An Estimate of the Length of Diagnostics Tests

The diagnosis of digital systems can be conveniently modelled as the recognition of distinct binary error-free patterns, Specifically, if for a given fault condition, the pass or fail responses to a set of applied tests are recorded as a column of a matrix M, a test schedule of length k is a subset of the rows of M which preserves column distinguishability. Since the determination of a minimal test schedule is a formidable problem for moderately complex networks, it appears desirable to have guidlines for the evaluation of heuristically or suboptimally computed test schedules. One such guideline is the median kmin of the minimal test schedule kmin over the set of all binary matrices M: while in general [log2m] ¿ kmin ¿ m - 1, this paper shows that kmin < [2 log2m], that is, for most practical cases, kmin is much closer to the lower bound [log2m] than to the upper bound (m - 1).