In this paper, we propose a new automated quality-aware electrocardiogram (ECG) heat classification method for effective diagnosis of ECG arrhythmias under unsupervised healthcare environments. The proposed method consists of three major stages: 1) the ECG signal quality assessment ({''}acceptable{''} or ``unacceptable{''}) based on our previous modified complete ensemble empirical mode decomposition and temporal features; 2) the ECG signal reconstruction and R-peak detection; and 3) the ECG beat classification including the ECG beat extraction, beat alignment, and normalized cross-correlation-based beat classification. The accuracy and robustness of the proposed method are evaluated using different normal and abnormal ECG signals taken from the standard MIT-BIH arrhythmia database. Evaluation results show that the proposed quality-aware ECG beat classification method can significantly achieve false alarm reduction ranging from 24\% to 93\% under noisy ECG recordings. The R-peak detector achieves the average Se = 99.67\% and positive predictivity (Pp) = 93.10\% and the average sensitivity (Se) = 99.65\% and Pp = 98.88\% without and with denoising approaches, respectively. Results further showed that the proposed ECG beat extraction approach can improve the classification accuracy by preserving the QRS complex portion and suppressing the background noises under acceptable level of noises. The quality-aware ECG beat classification methods achieve higher kappa values for the classification accuracies which can be consistent as compared with the heartbeat classification methods without the ECG quality assessment process.