An expected cost model was developed for failure detection in series systems under imperfect testing. Type I and type II error probabilities are included and single-pass sample paths are required. The model accounts for the expected costs of testing components, false positive termination, and no-defect-found outcomes. Based on the model, a heuristic was developed to construct the cost minimizing testing sequence. The heuristic algorithm utilizes elementary arithmetic computations and has been successfully applied to a variety of problems. Furthermore, the algorithm appears to be globally convergent. Choice of a starting solution affects the rate of convergence, and guidelines for selecting the starting solution were discussed. Implementation of the heuristic was illustrated by numerical example. / Master of Science