Test sequencing algorithms with unreliable tests

In this paper, we consider imperfect test sequencing problems under a single fault assumption. This is a partially observed Markov decision problem (POMDP), a sequential multistage decision problem wherein a failure source must be identified using the results of imperfect tests at each stage. The optimal solution for this problem can be obtained by applying a continuous-state dynamic programming (DP) recursion. However, the DP recursion is computationally very expensive owing to the continuous nature of the state vector comprising the probabilities of faults. In order to alleviate this computational explosion, we present an efficient implementation of the DP recursion. We also consider various problems with special structure (parallel systems) and derive closed form solutions/index-rules without having to resort to DP. Finally, we present various top-down graph search algorithms for problems with no special structure, including multistep DP, multistep information heuristics, and certainty equivalence algorithms.