This paper studies the correlation analysis for bivariate alarm signals in order to indicate whether two alarm signals are correlated, and their cause-effect direction if they are correlated. First, seven similarity coefficients are selected as the similarity measurements for binary data, in consideration of specialities of alarm signals. The upper bounds of these similarity coefficients are theoretically established for two independent alarm signals. Second, the distribution of a so-called correlation delay is shown to be indispensable and effective for the correlation analysis. Finally, a novel correlation analysis method for alarm signals is proposed based on the correlation ratio coefficient and distribution of the correlation delay. An industrial case study is provided to illustrate the proposed correlation analysis method.