A SEQUENTIAL TEST OF RANDOMNESS FOR EVENTS OCCURRING IN TIME OR SPACE

In a variety of practical problems it is necessary to test whether a sequence of events is occurring at random in time or space. To the casual observer even a random series will suggest fluctuations in the density of events, so that an objective test is clearly required to establish randomness or otherwise. The problem was discussed by Maguire, Pearson & Wynn (1952) as applied to industrial accidents; they pointed out that the basic data in such cases consisted of an ordered sequence of intervals between events. Recent investigations into the possible departures from randomness have shown that it is sometimes appropriate to use a test based on intervals, but on other occasions the times form the best starting point. In this paper we give a sequential test which utilizes the times at which events occur because the alternative envisaged requires this approach. A sequential test is of special value in this case because the observations become available one at a time; provided that they do not follow each other too rapidly it should be possible to carry out a test as the process develops.