The subject of the thesis belongs to the field of operations management. We deal with sequencing problems arising when there are multiple repair operations available to fix a broken man-made system and the true cause of the system failure is uncertain. It is assumed that the system is formally described by a probabilistic model, and it is to be repaired by a sequence of troubleshooting operations designed to identify the cause of the malfunction and fix the system. The challenge is to find a course of repair which has minimal expected cost. We study several variants of the problem proposed in the literature. We analyze computational complexity of those variants, apply integer linear programming to one variant of the problem, and examine the relation to machine scheduling.