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Robust $\bar{X}$ control chart for monitoring the skewed and contaminated process

Year 2018, Volume: 47 Issue: 1, 223 - 242, 01.02.2018

Abstract

In this paper, we propose the modified Shewhart, the modified weighted variance and the modified skewness correction methods by using trimmed mean and interquartile range estimators to construct the control limits of robust $\bar{X}$ control chart for monitoring the skewed and contaminated process. A comparison between the performances of the $\bar{X}$ chart for monitoring the process mean based on these three modified models is made in terms of the Type I risk probabilities and the average run length values for the various levels of skewness as well as different contamination models.

References

  • Abu-Shawiesh, M.O.A. A Simple Robust Control Chart Based on MAD, Journal of Mathematics and Statistics, 4(2), 102-107, 2008.
  • Ahsanullah, M., Nevzorov, V.B., Shakil, M., An Introduction to Order Statistics, 246 p., Hardcover ISBN: 978-94-91216-82-4, A product of Atlantis Press, 2013.
  • Bai, D.S. and Choi, I.S., X and R Control Charts For Skewed Populations, Journal Of Quality Technology, 27, 120-131, 1995.
  • Castagliola, P. and Khoo, M.B.C. A Synthetic Scaled Weighted Variance Control Chart for Monitoring the Process Mean of Skewed Populations, Communications in Statistics: Simulation and Computation, 38, 1659  1674, 2009
  • Chan, L.K. and Cui, H.J. Skewness Correction X and R Charts for Skewed Distributions, Naval Research Logistics, 50: 1-19, 2003.
  • Choobineh, F. and Ballard, J.L. Control-Limits of QC Charts For Skewed Distributions Using Weighted Variance, IEEE Transactions on Reliability, 473-477, 1987.
  • Chang, Y.S. and Bai, D.S. Control Charts for Positively Skewed Populations with Weighted Standard Deviations, Quality and Reliability Engineering International, 17, 397-406, 2001.
  • He, X., and Fung, W.K. Method of medians for lifetime data with Weibull models, Stat Med., 18, 1993-2009, 1999.
  • Huber, P. J. Robust Statistics, John Wiley & Sons, 1981.
  • Karagöz, D. and Hamurkaroğlu C. Control Charts for Skewed Distributions: Weibull, Gamma, and Lognormal, Metodoloski zvezki - Advances in Methodology and Statistics, 9(2), 95-106, 2012.
  • Maronna, R. A., Martin, D. R. and Yohai, V. J. Robust Statistics: Theory and Methods, Wiley, 2006.
  • Montgomery, D.C. Introduction to Statistical Quality Control, John Wiley&Sons. Inc., USA; 1997.
  • Nelson, P.R. Control Charts for Weibull Processes with Standards Given, IEEE Transactions on Reliability, 28, 283-387, 1979.
  • Schoonhoven, M. and Does, R.J.M.M. The X control chart under non-normality, Quality and Reliability Engineering International , 26: 167-176, 2010.
  • Schoonhoven, M., Nazir, H.Z., Riaz, M. and Does, R.J.M.M. Robust location estimations for the X control chart, Journal of Quality Technology, 43: 363-379, 2010.
  • Schoonhoven, M. and Does R.J.M.M. A Robust X Control Chart, Quality and Reliability Engineering International, 29: 951-970, 2013.
  • Rocke, D.M. XQ and RQ Charts: Robust Control Charts, The Statistician, 41: 97- 104, 1992.
  • Whaley, D. L. The Interquartile Range: Theory and Estimation, Master Thesis Presented to the Faculty of the Department of Mathematics East Tennessee State University, 2005.
  • Wilcox, R. Introduction to Robust Estimation and Hypothesis Testing, Academic press, University of Southern California, 2005.
  • Wu, C., Zhao, Y., Wang, Z. The median absolute deviations and their application to Shewhart X control charts, Communication in Statistics -Simulation and Computation, 31: 425-442, 2002.
Year 2018, Volume: 47 Issue: 1, 223 - 242, 01.02.2018

Abstract

References

  • Abu-Shawiesh, M.O.A. A Simple Robust Control Chart Based on MAD, Journal of Mathematics and Statistics, 4(2), 102-107, 2008.
  • Ahsanullah, M., Nevzorov, V.B., Shakil, M., An Introduction to Order Statistics, 246 p., Hardcover ISBN: 978-94-91216-82-4, A product of Atlantis Press, 2013.
  • Bai, D.S. and Choi, I.S., X and R Control Charts For Skewed Populations, Journal Of Quality Technology, 27, 120-131, 1995.
  • Castagliola, P. and Khoo, M.B.C. A Synthetic Scaled Weighted Variance Control Chart for Monitoring the Process Mean of Skewed Populations, Communications in Statistics: Simulation and Computation, 38, 1659  1674, 2009
  • Chan, L.K. and Cui, H.J. Skewness Correction X and R Charts for Skewed Distributions, Naval Research Logistics, 50: 1-19, 2003.
  • Choobineh, F. and Ballard, J.L. Control-Limits of QC Charts For Skewed Distributions Using Weighted Variance, IEEE Transactions on Reliability, 473-477, 1987.
  • Chang, Y.S. and Bai, D.S. Control Charts for Positively Skewed Populations with Weighted Standard Deviations, Quality and Reliability Engineering International, 17, 397-406, 2001.
  • He, X., and Fung, W.K. Method of medians for lifetime data with Weibull models, Stat Med., 18, 1993-2009, 1999.
  • Huber, P. J. Robust Statistics, John Wiley & Sons, 1981.
  • Karagöz, D. and Hamurkaroğlu C. Control Charts for Skewed Distributions: Weibull, Gamma, and Lognormal, Metodoloski zvezki - Advances in Methodology and Statistics, 9(2), 95-106, 2012.
  • Maronna, R. A., Martin, D. R. and Yohai, V. J. Robust Statistics: Theory and Methods, Wiley, 2006.
  • Montgomery, D.C. Introduction to Statistical Quality Control, John Wiley&Sons. Inc., USA; 1997.
  • Nelson, P.R. Control Charts for Weibull Processes with Standards Given, IEEE Transactions on Reliability, 28, 283-387, 1979.
  • Schoonhoven, M. and Does, R.J.M.M. The X control chart under non-normality, Quality and Reliability Engineering International , 26: 167-176, 2010.
  • Schoonhoven, M., Nazir, H.Z., Riaz, M. and Does, R.J.M.M. Robust location estimations for the X control chart, Journal of Quality Technology, 43: 363-379, 2010.
  • Schoonhoven, M. and Does R.J.M.M. A Robust X Control Chart, Quality and Reliability Engineering International, 29: 951-970, 2013.
  • Rocke, D.M. XQ and RQ Charts: Robust Control Charts, The Statistician, 41: 97- 104, 1992.
  • Whaley, D. L. The Interquartile Range: Theory and Estimation, Master Thesis Presented to the Faculty of the Department of Mathematics East Tennessee State University, 2005.
  • Wilcox, R. Introduction to Robust Estimation and Hypothesis Testing, Academic press, University of Southern California, 2005.
  • Wu, C., Zhao, Y., Wang, Z. The median absolute deviations and their application to Shewhart X control charts, Communication in Statistics -Simulation and Computation, 31: 425-442, 2002.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

Derya Karagöz

Publication Date February 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 1

Cite

APA Karagöz, D. (2018). Robust $\bar{X}$ control chart for monitoring the skewed and contaminated process. Hacettepe Journal of Mathematics and Statistics, 47(1), 223-242.
AMA Karagöz D. Robust $\bar{X}$ control chart for monitoring the skewed and contaminated process. Hacettepe Journal of Mathematics and Statistics. February 2018;47(1):223-242.
Chicago Karagöz, Derya. “Robust $\bar{X}$ Control Chart for Monitoring the Skewed and Contaminated Process”. Hacettepe Journal of Mathematics and Statistics 47, no. 1 (February 2018): 223-42.
EndNote Karagöz D (February 1, 2018) Robust $\bar{X}$ control chart for monitoring the skewed and contaminated process. Hacettepe Journal of Mathematics and Statistics 47 1 223–242.
IEEE D. Karagöz, “Robust $\bar{X}$ control chart for monitoring the skewed and contaminated process”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, pp. 223–242, 2018.
ISNAD Karagöz, Derya. “Robust $\bar{X}$ Control Chart for Monitoring the Skewed and Contaminated Process”. Hacettepe Journal of Mathematics and Statistics 47/1 (February 2018), 223-242.
JAMA Karagöz D. Robust $\bar{X}$ control chart for monitoring the skewed and contaminated process. Hacettepe Journal of Mathematics and Statistics. 2018;47:223–242.
MLA Karagöz, Derya. “Robust $\bar{X}$ Control Chart for Monitoring the Skewed and Contaminated Process”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 1, 2018, pp. 223-42.
Vancouver Karagöz D. Robust $\bar{X}$ control chart for monitoring the skewed and contaminated process. Hacettepe Journal of Mathematics and Statistics. 2018;47(1):223-42.