Process industries continue to suffer from accidents despite significant regulatory intervention since the mid-1980s. Human error is widely considered to be the major cause for most accidents today. Detailed analysis of various incidents indicates that reduced staffing levels in control rooms and inadequate operator training with complex automation strategies as common reasons for human errors. Therefore, there is a need to develop deeper understanding of human errors as well as strategies to prevent them. However, similar to hardware failures, traditionally human error has been quantified using likelihood approaches; this viewpoint abnegates the role of the cognitive abilities of the operators. Recent studies in other safety critical domains (aviation, health-care) show that operator's level of situation awareness as inferred by eye tracking is a good online indicator of human error. In this work, a novel attempt is made to understand the behavior of the operator in a typical chemical plant control room using the information obtained from eye tracker. Experimental studies conducted on 72 participants reveal that fixation patterns contain signatures about the operators learning and awareness at various situations. Implications of these findings on human error in process plant operations them are discussed.