In the process of industry

the most of the observation samples are polluted by random noises

which makes the probability model owning assumption of noises has been widely used. However

the factors obtained from the model may contain quality-unrelated information in the process monitoring. It is hard to identify the happened fault influencing the quality of product or not for traditional methods which monitor the factors directly. Meanwhile

aiming at the problem previously mentioned and the situation of unequal sample sizes of quality variables and process variables

a semi-supervised orthogonal factor analysis (Semi-SOFA) model was proposed. Firstly

it is formulated by the complete data collected in different sampling rates. Then

apply quality-related orthogonal decomposition to the factors

and construct statistics T2. At the same time

calculate the corresponding statistics SPE according to whether the new sample is labeled by quality variables or not. The proposed Semi-SOFA can effectively identify the period of quality influenced by fault. Finally

numerical simulation and Tennessee Eastman (TE) process simulation demonstrated effectiveness of the proposed approach.