Alarm systems are commonly deployed in complex industries to monitor the operation status of the production process in real time. Actual alarm systems generally have alarm overloading problems. One of the major factors leading to excessive alarms is the presence of many correlated or redundant alarms. Analyzing alarm correlations will not only be beneficial to the detection of and reduction in redundant alarm configurations, but also help to track the propagation of abnormalities among alarm variables. As a special problem in correlated alarm detection, the research on first-out alarm detection is very scarce. A first-out alarm is known as the first alarm that occurs in a series of alarms. Detection of first-out alarms aims at identifying the first alarm occurrence from a large number of alarms, thus ignoring the subsequent correlated alarms to effectively reduce the number of alarms and prevent alarm overloading. Accordingly, this paper proposes a new first-out alarm detection method based on association rule mining and correlation analysis. The contributions lie in the following aspects: (1) An association rule mining approach is presented to extract alarm association rules from historical sequences based on the FP-Growth algorithm and J-Measure; (2) a first-out alarm determination strategy is proposed to determine the first-out alarms and subsequent alarms through correlation analysis in the form of a hypothesis test on conditional probability; and (3) first-out rule screening criteria are proposed to judge whether the rules are redundant or not and then consolidated results of first-out rules are obtained. The effectiveness of the proposed method is tested based on the alarm data generated by a public simulation platform.