Abstract
In this paper, instead of using traditional sampling schemes, we newly introduce to use ranked set, neoteric ranked set and median ranked set sampling to construct range charts control limits under the bivariate skewed distributions. Shewhart, weighted variance and skewness correction methods are considered to construct the range charts in the statistical process control. We have compared the performance of the suggested range charts under simple random and different ranked set sampling schemes by simulation study. The simulation study has showed that range charts based on skewness correction method are the most efficient under neoteric and median ranked set sampling schemes, especially in highly skewed data.
Similar content being viewed by others
References
Abujiya MR, Lee MH (2013) The three statistical charts using ranked set sampling, In: 5th international conference on modeling, simulation and applied optimization, ICMSAO, Art. no. 6552684
Bai DS, Choi IS (1995) \(\bar{X}\) and \(R\) control charts for skewed populations. J Qual Technol 27:120–131
Chan LK, Cui HJ (2003) Skewness correction \(\bar{X}\) and \(R\) charts for skewed distributions. Naval Res Logist 50:1–19
Chang YS, Bai DS (2001) Control charts for positively skewed populations with weighted standard deviations. Qual Reliab Eng Int 17:397–406
Choobineh F, Ballard JL (1987) Control-limits of QC charts for skewed distributions using weighted variance. IEEE Trans Reliab R–36(4):473–477
Jose KK, Ristic MM, Joseph A (2011) Marshall–Olkin bivariate Weibull distributions and processes. Stat Pap 52:789–798
Karagöz D (2016) Robust X control chart for monitoring the skewed and contaminated process. Hacettepe J Math Stat. doi:10.15672/HJMS.201611815892
Karagöz D, Hamurkaroğlu C (2012) Control charts for skewed distributions: Weibull, gamma and lognormal. Metodoloski zvezki Adv Methodol Stat 9(2):95–106
Koyuncu N (2015) Ratio estimation of the population mean in extreme ranked set and double robust extreme ranked set sampling. Int J Agric Stat Sci 11(1):21–28
Koyuncu N (2016) New difference-cum-ratio and exponential type estimators in median ranked set sampling. Hacettepe J Math Stat 45(1):207–225
Marshall AW, Olkin I (1967) A multivariate exponential distribution. J Am Stat Assoc 62:30–41
McIntyre GA (1952) A method for unbiased selective sampling using ranked sets. Aust J Agric Res 3:385–390
Montgomery DC (2009) Introduction to statistical quality control, 6th edn. John Wiley and Sons, New York
Pongpullponsak A, Sontisamran P (2013) Statistical quality control based on ranked set sampling for multiple characteristics. Chiang Mai J Sci 40(3):485–498
Yaqub M, Abbas N, Riaz M, Shabbir J (2015) On modified successive sampling based control charting schemes. Qual Reliab Eng Int 32:2491–2497
Yerel S, Konuk A (2009) Bivariate lognormal distribution model of cut-off grade impurities: a case study of magnesite ore deposit. Sci Res Essay 4(12):1500–1504
Zamanzade E, Al-Omari AI (2016) New ranked set sampling for estimating the population mean and variance. Hacettepe J Math Stat. doi:10.15672/HJMS.20159213166
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
Derya Karagöz declares that she has no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by V. Loia.
Rights and permissions
About this article
Cite this article
Karagöz, D., Koyuncu, N. New ranked set sampling schemes for range charts limits under bivariate skewed distributions. Soft Comput 23, 1573–1587 (2019). https://doi.org/10.1007/s00500-017-2880-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-017-2880-4