Ranked Set Sampling Designs for Monitoring The Skew-Normal Process

Year 2019, Volume: 12 Issue: 1, 1 - 14, 28.06.2019

Derya Karagöz , Nursel Koyuncu

Abstract

In this study, we have proposed to use various ranked set sampling designs to

construct the mean charts based on Shewhart, Weighted Variance and Skewness

Correction methods that are applied to monitor the process variability under

the skew normal process. The performance of the mean charts based on var-

ious ranked set sampling designs are compared with simple random sampling

by Monte Carlo simulation. Simulation results revealed that the mean charts

based on various ranked set sampling perform much better than simple random

sampling.

Keywords

Weighted variance method, Skew-normal distribution, Ranked set sampling designs, Skewness correction method

Çarpık-normal sürecin izlenmesi için sıralı küme örnekleme tasarımları

Abstract

Bu çalışmada, çarpık-normal süreç altında süreç değişkenliğini
izlemek için uygulanan ortalama kartları oluşturmak için Shewhart, ağırlıklı
varyans ve düzeltilmiş çarpıklık yöntemlerine dayanan çeşitli sıralı küme
örnekleme tasarımlarını kullanmak önerilmiştir. Sıralı küme örnekleme
tasarımlarına dayanan ortalama kartlarının performansı Monte Carlo benzetimi
kullanılarak basit rastgele örnekleme ile karşılaştırılmıştır. Simülasyon
sonuçları, çeşitli sıralı küme örneklemesine dayanan ortalama kartlarının basit
rastgele örneklemeden çok daha iyi performans gösterdiğini ortaya koymuştur.

Keywords

Ağırlıklı varyans yöntemi, Çarpık-normal dağılım, Sıralı küme örnekleme tasarımları

References

• [1] Azzalini A., Dalla Valle A., "The multivariate skew-normal distribution",Biometrika, 83, 4, pp. 715-726, (1996).
• [2] Abujiya M.R., Muttlak H. A., "Quality control chart for the mean using doubleranked set sampling", Journal of Applied Statistics, 31:10, 1185-1201, (2004).
• [3] Al-Nasser A.D., Al-Rawwash M., "A control chart based on ranked data", Journalof Applied Sciences, 7:14, 1936-1941, (2007).
• [4] Bai D.S, Choi I.S., " Xand R Control charts for skewed populations", Journal OfQuality Technology, 27, 120-131, (1995).
• [5] Karagöz, D., Koyuncu N., "New ranked set sampling schemes for range charts limitsunder bivariate skewed distributions", Soft Computing, Doi: 10.1007/s00500-017-2880-4, (2018).
• [6] Koyuncu N., Karagöz, D.," Shewhart X-bar and R control charts using newranked set sampling schemes", Istatistik, Journal of the Turkish Statistical Association(IJTSA), 10, 3, 63-71, (2017).
• [7] Koyuncu N., Karagöz, D., "New mean charts for bivariate asymmetric distributionsusing dierent ranked set sampling designs", Quality Technology and QuantitativeManagement, 15(5), 602621, (2018).
• [8] Chan L.K, Cui H.J., "Skewness correction Xand R charts for skewed distributions",Naval Research Logistics, 50, 1-19 (2003).
• [9] Choobineh F., Ballard J.L., "Control-limits of QC Charts for skewed distributionsusing weighted variance", IEEE Transactions on Reliability, 36:4, 473-477, (1987).
• [10] McIntyre G.A., " A method for unbiased selective sampling using ranked sets",Australian Journal of Agricultural Research, 3, 385-390, (1952).
• [11] Montgomery D.C., "Introduction to Statistical Quality Control", JohnWiley&Sons. Inc., USA (1997) .
• [12] Muttlak H A, Al-Sabah W.S., "Statistical quality control based on ranked setsampling", Journal of Applied Statistics,30:9, 1055-78, (2003).
• [13] O'Hagan A., Leonard T., " Bayes estimation subject to uncertainty about parameterconstraints", Biometrika, 63, 201-203 (1976).
• [14] G.P. Silva, G.P., Taconeli, C. A., Zeviani, W.M., Guimares, I.S., " An improvedquality control chart to monitor the mean based on ranked sets", arXiv preprintarXiv:1709.04979, (2017).
• [15] Pongpullponsak A., Sontisamran P., "Statistical quality control based on rankedset sampling for multiple characteristics", Chiang Mai J Sci 40(3):485498, (2013).
• [16] Zamanzade, E. and Al-Omari, A.I., "New ranked set sampling for estimating thepopulation mean and variance", Hacettepe Journal of Mathematics and Statistics,45, 6, 1891-1905 , (2016).