A method of detecting abnormal process signals in fault diagnosis using statistical analysis for the residual sequence of an AR model estimation error by recursive maximum likelihood method is developed. It involves white noise tests for the residual sequence of an AR model estimation error by the recursive maximum likelihood method using a logarithmic likelihood function and an integrated square of the auto-correlation function. The method proposed in this study has the advantage of detecting online abnormal signals in industrial use. It 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 proposed method is effective in detecting abnormal process signals.