The aim of this work is to systematically quantify and rank the effects of nine different design parameters on the fluid mechanic abilities of a Dielectric Barrier Discharge (DBD) plasma actuator supplied with an Alternating Current. The ranking and quantification not only consider the parameters themselves but also their interactions with each other. In order to perform this ranking, a Design of Experiment approach is used. This allows the most significant design parameters for the thrust generation, power consumption and thrust to power consumed ratio (force efficiency) of DBD actuator performance to be determined in a systematic way. The results show that the thrust generation is driven by the voltage, distance between the electrodes, AC frequency, and geometry of the exposed electrode, in that order. A high voltage and high frequency, with a thin dielectric, a narrow inter-electrode gap, and a thin and narrow air-electrode results in an increase in the thrust generation.The thrust to power ratio of a DBD is employed as a proxy for the fluid mechanic efficiency. The analysis of the force efficiency shows that the voltage, frequency, distance between the electrodes, and geometry of the air electrode have significant effects. The higher force efficiency is obtained for a high voltage, low frequency, short inter-electrode gap, thin dielectric of low permittivity with a narrow and thin exposed electrode. Finally, two actuators are investigated to determine the best scaling laws for the power consumption as a function of voltage and frequency. In these experiments, the power consumption was a function of voltage to the power of 2.5 and frequency to the power of 1.5. This systematic study of the parameters and their interactions allows general guidelines to be obtained for the best fluid mechanic performance of a DBD, viz. its thrust generation and force efficiency.