  CUSUMs based on the signed sequential ranks of observations are developed for
detecting location and scale changes in symmetric distributions. The CUSUMs are
distribution free and fully self-starting: given a specified in-control median
and nominal in-control average run length, no parametric specification of the
underlying distribution is required in order to find the correct control
limits. If the underlying distribution is normal with unknown variance, a CUSUM
based on the Van der Waerden signed rank score produces out-of-control average
run lengths that are commensurate with those produced by the standard CUSUM for
a normal distribution with known variance. For heavier tailed distributions,
use of a CUSUM based on the Wilcoxon signed rank score is indicated. The
methodology is illustrated by application to real data from an industrial
environment.
