This Article 
 Bibliographic References 
 Add to: 
A Diagnosis Algorithm for Constant Degree Structures and Its Application to VLSI Circuit Testing
April 1995 (vol. 6 no. 4)
pp. 363-372

Abstract—A simple diagnosis algorithm is presented for constant degree systems such as rectangular grids connected as tori. The algorithm determines the status of a unit according to the size of its faction, a cluster of units that call each other fault-free but outsiders faulty. Almost all units are correctly identified with this algorithm under a binomial failure distribution even when the probability of failure is rather high. The complexity of the algorithm is $O(n),$ where $n$ is the number of units in a constant degree system. The application of the algorithm to production testing of VLSI chips is also considered. With a test board that houses a large number of chips to be tested, all the chips can be tested in parallel in a way that they test each other and the test outcomes, not necessarily correct, are reported to a host system for analysis. The actual status of each chip is determined by using this new diagnosis algorithm. The above chip screening process can be repeated for higher accuracy. It is shown that no more than two steps are needed in most real situations. Compared with testing by test equipment that usually tests only one chip at a time, the saving of test time and the test equipment cost could be significant with our approach.

Index Terms—Probabilistic diagnosis, system level diagnosis, diagnosis algorithm, production testing, VLSI testing.

[1] F. P. Preparata, G. Metze, and R. T. Chien,“On the connection assignment problem of diagnosable systems,”IEEE Trans. Electron. Comput.,vol. EC-16, pp. 848–854, Dec. 1967.
[2] A.K. Somani, V.K. Agarwal, and D. Avis, "A Generalized Theory for System Level Diagnosis," IEEE Trans. Computers, vol. 36, no. 5, pp. 538-546, May 1987.
[3] E. Scheinerman, "Almost Sure Fault-Tolerance in Random Graphs," SIAM J. Computing, vol. 16, pp. 1,124-1,134, 1987.
[4] D. M. Blough,Fault Detection and Diagnosis in Multiprocessor Systems,Ph.D. dissertation, The Johns Hopkins Univ., Baltimore, MD, 1988.
[5] D. M. Blough, G. F. Sullivan, and G. M. Masson,“Almost certain diagnosis for sparsely interconnected faulty systems,”inDigest FTCS-18,pp. 260–271, June 1988.
[6] D. M. Blough, G. F. Sullivan, and G. M. Masson,“Fault diagnosis for sparsely interconnected multiprocessor systems,”inDigest FTCS-19,pp. 62–69, 1989.
[7] D. M. Blough and A. Pelc,“Reliable diagnosis and repair in constant-degree multiprocessor systems,”inDigest FTCS-20, pp. 316–323, June 1990.
[8] D. Fussell and S. Rangarajan,“Probabilistic diagnosis of multiprocessor systems with arbitrary connectivity,”inDigest FTCS-19,pp. 560–565, 1989.
[9] S. Rangarajan and D. Fussell,“Probabilistic diagnosis algorithm tailored to system topology,”inDigest FTCS-21,pp. 230–237, 1991.
[10] A. Dahbura, K. Sabnani, and L. King, "The Comparison Approach to Multiprocessor Fault Diagnosis," IEEE Trans. Computers, vol. 36, no. 3, pp. 373-378, Mar. 1987.
[11] S. Lee and K. G. Shin,“Optimal multiple syndrome probabilistic diagnosis,”inDigest FTCS-20,June 1990, pp. 324–330.
[12] P. Berman and A. Pelc,“Distributed probabilistic fault diagnosis for multiprocessor systems,”inDigest FTCS-20,June 1990, pp. 340–346.
[13] S. Rangarajan, D. Fussell, and M. Malek,“Built-in testing of integrated circuit wafers,”IEEE Trans. Comput.,vol. 39, pp. 195–205, Feb. 1990.
[14] L. LaForge, K. Huang, and V. K. Agarwal,“Almost sure diagnosis of almost every good element,”IEEE Trans. Comput.,vol. C-43, pp. 295–305, Mar. 1994.
[15] E.B. Eichelberger and T.W. Williams, "A Logic Design Structure for LSI Testability," Proc. 14th Design Automation Conf., IEEE Press, Piscataway, NJ, 1977, pp. 462-468.
[16] B. Nadeau-Dostie, P. S. Wilcox, and V. K. Agarwal,“A scan-based BIST technique using pair-wise compare of identical components,”inProc. 4th CSI/IEEE Int. Symp. VLSI Design,Jan. 1991.
[17] F. Barsi, F. Grandoni, and P. Maestrini,“A theory of diagnosability of digital systems,”IEEE Trans. Comput.,vol. C-25, pp. 585–593, June 1976.
[18] A. O. Allen,Probability, Statistics, and Queueing Theory with Computer Science Applications.New York: Academic, 1978.

Kaiyuan Huang, Vinod K. Agarwal, Laurence LaForge, K. Thulasiraman, "A Diagnosis Algorithm for Constant Degree Structures and Its Application to VLSI Circuit Testing," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 4, pp. 363-372, April 1995, doi:10.1109/71.372790
Usage of this product signifies your acceptance of the Terms of Use.