Signed sequential rank Shiryaev–Roberts schemes

Abstract

AbstractWe develop Shiryaev–Roberts schemes based on signed sequential ranks to detect a persistent change in location of a continuous symmetric distribution with known median. The in‐control properties of these schemes are distribution‐free, hence they do not require a parametric specification of an underlying density function or the existence of any moments. Tables of control limits are provided. The out‐of‐control average run length properties of the schemes are gauged via theory‐based calculations and Monte Carlo simulation. Comparisons are made with two existing distribution‐free schemes. We conclude that the newly proposed scheme has much to recommend its use in practice. Implementation of the methodology is illustrated in an application to a data set from an industrial environment.