A Class of Enhanced Nonparametric Control Schemes Based on Order Statistics and Runs

Nikolaos I. Panayiotou and Ioannis S. Triantafyllou ()
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Nikolaos I. Panayiotou: Department of Computer Science & Biomedical Informatics, University of Thessaly, 38221 Volos, Greece
Ioannis S. Triantafyllou: Department of Statistics and Insurance Science, University of Piraeus, 18534 Pireas, Greece

Stats, 2023, vol. 6, issue 1, 1-14

Abstract: In this article, we establish a new class of nonparametric Shewhart-type control charts based on order statistics with signaling runs-type rules. The proposed charts offer to the practitioner the opportunity to reach, as close as possible, a pre-specified level of performance by determining appropriately their design parameters. Special monitoring schemes, already established in the literature, are ascertained to be members of the proposed class. In addition, several new nonparametric control charts that belong to the family are introduced and studied in some detail. Exact formulae for the variance of the run length distribution and the average run length (ARL) for the proposed monitoring schemes are also derived. A numerical investigation is carried out and demonstrates that the proposed schemes acquire competitive performance in detecting the shift of the underlying distribution. Although the large number of design parameters is quite hard to handle, the numerical results presented throughout the lines of the present manuscript provide practical guidance for the implementation of the proposed charts.

Keywords: average run length; nonparametric control schemes; Lehmann alternatives; runs-type signaling rules; statistical process control (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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