This paper introduces a novel approach to sequencing robotic diagnostic tasks performed on faulty electronic printed circuit board (PCB) products. By assuming that each product has a single fault, at any given moment of the diagnostic process, sequencing must consider only the diagnostic tasks that help identify possible faults not ruled out by the earlier tests. With this, the solution of the stochastic sequencing problem can be encoded into a policy tree that prescribes the next task to execute depending on the results of earlier tests. The paper proposes a local search approach to minimizing the expected duration of the diagnostic process by constructing an initial policy tree using a greedy entropy-per-cost heuristic, and then improving this solution further by a hill climbing search and an adaptation of the insertion neighborhood. An industrial application is presented and first experimental results are reported.