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

Ioannis S Triantafyllou; Nikolaos I Panayiotou

doi:10.1080/02664763.2019.1707518

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

J Appl Stat. 2019 Dec 28;47(12):2230-2257. doi: 10.1080/02664763.2019.1707518. eCollection 2020.

Authors

Ioannis S Triantafyllou¹, Nikolaos I Panayiotou¹

Affiliation

¹ Department of Computer Science & Biomedical Informatics, University of Thessaly, Lamia, Greece.

Abstract

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.

Keywords: Distribution-free monitoring schemes; Lehmann alternatives; average run length; false alarm rate; order statistics; statistical process control.