A Model-Based Active Testing Approach to Sequential Diagnosis A Model-Based Active Testing Approach to Sequential Diagnosis

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive diagnosis), measuring additional variables (probing) or executing additional tests (sequential testing/test sequencing). In this paper we combine the above approaches, as well as from Automated Test Pattern Generation (ATPG) and Model-Based Diagnosis (MBD) in a framework called Fractal (FRamework for ACtive Testing ALgorithms). In active testing, in addition to the traditional for MBD inputs and outputs, we also discern control variables, which allows automatic generation of tests and test dictionaries from models. We attack the computationally hard problem of computing optimal control assignments (as defined in Fractal) with a greedy approximation algorithm called Fractal. We model the decrease in the number of remaining minimal cardinality diagnoses produced by an active testing algorithm as a geometric decay process and measure the algorithm’s optimality in terms of the decay rate. We compare the optimality of Fractal to that of two more Fractal algorithms: Fractal and Fractal. Fractal is based on ATPG and sequential testing while Fractal, although not an active testing algorithm, provides a baseline for comparing the lower bound on the number of reachable diagnoses for the Fractal algorithms. Fractal employs approximation approaches, such as stochastic sampling for computing the expected number of remaining minimal cardinality diagnoses and greedy search for computing the optimal control assignment, which results in a computationally efficient method. We empirically evaluate the trade-offs of the three Fractal algorithms by performing extensive experimentation on the ISCAS85/74XXX benchmark of combinational circuits.