Neoteric ranked set sampling for robust $$\bar{X}$$ X
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METHODOLOGIES AND APPLICATION
Neoteric ranked set sampling for robust X¯ and R control charts Nursel Koyuncu1
· Derya Karagoz1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Neoteric ranked set sampling (NRSS) is defined as an efficient sampling design compared to counterparts in the literature. NRSS differs from ranked set sampling (RSS) by selecting ordered sample units, and this design provides more accurate results for estimation of population parameters compared to RSS. This sampling design is firstly used by Koyuncu and Karagöz (Qual Technol Quant Manag 15(5):602–621, 2018) to construct control charts under bivariate asymmetric distributions. Robust control charts are another important topic for monitoring of process when the contamination exists. The novelty of this paper is that we have used NRSS design firstly in statistical process control to monitor robust control charts. Moving this direction, we have proposed to use NRSS design in modified robust methods to construct X¯ and R charts under contaminated skewed distributions. The performances of the X¯ and R control charts for monitoring the process by using NRSS are evaluated according to Type I risk probabilities. Based on the simulation study, the NRSS design in modified robust methods gives the most efficient results compared to existing methods. Keywords Robust control chart · Neoteric ranked set sampling · Simulation · Relative efficiency
1 Introduction Shewart X¯ and R control charts are widely used techniques in the statistical process control (SPC). These charts are based on the normality assumption. However, this assumption is not valid in many situations such as skewed distributed data. To deal with this problem, asymmetric control limits for X¯ and R charts were constructed by considering weighted variance (WV), weighted standard deviation (WSD) and skewness correction methods (SC). The fact that the outliers in the process cause contamination of the process. In the case of contamination, recently proposed control charts have broken. In SPC, Karagöz (2018) solved this problem to monitor skewed and contaminated process by considering robust methods, namely; modified Shewart (MS), modified weighted variance (MWV) and modified skewness correction methods (MSC). Sampling designs also play important role in SPC. Especially using RSS design is common to develop the quality of Communicated by V. Loia.
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Nursel Koyuncu [email protected] Department of Statistics, Hacettepe University, Ankara, Turkey
control charts. NRSS is proposed by Zamanzade and AlOmari (2016) as alternative to RSS, and they found that NRSS is superior to counterparts whether the ranking is perfect or imperfect. Koyuncu (2017, 2018) used NRSS design in the estimation of population parameters and showed the superiority to other sampling designs. In the literature, authors have handled different RSS designs on control charts. We can list some key studies as follows: Koyuncu and Karagöz (2018) took into account the effect of skewed process by us
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