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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.

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Testability Measure

Keys To Testability

1. Controllability

2. Observability

3. Predictability

Testability = Controllability + Observability + Predictability

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Testability Measure

Design for Testability

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

Circuit Size

DFT

Unconstrained

Test Cost

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Testability Measure

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]

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Testability Measure

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.

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Testability Measure

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.

CY CTFn

CYj ii

n

z x 1

1

,

.

.

.

.

.

.DUT

ZZZ

x1x2xn

12

m

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Testability Measure

Stephenson & Grason,s Approach

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

0 CTF 1.

Each output controllability is assigned the same

value.

CTF

mj j

nj

m N N

11

0 1

21

.

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Testability Measure

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.

OY OTFm

OYi jj

m

x z 1

1

,

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Testability Measure

Stephenson & Grason,s Approach

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

NSi also 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.

OTFn

in

i

N NS1

21

.

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Testability Measure

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 .

CYCY s

k

1 log.

OY s OY ii

k

b 1 1

1

,

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Testability Measure

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.

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Testability Measure

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.

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Testability Measure

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.

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Testability Measure

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

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Testability Measure

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,.

N

P

RQ

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Testability Measure

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 88 88

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Testability Measure

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.

CTFN N

N N

10 1

0 1

( ) ( )

( ) ( ),

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Testability Measure

CAMELOT

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

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

CTF(XORn) = 1.

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Testability Measure

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.

J

C

KR

P

Q

Q

Q

Q

J

K

PRESET

RESET

SN7476

+

+

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Testability Measure

CAMELOT

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

where

f CYs inputsi j

CY i

CY j

( ( )) ( ( :

(

1 async inputs) +

: clock) (CY : sync inputs)).

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Testability Measure

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.

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Testability Measure

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.

OTF I O( ) ,

N(SP:I O)

N(SP:I O) N(IP:I O)

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Testability Measure

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).

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Testability Measure

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

CY av

i jCY i

CY CY j

( ) ( ( :

( : :

1 async supporting inputs)

clock) ( sync supporting inputs)) .

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Testability Measure

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).

OY stem OY branchii

k

( ( )) = 1- .11

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Testability Measure

CAMELOT

Testability

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

TY(circuit) = (TY(nodes))

No. of nodes .

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Testability Measure

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;

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Testability Measure

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.

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Bibliography(1) J. E. Stephenson and J. Grason, ,,A testability measure for register transfer level di

gital 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.

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(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.

Bibliography