In process plants, alarms are configured to notify operators of any abnormalities or faults. However, in practice a majority of raised alarms are false or nuisance and create problems for operators as they face an increasing number of alarms to handle. Adding delay-timers is a simple technique that can reduce this problem and is widely exercised in industry. In this work we propose a generalized delay-timer framework where instead of consecutive n samples in the conventional case, n(1) out of n consecutive samples (n(1) <= n) are considered to raise an alarm. For the generalized delay-timer, three important performance indices, namely, the false alarm rate (FAR), the missed alarm rate (MAR) and the expected detection delay (EDD), are calculated using Markov processes. Moreover, the performance and sensitivity of generalized delay-timers are compared with conventional delay-timers. (C) 2013 Elsevier Ltd. All rights reserved.