Distribution-free monitoring schemes based on order statistics: a general approach

In this article, we establish a new class of distribution-free Shewhart-type monitoring schemes based on order statistics. The setup of the proposed family of nonparametric control charts is presented in detail. Specific monitoring schemes, already introduced in the literature, are confirmed to be members of the new class. In addition, a new nonparametric monitoring scheme that belongs to the class is established, while explicit formulae for its basic characteristics are reached. The numerical study carried out reveals that the proposed scheme achieves adversarial in-control and out-of-control performance.