Fault diagnosis is an important issue in industrial processes to avoid economic losses, process damage, and to guarantee safe working conditions for the operators. For high scale industrial processes the data-driven based methods are the best solution for process monitoring and fault diagnosis. Thus, in this paper, the principal component analysis is shown to detect and isolate faults. Also, a dynamic threshold is implemented to avoid false alarms because incipient faults are difficult to be detected. As a case of study, the Tennessee Eastman (TE) process is used to apply this strategy because the interaction among five units with internal control loops makes difficult to have an approached model. As results are shown the detection times, for cases where were analyzed incipient faults, the time required for fault detection must be improved, in this work, an adaptive threshold was used to reduce the false alarms but it also increases the detection times. It was concluded that the Q chart gave a better result for fault detection; the isolation times were similar to the detection ones. Two incipient faults could not be detected, the fault detection rate was similar to the shown in literature, but the detection times were better in 35% of the cases, unfortunately for four faults the detection times were bigger than the reported in other papers. It is proposed to help this method with independent component analysis due it is not guaranteed to have a Gaussian distribution in the samples.