As the current healthcare system faces problems of budget, staffing, and equipment, telemedicine through wearable devices gives a means of solving them. However, their adoption by physicians is hampered by the quality of electrocardiogram (ECG) signals recorded outside the hospital setting. Due to the dynamic nature of the ECG and the noise that can occur in real-world conditions, Signal Quality Assessment (SQA) systems must use robust signal quality indices (SQIs). The aim of this study is twofold: to assess the robustness of the most commonly used SQIs and to report on their complexity in terms of computational speed. A total of 39 SQIs were explored, of which 16 were statistical, 7 were non-linear, 9 were frequency-based and 7 were based on QRS detectors. With 6 databases, we manually constructed 2 datasets containing many rhythms. Each signal was labelled as 'acceptable' or 'unacceptable' (subcategories: 'motion artefacts', 'electromyogram noise', 'additive white Gaussian noise', or 'power line interference'). Our results showed that the performance of an SQI in distinguishing a good signal from a bad one depends on the type of noise. Furthermore, 23 SQIs were found to be robust. The analysis of their extraction time on 10-second signals revealed that statistics-based and frequency domain-based SQIs are the least complex with an average computational time of (mean: 1.40 ms, standard deviation: 1.30 ms), and (mean: 4.31 ms, standard deviation: 4.50 ms), respectively. Then, our results provide a basis for choosing SQIs to develop more general and faster SQAs.