We propose a new design method for alarm systems, in which we assume that the pattern and the sequence of alarms generated by the alarm system are invariant for each possible malfunction. Operators can find the root causes of malfunctions not only from the patterns of generated alarms but also from their sequences, which means that the proposed method can identify more malfunctions than the previous one. Theoretical analysis showed that our method is especially effective for isolating the root causes of malfunctions that have corresponding nodes in the connected cause-effect graph. The proposed method was applied to the design of an alarm system for a basic chemical plant. The proposed method enables users to determine the maximum number of identifiable malfunctions, which clearly demonstrates its usefulness in the design of alarm systems.