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Test sequencing is a binary identification problem wherein one needs to develop a minimal expected cost testing procedure to determine which one of a finite number of possible failure sources, if any, is present. The problem can be solved optimally using dynamic programming or AND/OR graph search methods (AO*, CF, and HS). However, for large systems, the associated computation with dynamic programming or AND/OR graph search methods is substantial, due to the rapidly increasing number of OR nodes (denoting ambiguity states) and AND nodes (denoting tests) in the search graph. In order to overcome the computational explosion, the one-step or multistep lookahead heuristic algorithms have been developed to solve the test sequencing problem. In this paper, we propose to apply rollout strategies, which can be combined with the one-step or multistep lookahead heuristic algorithms, in a computationally more efficient manner than the optimal strategies, to obtain solutions superior to those using the one-step or multistep lookahead heuristic algorithms. The rollout strategies are illustrated and tested using a range of real-world systems. We show computational results, which suggest that the information-heuristic based rollout policies are significantly better than other rollout policies based on Huffman coding and entropy.