A SOFC based commercial mu-CHP system is characterized by Electrochemical Impedance Spectroscopy, using a 2(4) full factorial test plan. The studied factors are: natural gas input power, ratio between oxygen and natural gas flow rates at the reformer inlet, stack average temperature and average operating cell voltage. Six replicates are performed in the domain centre. We performed equivalent circuit analysis and extracted three responses from each spectrum: ohmic resistance together with the two parameters of the CPE used in the model. However, one of our experiment is an outlier. To circumvent this problem, two methods described in the literature were applied: recalculation of missing response and introduction of a dynamic variable. Due their unsatisfactory results, we developed an innovative approach combining an iterative fitting of the multilinear model underlying any factorial design and an N-way ANOVA. Our method is successfully validated on the different 2(4-1) fractional designs deriving from the full factorial one. The only impacted response is the ohmic resistance. It increases as temperature decreases or as applied voltage increases. It is impacted by a strong synergistic effect of pressure and temperature and a compensating effect of pressure and applied voltage. No significant quadratic effect is observed. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.