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<p><it>Abstract—</it>In the system-level fault diagnosis area, the fundamental problem of characterizing sequentially <math><tmath>t</tmath></math>-diagnosable systems in the PMC model has remained open for more than two decades. We resolve this problem by providing a complete characterization of such systems. Our solution to the characterization problem leads to the correct identification of optimal sequentially <math><tmath>t</tmath></math>-diagnosable <math><tmath>D_{\delta,k}</tmath></math> systems. Given a set of <math><tmath>n</tmath></math> units where <math><tmath>n = 2t + 1</tmath></math>, an optimal <math><tmath>D_{\delta,k}</tmath></math> system can be constructed with just <math><tmath>n(\lfloor(t + 2)/3\rfloor)</tmath></math> tests, rather than <math><tmath>n(\lfloor t/2\rfloor + 1)</tmath></math> tests—a previously misjudged bound. An efficient algorithm for identifying the set of faulty units in a sequentially <math><tmath>t</tmath></math>-diagnosable <math><tmath>D_{\delta,k}</tmath></math> system is given along the line of the proposed characterization, which is linear with respect to the number of tests in the system.</p><p><it>Index Terms—</it>Consistent fault sets, <math><tmath>$D_{\delta,k}$</tmath></math> systems, fault diagnosis, PMC model, sequentially diagnosable systems, syndrome, test assignment.</p>
Shi-ze Huang, Jie Xu, "Sequentially t-Diagnosable Systems: A Characterization and Its applications", IEEE Transactions on Computers, vol. 44, no. , pp. 340-345, February 1995, doi:10.1109/12.364544
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