With the rapid development of the modern process industry, the importance of the alarm system has become significant. In general, too many nuisance alarms exist in alarm systems and distract operators' attention from paying attention to the real abnormal situation. As an effective technique to remove nuisance alarms, the alarm delay-timer is applied extensively in practice. Due to the defects of the alarm delay-timer, the generalized alarm delay-timer is proposed recently as an improvement. But the alarm performance indices alarm rate (FAR), missed alarm rate (MAR), and average alarm delay (AAD) for the generalized alarm delay-timer are not obtained easily so far. In view of this fact; first, a generalization computing method is proposed in the form of three formulas based on the Markov models. Second, the application range of the generalized alarm delay-timer and conventional alarm delay-timer are compared through a numerical simulation. Finally, the procedures of applying the generalized alarm delay-timer are illustrated by a simulation example.