Journal of Korean Society for Quality Management (품질경영학회지)

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

DOI QR Code

Development of a New Index to Assess the Process Stability

공정 안정성 평가를 위한 새로운 척도 지수 계발

  • Kim, Jeongbae (BK21 Research Group(Industrial Big Data), Pusan National University) ;
  • Yun, Won Young (Major in Industrial Data Science & Engineering and Dept. of Industrial Engineering, Pusan National University) ;
  • Seo, Sun-Keun (Dept. of Industrial and Management Systems Engineering, Dong-A University)
  • 김정배 (부산대학교 BK21사업단(산업빅데이터)) ;
  • 윤원영 (부산대학교 산업공학과 산업데이터공학융합전공) ;
  • 서순근 (동아대학교 산업경영공학과)
  • Received : 2022.07.22
  • Accepted : 2022.08.29
  • Published : 2022.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Purpose: The purpose of this study is to propose a new useful suggestion to monitor the stability of process by developing a stability ratio or index related to investigating how well the process is controlled or operated to the specified target. Methods: The proposed method to monitor the stability of process is building up a new measure index which is making up for the weakness of the existing index in terms of short or long term period of production. This new index is a combined one considering both stability and capability of process to the specification limits. We suppose that both process mean and process variation(or deviation) are changing on time period. Results: The results of this study are as follows: regarding the stability of process as well as capability of process, it was shown that two indices, called SI(stability index) and PI(performance index), can be expressed in two-dimensional X-Y graph simultaneously. This graph is categorized as 4 separated partitions, which are characterized by its numerical value intervals of SI and PI which are evaluated by test statistics. Conclusion: The new revised index is more robust than the existing one in investigating the stability of process in terms of short and long period of production, even in case both process mean and variation are changing.

Keywords

Acknowledgement

본 논문은 교육부가 지원하는 한국연구재단 4단계 BK21 사업에 의하여 지원되었음(NO 5199990914451)

References

  1. Blanca, M. J., Alarcon, R., Arnau, J., Bono, R., and Bendayan, R. 2018. Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit. Behavior Research Methods 50(3):937-962. https://doi.org/10.3758/s13428-017-0918-2
  2. Box, G. E. P. 1954, Some theorems on quadratic forms applied in the study of analysis of variance problems: I. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics 25(2):290-302. https://doi.org/10.1214/aoms/1177728786
  3. Britt, K. A., Ramirez, B., and Mistretta, T. 2016. Process monitoring using statistical stability metrics: applications to biopharmaceutical processes. Quality Engineering 28(2):193-211. https://doi.org/10.1080/08982112.2015.1094705
  4. Brown, M. B. and Forsythe, A. B. 1974. The small sample behavior of some statistics which test the equality of several means. Technometrics 16(1):129-132. https://doi.org/10.1080/00401706.1974.10489158
  5. Cruthis, E. N. and Rigdon, S. E. 1992-93. Comparing two estimates of the variance to determine the stability of a process. Quality Engineering 5(1):67-74. https://doi.org/10.1080/08982119208918951
  6. Dean, A. and Voss, D. 1999. Design and Analysis of Experiments. USA, Springer-Verlag.
  7. Gauri, S. K. 2010. A quantitative approach for detection of unstable processes using a run chart. Quality Technology and Quantitative Management 7(3):231-247. https://doi.org/10.1080/16843703.2010.11673230
  8. Jensen, W. A., Szarka III, J., and White, K. 2019, Stability assessment with stability index. Quality Engineering 31(2):289-301. https://doi.org/10.1080/08982112.2018.1497179
  9. Mehrotra, D. V. 1997. Improving the Brown-Forsythe solution to the generalizied Behrens-Fisher problem. Communications in Statistics-Simulation and Computation 26(3):1139-1145. https://doi.org/10.1080/03610919708813431
  10. Montgomery, D. C. 2013. Introduction to Statistical Quality Control, 7th ed. USA, John Wiley & Sons.
  11. Parra-Frutos, I. 2013. Testing homogeneity of variances with unequal sample sizes. Computational Statistics 28(3):1269-1297. https://doi.org/10.1007/s00180-012-0353-x
  12. Patnaik, P. B. 1949, The non-central X2- and F-distributions and their applications. Biometrika 36(1/2):202-232.
  13. Podolski, G. 1989-90. Standard deviation: root mean square versus range conversion. Quality Engineering 2(2):155-161. https://doi.org/10.1080/08982118908962709
  14. Quevedo, V., S. Vegas, and G. Vining. 2016. A tutorial on an iterative approach for generating Shewhart control limits. Quality Engineering 28(3):305-312. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] https://doi.org/10.1080/08982112.2015.1121277
  15. Ramirez, B. 2018. Discussion of Scaling-up process characterization. Quality Engineering 30(1):79-87. https://doi.org/10.1080/08982112.2017.1382293
  16. Ramirez, B. and Runger, G. 2006. Quantitative techniques to evaluate process stability. Quality Engineering 18(1):53-68. https://doi.org/10.1080/08982110500403581
  17. Ramirez, J. G. 2016. A health screening for your processes. JMP Foreword 11-12. [Google Scholar]
  18. Sall, J. 2018. Scaling-up process characterization. Quality Engineering 30(1):62-78. https://doi.org/10.1080/08982112.2017.1361539
  19. Shper, V. and Adler, Y. 2017. The importance of time order with Shewhart control charts. Quality and Reliability Engineering International 33(6):1169-1177. https://doi.org/10.1002/qre.2185
  20. Wheeler, D. J. 2004. Advanced Topics in Statistical Process Control, 2nd ed. USA, SPC Press.
  21. White, K., Szarka III, J., Childress, A., and Jensen, W. A. 2021. A recommended set of indices for evaluating process health. Quality Engineering 33(1):1-12. https://doi.org/10.1080/08982112.2020.1787442
  22. Woodall, W. H. 2016. Bridging the Gap between Theory and Practice in Basic Statistical Process Monitoring. Quality Engineering 29(1):2-15. [Taylor & Francis Online], [Google Scholar]
  23. Wooluru, Y., Swamy, D. R., and Nagesh, P. 2015. Approaches for detection of unstable processes: A comparative study. Journal of Modern Applied Statistical Methods 14(1):219-235. https://doi.org/10.22237/jmasm/1446351360
  24. Yun, W. Y., Lee, S. H., Cha, M. S., Kwon, H. M., Kim, H. G., and Seo, S.-K. 2018. Statistical Quality Control. Korea, Cheongmungak.