This thesis investigates diagnosis strategies for k-out-of-n systems under the general type precedence constraints. Given the testing costs and the prior working probabilities, the problem is to devise strategies that minimizes the total expected cost of finding the correct state of the system. The true state of the system is determined by sequential inspection of these n components. We try to find good strategies for the problem under general type precedence constraints by adapting an optimal algorithm that works when there are no precedence constraints. We refer to this algorithm Intersection-Precedence and represent the strategy that we obtain efficiently by a Block-Walking Diagram structure. Since no computational results are reported in the literature for this particular problem, in order to benchmark the performance of the Intersection-Precedence algorithm, we develop Tabu Search and Simulated Annealing algorithms that find permutation strategies.We conduct an extensive computational study to compare the results obtained by the alternative algorithms and we observe that Intersection- Precedence algorithm, in general, outperforms the other algorithms
