Jin-Fu Li. Department of Electrical Engineering. Jhongli, Taiwan
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1 Chpter 3 Testbility Mesures Jin-Fu Li Advnced Relible Systems (ARES) Lb. Deprtment of Electricl Engineering Ntionl Centrl University it Jhongli, Tiwn
2 Outline Purpose Controllbility nd Observbility SCOAP Mesures Summry Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 2
3 Purpose Assessments Difficulty of setting internl circuit lines to 0 or 1 by setting primry circuit inputs Difficulty of observing internl circuit lines by observing primry outputs Uses Anlysis of difficulty of testing internl circuit prts redesign or dd specil test hrdwre Guidnce for lgorithms computing test ptterns void using hrd-to-control lines Estimtion of fult coverge Estimtion of test length Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 3
4 Testbility Definition A fult is testble if there exists well-specified procedure to expose it, which is implementble with resonble cost using current technologies. A circuit it is testble t with respect to fult set when ech nd every fult in this set is testble Testbility Controllbility Observbility Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 4
5 Testbility Anlysis Involves circuit topologicl nlysis, but no test vectors nd no serch lgorithm Sttic nlysis Liner computtionl complexity Otherwise, is pointless-since we cn use utomtic t test pttern genertion e to cculte te Exct fult coverge Exct test vectors Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 5
6 Testbility Mesures Testbility (controllbility/observbility) mesures TMEAS SCOAP TESTSCREEN CAMELOT VICTOR COMET Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 6
7 SCOAP SCOAP Sndi Controllbility y Observbility y Anlysis y Progrm Metrics: higher numbers indicte more difficult to control or observe Combintionl mesureses CC0 difficulty of setting circuit line to logic 0 CC1 difficulty of setting circuit line to logic 1 CO difficulty of observing circuit line Sequentil mesures SC0 difficulty of setting circuit line to logic 0 SC1 difficulty of setting circuit line to logic 1 SO difficulty of observing circuit line Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 7
8 SCOAP Mesures Rnge of metrics Controllbility 1 (esiest) to infinity (hrdest) Observbility 1 (esiest) to infinity (hrdest) Controllbility clcultion Proceed from the inputs to the outputs Controllbility mesures of primry inputs (including brnches) ) re ll equl to 1 Observbility clcultion Strt t from the most observble bl nodes, the primry outputs, nd proceed bckwrd to the primry inputs Initilly, ll testbility mesures re set to infinity Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 8
9 An Exmple for Combintionl Ckt Consider 3-input AND gte s shown below CC1(Y)=CC1(A)+CC1(B)+CC1(C)+1 CC0(Y)=min{CC0(A),CC0(B),CC0(C)}+1 ( ), ( ), ( )} A B C The result is incremented by 1 so tht the vlue reflects the distnce to the PIs Working bredth-first from primry inputs (PIs) towrd primry outputs (POs), we clculte the CC of the output line of ech logic cell s function of the CCs of its input lines Y Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 9
10 SCOAP Mesures Summry If logic gte output is produced by setting only one input to controlling vlue Output controllbility=min(input controllbilities)+1 If logic gte output cn only be produced by setting ll inputs to non-controlling vlue Output t controllbility=sum(input S t controllbilities)+1 Controlling vlue & non-controlling vlue A B C Y A B C Y Controlling vlue = 0 Non-controlling vlue = 1 Controlling vlue = 1 Non-controlling vlue = 0 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 10
11 Controllbility Exmples b b b z z z CC0(z)=min (CC0(), CC0(b))+1 CC1(z)=CC1()+CC1(b)+1 CC0(z)=CC0()+CC0(b)+1 CC1(z)=min (CC1(), CC1(b))+1 CC0(z)=min (CC0()+CC0(b), CC1()+CC1(b))+1 CC1(z)=min (CC1()+CC0(b), CC0(b)+CC1(b))+1 z CC0(z)=CC1()+CC1(b)+1CC1()+CC1(b)+1 b CC1(z)=min (CC0(), CC0(b))+1 b z CC0(z)=min (CC1(), CC1(b))+1 CC1(z)=CC0()+CC0(b)+1 b z z CC0(z)=min (CC0()+CC1(b), CC1()+CC0(b))+1 CC1(z)=min i (CC0()+CC0(b), CC0(b) CC1(b)+CC1(b))+1CC1(b)) 1 CC0(z)=CC1()+1 CC1(z)=CC0()+1 CC0( ) 1 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 11
12 Observbility Exmples To observe gte input Observe output nd mke other input vlues non-controlling CO()=CO(z)+CC1(b)+1 CO(b)=CO(z)+CC1()+1 CO()=CO(z)+CC0(b)+1 CO(b)=CO(z)+CC0()+1 b CO()=CO(z)+min CO(z)+min (CC0(b), CC1(b))+1 CO(b)=CO(z)+min (CC0(), CC1())+1 b CO()=CO(z)+CC1(b)+1 CO(b)=CO(z)+CC1()+1 ) CC1( ) 1 b CO()=CO(z)+CC0(b)+1 CO(b)=CO(z)+CC0()+1 CO()=CO(z)+min (CC0(b), CC1(b))+1 CO(b)=CO(z)+min (CC0(), CC1())+1 CO()=CO(z)+1 ) Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 12 b b b z z z z z z z
13 Observbility Exmples To observe fnout stem Observe it through brnch with best observbility CO()=min (CO(), CO(b),, CO(zn)) z1 z2 zn CO(stem)=min(CO(brnches)) ( ( )) Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 13
14 Controllbility Clcultion level1 PI1 PI2 1) (2,2) (CC0, CC1) PO0 PO1 PI3 (2,2) PO2 PI1 PI2 level2 (2,2) (2,2) PI3 (3,5) (3,5) PO0 PO1 PO2 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 14
15 Controllbility Clcultion 1) 1) PI1 (CC0, CC1) (2,6) PI2 (2,7) PO0 (2,2) (3,5) (2,7) PO1 level3 PO2 PI3 (2,2) (3,5) level4 PI1 PI2 (2,2) (2,2) PI3 (3,5) (3,5) (2,6) (2,7) (2,7) PO0 (5,7) PO1 PO2 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 15
16 Observbility Clcultion level1 PI1 PI2 (2,2) (3,5) PI3 (3,5) (2,2) 3 (2,6) (2,7) (2,7) 3 0 PO0 (5,7) 0 0 PO1 PO2 level2 PI PI2 (2,2) PI3 (2,2) 2) 6 2 (3,5) (3,5) 3 (2,6) (2,7) 0 (2,7) 3 (5,7) 0 0 PO0 PO1 PO2 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 16
17 Observbility Clcultion PI PI2 level3 3 PI3 (2,2) 6 2 (2,2) (3,5) 3 (3,5) 3 3 (2,6) (2,7) (2,7) 0 PO0 (5,7) 0 0 PO1 PO2 PI1 4 level PI2 4 (2,2) 3 2) PI3 (2,2) (3,5) (3,5) 3 3 (2,6) (2,7) 0 (2,7) (5,7) 0 0 PO0 PO1 PO2 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 17
18 Sequentil Mesure Difference Combintionl Increment CC0, CC1, CO whenever you pss through gte, either forwrds or bckwrds Sequentil Increment SC0, SC1, SO only when you pss through flip-flop, either forwrds or bckwrds, to Q, Q, D, C, SET, or RESET Both Must iterte on feedbck loops until controllbilities stbilize Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 18
19 D Flip-Flop Exmples Consider D flip flop s shown below D Q C RESET The combintionl nd sequentil difficulties of controlling Q to 1 re CC1(Q)=CC1(D)+CC1(C)+CC0(C)+CC0(RESET) CC1(D) CC1(C) CC0(C) CC0(RESET) SC1(Q)=SC1(D)+SC1(C)+SC0(C)+SC0(RESET) +1 CC1 mesures how mny lines in the circuit must be set to mke Q s 1 SC1 mesures how mny flip-flops in the circuit must be clocked to set Q to 1 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 19
20 D Flip-Flop Exmples Set Q to 0 CC0(Q)=min (CC1(RESET)+CC0(C), ( ( ), CC0(D)+ CC1(C)+CC0(C)+CC0(RESET)) SC0(Q)=min (SC1(RESET)+SC0(C), SC0(D)+ SC1(C)+SC0(C)+SC0(RESET)+1 Observbility of D CO(D)=CO(Q)+CC1(C)+CC0(C)+CC0(RESET) SO(D)=SO(Q)+SC1(C)+SC0(C)+SC0(RESET)+ (Q) ( ) ( ) ( ) 1 Observbility of RESET CO(RESET)=CO(Q)+CC1(Q)+CC0(C)+CC1(RES ET) Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 20
21 D Flip-Flop Exmples SO(RESET)= CO(Q)+CC1(Q)+CC0(C) + CC1(RESET)+1 Observbility of C CO(C)=min [CO(Q)+CC0(RESET)+CC1(C)+ CC0(C)+CC0(D)+CC1(Q), CO(Q)+CC1(RESET) +CC1(C)+CC0(C)+CC1(D)] SO(C)=min [SO(Q)+SC0(RESET)+SC1(C)+ SC0(C)+SC0(D)+SC1(Q), ( ) (Q), SO(Q)+SC1(RESET)+SC1(C)+SC0(C)+SC1(D)] +1 Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 21
22 Algorithm 1. For ll PIs, CC0=CC1=1 nd SC0=SC1=0 2. For ll other nodes, CC0=CC1=SC0=SC1=infinity 3. Go from PIs to POs, using CC nd SC equtions to get controllbilities -- iterte on loops until SC stbilizes -- convergence gurnteed 4. For ll POs, set CO = SO =infinity 5. Work from POs to PIs, Use CO, SO, nd controllbilities to get observbilities 6. Fnout stem (CO, SO) = min brnch (CO, SO) 7. If CC or SC (CO or SO) is infinity, tht node is uncontrollble (unobservble) Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 22
23 Sequentil SCOAP Mesures Initiliztion R 1) 1) (CC0,CC1) [SC0,SC1] SC1] 0] D Q Z (inf,inf) [inf,inf] (inf,inf) [inf,inf] D Q (inf,inf) [inf,inf] CL Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 23
24 Sequentil SCOAP Mesures After one itertion R 1) 1) (2,inf) [0,inf] (4,inf) [0,inf] (inf,inf) [inf,inf] 0] (2,2) (inf,inf) [inf,inf] (3,inf) [0,inf] D Q D Q (4,inf) [0,inf] Z (inf,inf) [inf,inf] (inf,inf) [inf,inf] CL (7,inf) [0,inf] Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 24
25 Sequentil SCOAP Mesures After two itertions R 1) 1) (2,14) [0,1] (4,inf) [0,inf] (5,inf) [1,inf] 0] (2,2) (inf,6) [inf,1] (3,9) [0,1] D Q D Q (4,inf) [0,inf] Z (9,inf) [1,inf] (5,inf) [1,inf] CL (7,10) [0,1] Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 25
26 Sequentil SCOAP Mesures After three itertions R 1) 1) (2,14) [0,1] (4,27) [0,3] (5,11) [1,2] 0] (2,2) (12,6) [2,1] (3,9) [0,1] D Q D Q (4,27) [0,3] Z (9,17) [1,2] (5,11) [1,2] CL (7,15) [0,1] Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 26
27 Sequentil SCOAP Mesures After stbiliztion R 1) 1) (2,14) [0,1] (4,27) [0,3] (5,11) [1,2] 0] (2,2) (12,6) [2,1] (3,9) [0,1] D Q D Q (4,27) [0,3] Z (9,17) [1,2] (5,11) [1,2] CL (7,15) [0,1] Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 27
28 Sequentil SCOAP Mesures Observbility mesures R 261) 3 1)53 3 (2,14) 40 [0,1] 2 (4,27) 0 [0,3] 0 (5,11) 22 [1,2] ] 3 (2,2) 25 3 (12,6) 21 [2,1] (3,9) 24 [0,1] 3 D Q D Q (4,27) 0 [0,3] Z 0 (9,17) 10 [1,2] ] 4 (5,11) 22 [1,2] 2 CL (7,15)12 [0,1] Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 28
29 Summry Testbility pproximtely mesures Difficulty of setting circuit lines to 0 or 1 Difficulty of observing internl circuit lines Uses Anlysis of difficulty of testing internl circuit prts Redesign circuit hrdwre or dd specil test hrdwre where mesures show bd controllbility or observbility Guidnce for lgorithms computing test ptterns void using hrd-to-control lines Estimtion of test vector length Estimtion of fult coverge 3-5 % error Advnced Relible Systems (ARES) Lb. Jin-Fu Li, EE, NCU 29
Jin-Fu Li. Department of Electrical Engineering National Central University Jhongli, Taiwan
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