Dead-time problems

The usual two types of dead times, extended and non-extended, are reviewed and fundamental properties of their effect on the interval distribution and the count rate are discussed briefly. The application of renewal theory to counting processes is sketched and it is shown how the interval distribution, which is distorted by the presence of a dead time, can be used to determine the resulting counting statistics. In particular, the modifications of an original Poisson process, due to a non-extended dead time, are indicated for the case where the origin of the measuring interval has been chosen at random. A simple application then shows the fallacy of the so-called zero-probability analysis. When renewal processes are superimposed, their convolution property is lost. Therefore, a general formula for the density of multiple intervals is given for the superposition of two component processes. These results have proved useful for studying two recently reported methods of measuring dead times. Finally, formulae are given for the four different ways of arranging two dead times in series. The review is confined to one-channel problems and the emphasis is on exact results.