This paper presents a novel strategy based on derivatives time series and advanced machine learning for medical decision-support especially for cardiac arrhythmia diagnosis. Most of recent technologies (smartphones, smart watches, etc.) are focusing on a unique source of information extracted from electrocardiography/photoplethysmography (i.e. heat inter-beat (RR) interval time series) coupled with classical pattern recognition methods to build efficient data-driven models. Herein, we demonstrate that the second derivative time series coupled with principal component analysis (PCA) and relevance vector machine (RVM) allow detection of abnormal rhythm. To achieve this aim, four features were extracted from one minute RR time series as well as from their derivatives and were subjected to PCA and RVM. PCA, as explanatory method, has shown that detection of AF arrhythmia became straightforward by targeting the second derivative time series. RVM was optimized through four kernel functions and the best model has reached 99.83% success rate to diagnosis AF and normal rhythm. The proposed approach outperformed several recent studies dealing with automatic AF diagnosis. Therefore, this method, which can be easily embedded in personal monitoring devices for real time cardiac arrhythmia detection, could be adapted for various medical decision-support involving time series recordings.