In statistics, Entropy is a measure of disorder of time series. Entropy is used in physiologic for signal analysis. In physiologic science, Entropy is used for performance analysis of body organs such as heart and brain. Epileptic patients have been diagnosed by this technique. In this paper for the first time, Entropy is used to determine the health condition of mechanical systems. A special kind of Entropy, namely Permutation Entropy is used for this purpose.To perform the experiment an apparatus consisting of a motor coupled with a shaft has been designed and manufactured. Vibration signals from supporting bearing of this system in different shaft states namely healthy shaft, and shafts with 3, 5 and 7 mm crack were gathered with a vibration data analyzer. The vibration were taken from sensors mounted on bearing supports of the shaft. Shaft was subjected to a constant bending moment. The vibration signals were preprocessed by permutation Entropy method. Nine different features were extracted from the Entropy signals which are fed to an Adaptive Neuro Fuzzy Inference System (ANFIS). The designed ANFIS was capable of classifying different shaft states with an overall %96 percision.