The throughput of a manufacturing system is constrained by the bottlenecks in the manufacturing system. Improving the bottlenecks improves the manufacturing system. Finding the bottlenecks is nontrivial for static manufacturing systems. Detecting bottlenecks in flexible manufacturing systems is even more complicated, as bottlenecks in flexible manufacturing systems change frequently. This paper provides a novel method for detecting bottlenecks and the shifting thereof in flexible manufacturing systems based on the duration a machine is active. The presented active duration method determines the bottleneck based on the duration a machine is active without interruption. The method detects not only the short term shifting bottlenecks but also determines the long-term bottleneck in form of the probability of a machine being the bottleneck. The method is very robust, easy to apply and able to detect the primary and secondary bottlenecks in a wide range of manufacturing systems. The method is demonstrated using different examples and compared to conventional examples. The measurement of the likelihood of a machine being the bottleneck aids in the decision-making regarding the allocation of the available resources.