Sequential rank CUSUMs for location and dispersion

Abstract

We develop CUSUMs based on sequential ranks of the observations to detect changes over time in the location and dispersion of a distribution. The CUSUMs are distribution free in the sense that the appropriate control limits do not depend on the form or any parameters of the unknown underlying distribution. As such the CUSUMs are fully self starting. The inand out-of-control average run length properties of the CUSUMs are gauged qualitatively via theory-based calculations and quantitatively by Monte Carlo simulation. The CUSUMS are shown to perform very well when compared to some existing parametric and nonparametric CUSUMS. Implementation of the CUSUMs is illustrated in an application based on real data from an industrial environment.