Industrial Engineering and Management Systems

Korean Institute of Industrial Engineers (대한산업공학회)
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A Study of the PDCA and CAPD Economic Designs of the $\bar{x}$ Control Chart

  • Published : 2007.06.30
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Abstract

The PDCA (Plan, Do, Check and Act) cycle is often used in the field of quality management. Recently, business environments have become more competitive, and the due time of products has shortened. In a short production run process, to increase efficiency of management, the necessity for distinguishing the PDCA design that starts with PLAN and the CAPD design that starts with CHECK has been clarified. Starting from Duncan (1956), there have been a number of papers dealing with the economic design of control charts from the viewpoint of production run. Some authors (Gibra, 1971; Ladany and Bedi, 1976; etc.) have studied the economic design for finite-length runs; other authors (Crowder, 1992; Del Castillo and Montgomery, 1996; etc.) have studied the economic design for short runs. However, neither the PDCA nor the CAPD design of control charts has been considered. In this paper, both the PDCA and CAPD designs of the $\bar{\x}$ chart are defined based on Del Castillo and Montgomery's design (1996), and their mathematical formulations are shown. Then from an economic viewpoint, the optimal values of the sample size per each sampling, control limits width, and the sampling interval of the two designs are studied. Finally, by numerically analyzing the relations between the key parameters and the total expected cost per unit time, the comparisons between the two designs are considered in detail.

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References

  1. Amasaka, K. ed. (2003), Manufacturing Fundamentals: The Application of Intelligence Control Chart-Digital Engineering for Superior Quality Assurance, Japanese Standards Association (in Japanese).
  2. Bai, D. S. and Lee, M. K. (1998), An economic design of variable sampling interval x control Charts, International Journal of Production Economics, 54, 57-64.
  3. Chen, Y. K. (2003) An economic-statistical designed for a VSI x control chart under non-normality, The International Journal of Advanced Manufacturing Technology, 22, 602-610. https://doi.org/10.1007/s00170-003-1612-3
  4. Chou, C.-Y., Li, M.-H. C., Wang, P.-H. (2001), Economic Statistical Design of Averages Control Charts for Monitoring a Process under Non-normality, The International Journal of Advanced Manufacturing Technology, 17, 603-609. https://doi.org/10.1007/s001700170144
  5. Chou, C. Y., Liu, H. R., Chen, C. H., Huang, X. R. (2002), Economic-statistical design of multivariate control charts using quality loss function, The International Journal of Advanced Manufacturing Technology, 20, 916-924. https://doi.org/10.1007/s001700200215
  6. Crowder, S. V. (1992), An SPC designs for short production run: minimizing expected cost, Technometrics, 34, 64-73. https://doi.org/10.2307/1269553
  7. Del Castillo, E. and Montgomery, D. C. (1996), A General Design for the Optimal Economic Design of x Charts Used to Control Short or Long Run Processes, IIE Transactions, 28, 193-201. https://doi.org/10.1080/07408179608966266
  8. Duncan, A. J. (1956), The economic design of charts used to maintain current control of a process, Journal of the American Statistical Association, 51, 228-242. https://doi.org/10.2307/2281343
  9. Gibra, I. N. (1971), Economically Optimal Determination of the Parameters of x Control Charts, Management Science, 17, 635-647. https://doi.org/10.1287/mnsc.17.9.635
  10. Ikezawa, T. (1985), I have leaned from TQC, Quality Management, 36(1), 6-12 (in Japanese).
  11. Jones, L. L. and Case, K. E. (1981), Economic design of a joint x and R Chart, IIE Transactions, 13, 182-195. https://doi.org/10.1080/05695558108974551
  12. Ladany, S. P. and Bedi, D. N. (1976), Selection of the Optimal Setup Policy, Naval research Logistics Quarterly, 23, 219-233. https://doi.org/10.1002/nav.3800230205
  13. Lowry, C. A. and Montgomery, D. C. (1995), A review of multivariate control chart, IIE Transactions, 27, 800-810. https://doi.org/10.1080/07408179508936797
  14. Matsui, M. (2005), A management cycle model: switching control under lot processing and time span, Journal of Japan Industrial Management Association, 56, 256-264.
  15. Miyakawa, M. (2000), Technologe for Getting Quality-What the Taguchi Method has Brought Us, Union of Japanese Scientists and Engineers (in Japanese).
  16. Montgomery, D. C. (1985), Introduction to Statistical Quality Control, John Wiley ＆ Sons, Inc.
  17. Reynolds, M. R., Amin, R. W., Arnold, J. C., Nachlas, J. A. (1988), $\bar{x}$ Charts with variable sampling intervals, Technometrics, 30, 181-192. https://doi.org/10.2307/1270164
  18. Saniga, E. M. (1989), Economic statistical Design of control Charts with an application to $\bar{x}$and R Chart, Technometrics, 31, 313-320. https://doi.org/10.2307/3556141
  19. Shiba, S. and Walden, D. (2001), Four Practical Revolutions in Management: Systems for Creating Unique Organizational Capability (Total Quality Management), Productivity Pr.
  20. Sun, J., Tsubaki, M. and Matsui, M. (2005), Economic considerations in CAPD Model of P Control Chart for Quality Improvement. ICQ'05-Tokyo International Conference on Quality Proceedings, VI-10.
  21. Takahashi, T. (1999), The basic concept of quality management and SQC/TQM, Communications of Japan Industrial Management Association, 9, 60-63 (in Japanese).
  22. Yu, F. J. and Wu, H. H. (2004), An economic design for variable sampling interval MA control charts, The International Journal of Advanced Manufacturing Technology, 24, 41-47.