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http://dx.doi.org/10.7469/JKSQM.2022.50.3.473

Development of a New Index to Assess the Process Stability  

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)
Publication Information
Journal of Korean Society for Quality Management / v.50, no.3, 2022 , pp. 473-490 More about this Journal
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
Process Stability and Capability Index; Process Performance Graph;
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1 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.   DOI
2 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.
3 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.   DOI
4 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.   DOI
5 Jensen, W. A., Szarka III, J., and White, K. 2019, Stability assessment with stability index. Quality Engineering 31(2):289-301.   DOI
6 Montgomery, D. C. 2013. Introduction to Statistical Quality Control, 7th ed. USA, John Wiley & Sons.
7 Parra-Frutos, I. 2013. Testing homogeneity of variances with unequal sample sizes. Computational Statistics 28(3):1269-1297.   DOI
8 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]   DOI
9 Wheeler, D. J. 2004. Advanced Topics in Statistical Process Control, 2nd ed. USA, SPC Press.
10 Shper, V. and Adler, Y. 2017. The importance of time order with Shewhart control charts. Quality and Reliability Engineering International 33(6):1169-1177.   DOI
11 Ramirez, J. G. 2016. A health screening for your processes. JMP Foreword 11-12. [Google Scholar]
12 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]
13 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.   DOI
14 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.   DOI
15 Ramirez, B. and Runger, G. 2006. Quantitative techniques to evaluate process stability. Quality Engineering 18(1):53-68.   DOI
16 Podolski, G. 1989-90. Standard deviation: root mean square versus range conversion. Quality Engineering 2(2):155-161.   DOI
17 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.   DOI
18 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.   DOI
19 Dean, A. and Voss, D. 1999. Design and Analysis of Experiments. USA, Springer-Verlag.
20 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.   DOI
21 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.   DOI
22 Sall, J. 2018. Scaling-up process characterization. Quality Engineering 30(1):62-78.   DOI
23 Patnaik, P. B. 1949, The non-central X2- and F-distributions and their applications. Biometrika 36(1/2):202-232.
24 Ramirez, B. 2018. Discussion of Scaling-up process characterization. Quality Engineering 30(1):79-87.   DOI