Algorithms for sequential fault diagnosis

Date of Completion

January 1996


Engineering, Electronics and Electrical|Computer Science




In this thesis, optimal and near-optimal algorithms are developed for various classes of single fault test-sequencing algorithms. We first present a novel multi-signal modeling methodology that alleviates some of the model validation problems of traditional dependency modeling, while achieving the same diagnostic resolution. We discuss the failure probability estimation and reachability analysis algorithms for dependency and multi-signal models. We also present efficient static analysis algorithms to rapidly evaluate topological testability deficiencies of a system based on the results of reachability analysis and directed graph processing, including the determination of ambiguity groups of faults, redundant tests, hidden and masking false failure sets.^ Next, we present an array of optimal and near-optimal test-sequencing algorithms that incorporate real-world testing features such as precedence constraints on tests, setup operations for tests, and traveling costs for tests. We develop efficient implementation techniques to speed up the test sequencing algorithms, including bit-compacted representation of the fault dictionary (D-matrix) and a fast, efficient, in-place transposition algorithm for the compacted D-matrix. The algorithms have been used for developing diagnostic strategies for systems having 50,000 failures and 50,000 test points.^ We extend these algorithms to the case of imperfect tests, where tests have false alarms and missed detections. Specifically, we develop a dynamic programming formulation for the problem of imperfect test sequencing and obtain closed form solutions for systems of special structure. We present practical test sequencing algorithms based on Information Gain and Certainty Equivalence, and compare them with the optimal DP method for small systems. We also present top-down graph search techniques which enabled us to construct static diagnostic strategies for large systems (up to 2000 faults and 2000 unreliable tests). Finally, we consider the various test sequencing problems that arise in the Design for Testability including Minimax test sequencing, test sequencing with a constraint on the expected testing time, test sequencing with a constraint on the number of tests used, and minimal storage test sequencing, for which we derive optimal and near-optimal top-down graph search solution algorithms. ^