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The bottleneck (BN) of a production system is a machine with the strongest effect on the system's throughput. In this paper, a method for BN identification in serial lines with rework and Bernoulli machines is developed. The method can be applied using either calculated or measured data on blockages and starvations of the machines. For the case of calculated data, a technique for evaluating performance measures of Bernoulli lines with rework is developed. Along with these quantitative contributions, the paper provides three qualitative results. First, it shows that Bernoulli lines with rework do not observe the property of reversibility. Second, it demonstrates that downstream machines may have a larger effect on the throughput than upstream ones. Third, it demonstrates that BNs may be shifting not only because of changes in machine and buffer parameters but also due to changes in quality of parts produced.