Title: Sensitivity comparison of control charts under MAD shift detector using the rank set sampling scheme

Authors: Nadia Saeed; Moustafa Omar Ahmed Abu-Shawiesh

Addresses: College of Statistical Sciences, University of the Punjab (PU), Lahore 54000, Pakistan ' Department of Mathematics, Faculty of Science, The Hashemite University (HU), P.O. Box 330127, Zarqa 13133, Jordan

Abstract: In this article, the sensitivity comparison of the standard Shewhart S-control chart is done with the MAD-control chart under the rank set sampling (RSS) scheme. The median absolute deviation (MAD) from the sample median is considered a robust estimator for the outlier's detection relative to the sample standard deviation (SD). Extensive simulations are conducted to evaluate the control charts' performance using both estimators under the RSS scheme for different sample sizes. The values for the out-of-control average run length (ARL₁), standard deviation of run length (SDRL) and percentile points under different shifts are used as performance measures. On the basis of Monte Carlo simulations, it is revealed that as the shift gets large; control charts are equally effective to detect it while for small shifts, the suggested robust MAD-control chart performed well and better. A real-life dataset is analysed to support our findings from the simulation study for illustrative intents justified that the MAD robust estimator is a better outlier detector. [Received: 26 November 2022; Accepted: 11 August 2023]

Keywords: rank set sampling; RSS; control chart; shift detector; outliers; median absolute deviation; MAD; percentile points; average run length; ARL.

DOI: 10.1504/EJIE.2025.143089

European Journal of Industrial Engineering, 2025 Vol.19 No.1, pp.68 - 85

Received: 26 Nov 2022
Accepted: 11 Aug 2023
Published online: 03 Dec 2024 *

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