A plant alarm system provides critical information to operators as the third layer of independent protection layers when a chemical plant is undergoing an abnormal situation. Therefore, methods for designing plant alarm systems are crucial for plant safety. Because plants are maintained as part of the plant lifecycle, plant alarm systems should be properly managed and adapted to changes that occur throughout the lifecycle. To manage changes, the design rationale of the plant alarm system should be explained explicitly. In the present paper, we explain a design problem for plant alarm systems and propose a method for designing alarm systems by using differential and algebraic equations, cause-effect matrices, and preference indices.