use sophisticated pipelining and multi-level trigger logic to reduce the readout rates. From the total time a detection system is running, the dead time must be subtracted to obtain the live time. Paralyzable and non-paralyzable behaviour A detector, or detection system, can be characterized by a paralyzable or non-paralyzable behaviour. In a non-paralyzable detector, an event happening during the dead time is simply lost, so that with an increasing event rate the detector will reach a saturation rate equal to the inverse of the dead time. In a paralyzable detector, an event happening during the dead time will not just be missed, but will restart the dead time, so that with increasing rate the detector will reach a saturation point where it will be incapable of recording any event at all. A semi-paralyzable detector exhibits an intermediate behaviour, in which the event arriving during dead time does extend it, but not by the full amount, resulting in a detection rate that decreases when the event rate approaches saturation. Analysis It will be assumed that the events are occurring randomly with an average frequency of f. That is, they constitute a Poisson process. The probability that an event will occur in an infinitesimal time interval dt is then f dt. It follows that the probability P(t) that an event will occur at time t to t+dt with no events occurring between t=0 and time t is given by the exponential distribution (Lucke 1974, Meeks 2008): The expected time between events is then Non-paralyzable analysis For the non-paralyzable case, with a dead time of , the probability of measuring an event between and is zero. Otherwise the probabilities of measurement are the same as the event probabilities. The probability of measuring an event at time t with no intervening measurements is then given by an exponential distribution shifted by : for for The expected time between measurements is then In other words, if counts are recorded during a particular time interval and the dead time is known, the actual number of events (N) may be estimated by If the dead time is not known, a statistical analysis can yield the correct count. For example, (Meeks 2008), if are a set of intervals between measurements, then the will have a shifted exponential distribution, but if a fixed value D is subtracted from each interval, with negative values discarded, the distribution will be exponential