A method of setting the threshold is said to be difficult for detecting abnormal signals in fault diagnosis. In this paper, a method of detecting abnormal signals using hypothesis testing for residual sequence of AR model estimation error by recursive maximum likelihood method was studied. It involves F-testing the difference between present and past unbiased variance and t-testing the difference between present and past mean for residual sequence of AR model estimation error. The method was applied to abnormal detection of the catalyst feed flow in a linear low-density polyethylene plant to confirm the design philosophy. The actual result indicates that the F-testing method is effective in detecting abnormal process signals.