (X 3 )] + 1 SC^0 (Y) = SC^0 (X 1 ) + SC^0 (X 2 ) + SC^0 (X 3 ) SC^1 (Y) = min[SC^1 (X 1 ), SC^1 (X 2 ), SC^1 (X 3 )]

  • The observabiliy of X 1 is a function of the output obsevability and of the cost of holding all other inputs at 0. CO(X 1 ) = CO(Y) + CC^0 (X 2 ) + CC^0 (X 3 ) + 1 & SO(X 1 ) = SO(Y) + SC^0 (X 2 ) + SC^0 (X 3 )
  • Boundary conditions: (1) CC 0 = CC^1 = 1 & SC^0 = SC^1 = 0 for all PIs (2) CO = SO= 0 for all POs

X 1 X 2 Y X 3

Testability Analysis ECE 255 6

Controllability Examples

Testability Analysis ECE 255 7

More Controllability Examples

Testability Analysis ECE 255 8

Observability Examples

To observe a gate input: Observe output and make other input values non-controlling

Testability Analysis ECE 255 9

More Observability Examples

To observe a fanout stem: Observe it through branch with best observability

Testability Analysis ECE 255 10

Error Due to Stems &

Reconverging Fanouts

SCOAP measures wrongly assume that controlling or

observingx,y,z are independent events

  • CC0 (x), CC0 (y), CC0 (z) correlate
  • CC1 (x), CC1 (y), CC1 (z) correlate
  • CO (x), CO (y), CO (z) correlate x

y

z

Testability Analysis ECE 255 11

Correlation Error Example

  • Exact computation of measures is NP-Complete and impractical
  • Italicized (green) measures show correct values – SCOAP measures are in red or bold CC0,CC1 (CO)

x

y z

1,1(6) 1,1(5, ) 1,1(5) 1,1(4,6)

1,1(6) 1,1(5, )

6,2(0) 4,2(0)

2,3(4) 2,3(4, ) (5) (4,6) (6)

(6) 2,3(4) 2,3(4, (^8) )

8 8

8 Testability Analysis ECE 255 12

Applications of Testability Measures

  • Can be used to guide the selection of test points for improving testability
  • Can be used to guide the search in test generation
    • For example, used to determine “hardest” & “easiest” inputs in backtrace of PODEM
  • Note that testability measures are only approximate.
    • Reconvergent fanouts cause inaccuracy.