This paper investigates experimentally two generalized methods, i.e., a simple universal index and oscillation frequency, for the quantitative assessment of flame stability at fossilfuel-fired furnaces. The index is proposed to assess the stability of flame in terms of its color, geometry, and luminance. It is designed by combining up to seven characteristic parameters extracted from flame images. The oscillation frequency is derived from the spectral analysis of flame radiation signals. The measurements involved in these two methods do not require prior-knowledge about fuel property, burner type and other operation conditions. They can therefore be easily applied for flame stability assessment without costly and complex adaption. Experiments were carried out on a 9MWth heavy-oil-fired combustion test rig over a wide range of combustion conditions including variations in swirl vane position of tertiary air, swirl vane position of secondary air, and ratio of primary air to total air. The impact of these burner parameters on the stability of heavy oil flames is investigated by using the index and oscillation frequency proposed. The experimental results obtained demonstrate the effectiveness of the methods and the importance of maintaining a stable flame for reduced NOx emissions. It is envisaged that such methods can be easily transferred to existing flame CCTV (Closed-Circuit Television) systems and flame failure detectors in power stations for flame stability monitoring.