A new scoring function to learn the dependence structure from a process alarm dataset is proposed here. Based on the new function, a Bayesian network based method is developed to analyze alarm system performance. The proposed method is composed of four features: i) identifying essential variables from alarm data, ii) learning the structure of the Bayesian network from the alarm data; iii) learning the quantitative dependence of the variables in the Bayesian network, and iv) quantitatively describing the strength among the dependent variables. The proposed method helps to describe alarm variables relationships better, enable alarm diagnostic to identify the root causes, and study the variables dependence strength and finally improve the alarm system performance. The proposed method is first explained with a simple example, and further application is demonstrated with a case study of an industrial distributed control system-based alarm system.