Some Characteristics of Page's Two-sided Procedure for Detecting a Change in a Location Parameter

Abstract

We study a two-sided procedure proposed by E. S. Page for detecting a change in the location of the distribution of a sequence of independent observations which are ordered in time. We approximate the null distribution of Page's statistic and the power of his test for finite sequences. When the procedure is applied to an infinite sequence we approximate the average run length. In order to obtain these approximations we find the distribution function of the range of a Wiener process with drift and the Laplace transform of the time at which the range first exceeds some given value.