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Testability Measure. What do we mean when we say a circuit is testable? Definition: A fault is testable if there exists a well-specified procedure to expose it within a reasonable cost. A circuit is testable if each and every fault in its specified fault set is testable. Keys To Testability.

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Testability measure

Testability Measure

What do we mean when we say a circuit is testable?

Definition: A fault is testable if there exists a well-specified procedure to expose it within a reasonable cost. A circuit is testable if each and every fault in its specified fault set is testable.


Keys to testability

Keys To Testability

1. Controllability

2. Observability

3. Predictability

Testability = Controllability + Observability + Predictability


Design for testability

Design for Testability

To constrain the design to make test generation and diagnosis easier.


Testability controllability observability measures

Testability (Controllability/Observability) Measures

1. TMEAS [Stephenson & Grason, FTCS, 1976; DAC,

1979]

2. SCOAP [Goldstein, IEEE TCAS-26(9), 1979]

3. TESTSCREEN [Kovijanic 1979]

4. CAMELOT [Bennetts et al., 1980]

5. VICTOR [Ratiu et al., ITC, 1982]


Stephenson grason s approach

Stephenson & Grason,s Approach

Developed for register-transfer-level (RTL) circuits, but can also be applied at the gate level.

The measures are normalized between 0 and 1 to reflect the ease of controlling and observing the internal nodes.


Stephenson grason s approach1

Stephenson & Grason,s Approach

1. For each signal line s, we denote the controllability of s as CY(s) and the observability of s as OY(s).

2. The values for the CYs and the OYs of all the signal lines are derived by solving a system of simultaneous equations with the CYs and the OYs as unknowns.

The expression used to calculate CY for each output

zj is

where CTF is the controllability transfer factor of the

component.


Stephenson grason s approach2

Stephenson & Grason,s Approach

Let Nj(0) and Nj(1) be the numbers of input combinations for which zjhas value 0 and 1, respectively. Then

0 CTF 1.

Each output controllability is assigned the same

value.


Stephenson grason s approach3

Stephenson & Grason,s Approach

The expression used to calculate OY for each input xi is

where OTF is the observability transfer factor of the component.


Stephenson grason s approach4

Stephenson & Grason,s Approach

Let NSibe the numbers of input combinations for which the change of xi results in a change of output. Then

NSialso means the number of input combinations that can

sensitize a path from xi to the output.

The OTF measures the probability that a faulty value at any

input will propagate to the outputs.

0 OTF 1

Each input observability is assigned the same value.


Stephenson grason s approach5

Stephenson & Grason,s Approach

3. Fanouts: Let s be a fanout stem and k be the number of its branches. Then the CYs of each fanout branch is

The observability of the fanout stem s is

where bi are fanout branches of s.

4. Sequential components: Sequential components are modeled by adding feedback links around the components that represent internal states .


Goldstein s approach scoap

Goldstein,s Approach---SCOAP

Sandia Controllability Observability Analysis

Program.

The measures reflect the difficulty of controlling and observing the internal nodes; higher numbers indicate more difficult to control or observe.

The measures are, in a sense, minimum cost values for controlling and observing.


Goldstein s approach scoap1

Goldstein,s Approach---SCOAP

Combinational 1- and 0-controllabilities of Y = AND(A,B,C):

CC1(Y) =CC1(A) + CC1(B) + CC1(C) + 1;

CC0(Y) = min{CC0(A),CC0(B),CC0(C)} + 1.

The result is incremented by 1 so that the number reflects (in part) the distance to the PIs.

Working breadth-first from PIs toward POs, we calculate the CC of the output line of each logic cell as a function of the CCs of its input lines.


Goldstein s approach scoap2

Goldstein,s Approach---SCOAP

The sequential controllability provides an estimate of the number of time frames needed to provide a 0 or 1 at a particular node.

For Y=XOR(A, B):

CC0(Y) = min{CC0(A) +CC0(B), CC1(A) + CC1(B)} + 1

CC1(Y) = min{CC0(A) + CC1(B), CC1(A) + CC0(B)} + 1

SC0(Y) = min{SC0(A) + SC0(B), SC1(A) + SC1(B)}

SC1(Y) = min{SC0(A) + SC1(B), SC1(A) + SC0(B)}

When computing the sequential controllabilities through combinational circuits, the values are not incremented---no additional time frames needed.


Goldstein s approach scoap3

Goldstein,s Approach---SCOAP

When deriving equations for sequential circuits, SCs are incremented by 1, but CCs are not incremented.

Positive edge-triggered DFF with active low reset:

CC0(Q) = min{CC0(R), CC1(R) + CC0(D) + CC0(C) + CC1(C)}

CC1(Q) = CC1(R) + CC1(D) + CC0(C) + CC1(C)

SC0(Q) = min{SC0(R), SC1(R) + SC0(D) + SC0(C) + SC1(C)} + 1

SC1(Q) = SC1(R) + SC1(D) + SC0(C) + SC1(C) + 1


Goldstein s approach scoap4

Goldstein,s Approach---SCOAP

Observabilities:

CO(P) = CO(N) + CC1(Q) + CC1(R) + 1

SO(P) = SO(N) + SC1(Q) + SC1(R)

Positive edge-triggered DFF with active low reset:

CO(R) = CO(Q) + CC1(Q) + CC0(R)

SO(R) = SO(Q) + SC1(Q) + SC0(R) +1

To watch R, then have to watch Q and drive FF to ,1, and then reset it to ,0,.


Goldstein s approach scoap5

Goldstein,s Approach---SCOAP

May define testability as follows:

T(l/o) = CC1(l) + CO(l)

T(l/1) = CC0(l) + CO(l)

Initial Condition

Node

PI

PO

IN

CC0 CC1 SC0 SC1 CO SO

1 1 1 1 1 1

- - - - 0 0

8

8

8

8

8

8


Camelot

CAMELOT

Controllability:

CY(output) = CTF(output) x f(CYs(inputs));

controllability transfer factor

where N(0) and N(1) are the numbers of input combinations for which the output has value 0 and 1, respectively.


Camelot1

CAMELOT

CTF(NOT) = 1; CTF(NAND2) = 1/2;

CTF(NAND3) = 1/4; CTF(ORn) =1/2n-1

CTF(XORn) = 1.


Camelot2

CAMELOT

Q+ = [(JQ + KQ)C + QC]PR + P

= JQCPR + KQCPR + QCPR + P

Minterms in the final expression is 40; 24 invalid states; 16 common terms in this set of invalid states and the set of minterms derived above. N(1) = 40 - 16 = 24, and N(0) = (26 - 24) - N(1) = 40 - 24 = 16. CTF = 1- (24-16)/40 = 0.8. By symmetry, the CTF for Q+ is also 0.8.


Camelot3

CAMELOT

CY(output) = CTF(output) x f(CYs(input)),

where


Camelot4

CAMELOT

Observability

OY(at output) = OTF x OY(at input) x g(CYs(supporting inputs)),

Where OTF is the observability transfer factor of the component for the input concerned.


Camelot5

CAMELOT

where N(SP:I-O) is the total number of distinct sensitive paths from I to O, and N(IP:I-O) is the total number of insensi- tive paths.


Camelot6

CAMELOT

OTF(NOT) = 1;

OTF(NAND2) = 1/2 for each input;

OTF(NAND3) = 1/4 for each input (1 PDC & 3 NPDCs);

OTF (XORn) = 1 for each input (0 NPDC).


Camelot7

CAMELOT

Let OY(A-B) denote the observability of node A at node B, then

OY(I-O) = OTF(I-O) x OY(I-I) x CY(av),

where


Camelot8

CAMELOT

Fanouts:

For a reconvergent fanout, select the shortest I-O path which is to be sensitized (while others are blocked), which is more likely to result in a higher OY.

For feedback paths, the strategy is similar to that for reconvergent fanouts with unequal path lengths (i.e., select the shortest path).


Camelot9

CAMELOT

Testability

TY(node) = CY(node) x OY(node).


Camelot10

CAMELOT

CAMELOT()

1. input, check, and initialize circuit;

2. calculate nodal CY values from PIs

to POs;

3. calculate nodal OY values from POs

to PIs;

4. calculate nodal TY values;

5. calculate TY and interpret the results;


Importance of testability measures

Importance of Testability Measures

They can guide the designers to improve the testability of their circuits.

Test generation algorithms using heuristics usually apply some kind of testability measures to their heuristic operations (e.g., in making search decisions), which greatly speed up the test generation process.


Bibliography

Bibliography

(1) J. E. Stephenson and J. Grason, ,,A testability measure for register transfer level digital circuits,,, in Proc. Int. Symp. Fault tolerant Computing (FTCS), (Pittsburgh, PA), pp. 101-107, June 1976.

(2) J. Grason, ,,TMEAS-a testability measurement program,,, in Proc. IEEE/ACM Design Automation Conf. (DAC) , vol. 26, no. 9, pp. 156-161, 1979.

(3) L. H. Goldstein, ,,Controllability/observability analysis for digital circuits,,, IEEE Trans. Circuits and Systems, vol. 26, no. 9, pp. 685-693, Sept. 1979.

(4) P. G. Kovijanic, ,,Testability analysis,,, in Proc. IEEE Semiconductor Test Conf., pp. 310-316, 1979.

(5) P. G. Kovijanic, ,,Computer-aided testability analysis,,, in Proc. IEEE Autotestcon, pp. 292-294, 1979.

(6) R. G. Bennetts, C. M. Maunder, and G. D. Robinson, ,,CAMELOT:a computer-aided measure for logic testability,,, IEE Proc. Pt. E, vol. 128, no. 5, pp. 177-189, 1981.

(7) R. G. Bennetts, Design of Testable logic Circuits. Reading, MA: Addison-Wesley, 1984.


Bibliography

(8) I. M. Ratiu, A. Sangiovanni-Vincentelli, and D. O. Pederson, ,,VICTOR: a fast VLSI testability analysis program,,, in Proc. Int. Test Conf. (ITC), (Philadelphia, PA), pp. 397-401, Nov. 1982.

(9) W. C. Berg and R. C. Hess, ,,COMET : a testability analysis and design modification package,,, in Proc. Int. Test Conf. (ITC), (Philadelphia, PA), pp. 364-378, Nov. 1982.


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