Tsunamis are normally generated by underwater earthquakes. The earthquakes are normally easily detected by seismographs. However, the earthquake may not always generate a tsunami. Further, the severity of the earthquake is not linearly related to the severity of the tsunami. The tsunami may be detected by a deep-sea pressure transducer communicating through a surface rider buoy, through satellites to a tsunami warning centre. The detectors are expensive to build and maintain, need to be placed near surface-rider buoys, and the placement of these detectors needs to be optimal. The provision of adequate warnings from the network of detectors, called the tsunami warning potential, depends on the network of the deployed detectors, the number of detectors used, and the response times of the detectors, warning centre, and of the emergency services which need to convey the warning. The warning potential is also a function of the number in the population at risk. The sensitivity of the warning potential is analysed for first-order effects, particularly with respect to time delays arising from detection and operation of the emergency services to deliver the warning to the population. The sensitivity of the warning potential to population shifts is also considered. Areas for improvement are identified, together with suggestions of how the system can be optimised.