The Sleeping Cell problem is a particular type of cell degradation in Long-Term Evolution (LTE) networks. In practice such cell outage leads to the lack of network service and sometimes it can be revealed only after multiple user complains by an operator. In this study a cell becomes sleeping because of a Random Access Channel (RACH) failure, which may happen due to software or hardware problems. For the detection of malfunctioning cells, we introduce a data mining based framework. In its core is the analysis of event sequences reported by a User Equipment (UE) to a serving Base Station (BS). The crucial element of the developed framework is an anomaly detection algorithm. We compare performances of distance, centroid distance and probabilistic based methods, using Receiver Operating Characteristic (ROC) and Precision-Recall curves. Moreover, the theoretical comparison of the methods' computational efficiencies is provided. The sleeping cell detection framework is verified by means of a dynamic LTE system simulator, using Minimization of Drive Testing (MDT) functionality. It is shown that the sleeping cell can be pinpointed.