Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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A Note for 1.5σ Shift of Six Sigma

식스시그마의 1.5σ 이동에 대한 소고

  • Park, Jong Hun (Department of Business Administration, Daegu Catholic University)
  • Received : 2022.02.03
  • Accepted : 2022.02.16
  • Published : 2022.03.31
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Abstract

Six Sigma is a philosophy and systematic methodology for quality improvement. It encourages continuous quality improvement efforts to achieve the ideal goal of 6σ. Sigma(σ) is a statistic representing the standard deviation of the normal distribution, and 6σ level means a level where the tolerance of the specification is six times the standard deviation of the process distribution. In terms of the defective rate, the 6σ level achieves the 0.002 defectives per one million units. However, in the field, the 6σ level is used in the sense of achieving 3.4 defects per one million opportunities, which shows a large gap from the 6σ level in the statistical viewpoint. This is because field practitioners accept a 1.5σ shift of the mean of process when calculating the defective rate under sigma level. It said that the acceptance of 1.5σ shift of the mean is from experience, but there is no research or theoretical explanation to support it logically. Although it is a non-scientific explanation based on experience, considering that there has been no objection to the 1.5σ shift for a long time and it is rather accepted, it is judged that there is a reasonable basis for the 1.5σ shift. Therefore, this study tries to find a reasonable explanation through detective power of control chart via the run-rules to the 1.5σ shift empirically recognized by practitioners.

Keywords

Acknowledgement

This work was supported by research grants from Daegu Catholic University in 2019.

References

  1. Aldowaisan, T., Nourelfath, M., and Hassan, J., Six Sigma performance for non-normal processes, European Journal of Operational Research, 2015, Vol. 247, No. 3, pp. 968-977. https://doi.org/10.1016/j.ejor.2015.06.036
  2. An, Y.S. and Hwang, I., A New Management Innovation Strategy Through 6sigma for R&D linked with TRIZ, Journal of Korean Society of Industrial and Systems Engineering, 2009, Vol. 32, No. 3, pp. 178-187.
  3. Basu, R. and Wright, J. N., Quality beyond six sigma, Routledge, 2012.
  4. Bothe, D.R., Statistical reason for the 1.5 σ shift, Quality Engineering, 2002, Vol. 14, No. 3, pp. 479-487. https://doi.org/10.1081/QEN-120001884
  5. Champ, C.W. and Woodall, W.H., Exact results for Shewhart control charts with supplementary runs rules, Technometrics, 1987, Vol. 29, No. 4, pp. 393-399. https://doi.org/10.1080/00401706.1987.10488266
  6. Duncan, A.J., Quality Control and Industrial Statistics, Homewood, IL: Richard D. Irwin. Duncan5 Quality Control and Industrial Statistics, 1986.
  7. Evans, D H., Statistical Tolerancing: The State of the Art: Part II. Methods for Estimating Moments, Journal of Quality Technology, 1975, Vol. 7, No. 1, pp. 1-12. https://doi.org/10.1080/00224065.1975.11980657
  8. Evans, J.R. and Lindsay, W.M., An introduction to Six Sigma and process improvement, Cengage Learning, 2014.
  9. Griffiths, D., Bunder, M., Gulati, C., and Onizawa, T., The probability of an out of control signal from Nelson's supplementary Zig-Zag test, Journal of Statistical Theory and Practice, 2010, Vol. 4, No. 4, pp. 609-615. https://doi.org/10.1080/15598608.2010.10412007
  10. Hahn, G.J., Doganaksoy, N., and Hoerl, R., The evolution of six sigma, Quality Engineering, 2000, Vol. 12, No. 3, pp. 317-326. https://doi.org/10.1080/08982110008962595
  11. Hahn, G.J., Hill, W.J., Hoerl, R.W., and Zinkgraf, S.A., The impact of Six Sigma improvement- a glimpse into the future of statistics, The American Statistician, 1999, Vol. 53, No. 3, pp. 208-215. https://doi.org/10.2307/2686099
  12. Harry, M.J., Resolving the mysteries of Six Sigma: statistical constructs and engineering rationale, Phoenix: Palladyne Publishing, 2003.
  13. https://www.gigacalculator.com/calculators/six-sigma-dpmo-calculator.php.
  14. https://www.isixsigma.com/new-to-six-sigma/dmaic/15-sigma-process-shift/.
  15. https://ko.wikipedia.org/wiki/6_시그마.
  16. https://www.managementstudyguide.com/six-sigma-shift.htm.
  17. https://www.qualitydigest.com/inside/six-sigma-column/15-sigma-shift-explained-040406.html.
  18. https://www.sixsigma-institute.org/Six_Sigma_DMAIC_Process_Measure_Phase_Process_Capability.php.
  19. Hwang, G.H., A Study on the Performances of Driving Six Sigma in a ICT Industry, Journal of Korean Society of Industrial and Systems Engineering, 2012, Vol. 35, No. 2, pp. 220-227.
  20. Lee, P.H., Understanding the 1.5 σ shift, Samsung Economic Research Institute(SERI), 2005.
  21. Linderman, K., Schroeder, R.G., Zaheer, S., and Choo, A.S., Six Sigma: A goal-theoretic perspective, Journal of Operations Management, 2003, Vol. 21, No. 2, pp. 193-203. https://doi.org/10.1016/S0272-6963(02)00087-6
  22. Mehrjerdi, Y.Z., Six-Sigma: Methodology, tools and its future, Assembly Automation, 2011, Vol. 31 No. 1, pp. 79-88 https://doi.org/10.1108/01445151111104209
  23. Montgomery, D.C. and Woodall, W.H., An overview of six sigma. International Statistical Review/Revue, Internationale de Statistique, 2008, pp. 329-346.
  24. Nelson, L.S., The Shewhart control chart- tests for special causes, Journal of Quality Technology, 1984, Vol. 16, No. 4, pp. 237-239. https://doi.org/10.1080/00224065.1984.11978921
  25. Ninerola, A., Sanchez-Rebull, M.V., and Hernandez-Lara, A.B., Six Sigma literature: a bibliometric analysis, Total Quality Management and Business Excellence, 2019, pp. 1-22.
  26. Perera, A.D., Jayamaha, N.P., Grigg, N.P., Tunnicliffe, M., and Singh, A., The application of machine learning to consolidate critical success factors of lean six sigma, IEEE Access, 2021, Vol. 9, pp. 112411-112424. https://doi.org/10.1109/ACCESS.2021.3103931
  27. Pyzdek, T. and Keller, P.A., The six sigma handbook (Vol. 4). New York, NY, USA: McGraw-Hill Education, 2014.
  28. Raval, N. and Muralidharan, K., A note on 1.5 Sigma shift in performance evaluation, International Journal of Reliability, Quality and Safety Engineering, 2016, Vol. 23, No. 6, pp. 1640007. https://doi.org/10.1142/S0218539316400076
  29. Roberts, S.W., Properties of control chart zone tests, Bell System Technical Journal, 1958, Vol. 37, No. 1, pp. 83-114. https://doi.org/10.1002/j.1538-7305.1958.tb03870.x
  30. Saxena, M.M., Six Sigma Methodologies and its Application in Manufacturing Firms, International Journal Of Engineering And Management Research, 2021, Vol. 11, No. 4, pp. 79-85.
  31. Sony, M., Antony, J., Park, S., and Mutingi, M., Key criticisms of Six Sigma: A systematic literature review, IEEE Transactions on Engineering Management, 2019, Vol. 67, No. 3, pp. 950-962. https://doi.org/10.1109/tem.2018.2889517
  32. Stevenson, J.R., Detecting the process' 1.5 sigma shift: A quantitative study. University of Northern Iowa, 2009.
  33. Tennant, G. (2017) Six Sigma: SPC and TQM in manufacturing and services. Routledge.
  34. Yang, K., Basem, S., and El-Haik, B., Design for six sigma (pp. 184-186). New York: McGraw-Hill, 2003.