Industrial plant alarm systems form an essential part of the operator interfaces for automatically monitoring of plant state deviations and for attracting the plant operator's attention to the changes that require his/her intervention. To design an efficient alarm system that assists operators to quickly identify the causes of abnormalities and to respond to the situations is vital for the safe operation of the plant. The Engineering Equipment and Materials Users Association (EEMUA) provided the general design and evaluation principles of plant alarm systems. We are proposing a systematic design approach for plant alarm systems using this guide. In the design stage, a set of alarm source signals are selected and then the alarm limits setting is determined. For alarm system rationalization, we have prepared countermeasures against repeating alarm suppression. To evaluate the designed alarm system, we used the criteria provided by the EEMUA 191 guide and other simulation evaluation indexes, such as the malfunction identification time of a human operator model. The design methods were applied to a boiler plant alarm system for this case study and the evaluation results prove the usefulness of the proposed approach.