Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
권호 표지
DOI QR코드

DOI QR Code

Development of a p Control Chart for Overdispersed Process with Beta-Binomial Model

베타-이항모형을 이용한 과산포 공정용 p 관리도의 개발

  • Bae, Bong-Soo (Dept. of Industrial & Management Systems Engineering, Dong-A University) ;
  • Seo, Sun-Keun (Dept. of Industrial & Management Systems Engineering, Dong-A University)
  • 배봉수 (동아대학교 산업경영공학과) ;
  • 서순근 (동아대학교 산업경영공학과)
  • Received : 2017.04.08
  • Accepted : 2017.06.14
  • Published : 2017.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

Purpose: Since traditional p chart is unable to deal with the variation of attribute data, this paper proposes a new attribute control chart for nonconforming proportions incorporating overdispersion with a beta-binomial model. Methods: Statistical theories for control chart developed under the beta-binomial model and a new approach using this control chart are presented Results: False alarm probabilities of p chart with the beta-binomial model are evaluated and demerits of p chart under overdispersion are discussed from three examples. Hence a concrete procedure for the proposed control chart is provided and illustrated with examples Conclusion: The proposed chart is more useful than traditional p chart, individual chart to treat observed proportions nonconforming as variable data and Laney p' chart.

Keywords

References

  1. Capanu, Marinela, and Presnell, Brett. 2008. "Misspecification Test for Binomial and Beta-Binomial Models." Statistical in Medicine 27:2536-54. https://doi.org/10.1002/sim.3049
  2. Cryer, Jonathan D., and Ryan, Thomas P. 1990. "The estimation of sigma for an X chart: $MR/d_2$ or $S/c_4$?." Journal of Quality Technology 22:187-92. https://doi.org/10.1080/00224065.1990.11979238
  3. Ennis, Daniel M., and Bi, Jian. 1998. "The Beta-Binomial Model: Accounting for Intertrial Variation in Replicated Difference and Preference Tests." Journal of Sensory Studies 13: 389-412. https://doi.org/10.1111/j.1745-459X.1998.tb00097.x
  4. Garren, Steven T., Smith, Richard L., and Piegorsch, Walter W. 2000. "On a Likelihood-Based Goodness-of-Fit Test of the Beta-Binomial Model." Biometrics 56:947-949. https://doi.org/10.1111/j.0006-341X.2000.947_1.x
  5. Heimann, Peter A. 1996. "Attributes Control Charts with Large Sample Sizes." Journal of Quality Technology 28:451-9. https://doi.org/10.1080/00224065.1996.11979703
  6. Jones, G. and Govindaraju, K. 2000. "Graphical Method for Checking Attribute Control Chart Assumptions." Quality Engineering 13:19-26.
  7. Kleinman, Joel C. 1973. "Proportions with Extraneous Variance: Single and Independent Samples." Journal of American Statistical Association 68:46-54.
  8. Laney, David B. 2002. "Improved Control Charts for Attributes." Quality Engineering 14:531-7. https://doi.org/10.1081/QEN-120003555
  9. Liang, Kung-Yee, and Mccullagh, Peter. 1993. "Case Studies in Binary Dispersion." Biometrics 49:623-630. https://doi.org/10.2307/2532575
  10. Minitab. 2014. "Minitab 17 Statistical Software." Accessed September 2, 2015. http://www.minitab.com.
  11. Mohammed, Mohammed A., and Worthington, Peter. 2013. "Why Traditional Statistical Process Control Charts for Attribute Data Should Be Viewed Alongside an xmr-Chart." BMJ Quality and Safety 22:263-9. https://doi.org/10.1136/bmjqs-2012-001324
  12. Mohammed, Mohammed A., Panesar, Jagdeep S., Laney, David. B., and Wilson Richard. 2013. "Statistical Process Control Charts for Attribute Data Involving Very Large Sample Sizes: a Review of Problems and Solutions." BMJ Quality and Safety 22:362-68. https://doi.org/10.1136/bmjqs-2012-001373
  13. Mohammed, Mohammed A., Worthington, Peter, and Woodall, William H. 2008. "Plotting Basic Control Charts: Tutorial Notes for Healthcare Practitioners." BMJ Quality and Safety 17: 137-145. https://doi.org/10.1136/qshc.2004.012047
  14. Moore Dirk F. 1987. "Modeling the Extraneous Variance in the Presence of Extra-Binomial Variation." Applied Statistics 36:8-14. https://doi.org/10.2307/2347840
  15. Quarshie, B. L., and Shindo, Hisakazu. 1996. "A Comparison of Operating Characteristics of the ${\bar{p}}-V$ and the ${\bar{p}}-R_p$ Charts." Quality Engineering 9:221-8. https://doi.org/10.1080/08982119608919038
  16. Ryan, Thomas P. 2011. Statistical Methods for Quality Improvement, 3rd ed. New Jersey(USA): John Wiley & Son.
  17. Raubenheimer, L., and van der Merwe, A. J. 2016. "Bayesian Process Control for the Phase II Shewart-Type p-Chart." Quality Technology and Quantitative Management 13:453-72. https://doi.org/10.1080/16843703.2016.1191144
  18. Tarone, Robert E. 1979. "Testing the Goodness of Fit of the Binomial Distribution." Biometrika 66:585-590. https://doi.org/10.1093/biomet/66.3.585
  19. Wheeler, Donald J. 2001. Understanding Statistical Process Control, 3rd ed., Knoxville(USA): SPC Press.
  20. Woodall, William H. 1997. "Control Charts Based on Attribute Data: Bibliography and Review." Journal of Quality Technology 29:172-183. https://doi.org/10.1080/00224065.1997.11979748
  21. Young-Xu, Yinong, and Chan, K. Arnold. 2008. "Pooling Overdispersed Binomial Data to Estimate Event Rate." BMC Medical Research Methodology 8: Accessed November 22, 2016. doi:10.1186/1471-2288-8-58.