A new distribution-free control scheme based on order statistics

We establish a class of nonparametric Shewhart-type control charts based on a reference sample drawn from the process. The proposed nonparametric control chart takes advantage of the location of two different order statistics of the reference and test sample respectively. The decision rule of the new monitoring scheme is filled out by the number of test observations that are located between the control limits. The general setup of the new class of control charts is presented in detail, while the operating characteristic function is studied for both in- and out-of-control processes. Closed formulae for the evaluation of the alarm rate and the average run length are concluded for plausible shift in the underlying distribution to Lehmann alternatives. Several numerical results, displayed for the new family of nonparametric control charts, depict that the proposed control scheme attains competitive performance.