Statistical process control using shewhart control charts with supplementary runs rules

Methodology and Computing in Applied Probability

Volumn 9, Issue 2, 2007, Pages 207-224

  Koutras, M V ^a   Bersimis, S ^a   Maravelakis, P E ^a  

^a UNIVERSITY OF PIRAEUS   (Greece)

Author keywords

Average run length; Control charts; Markov chain; Patterns; Runs rules; Scans rules; Shewhart; Statistical process control

Indexed keywords

EID: 34248161040     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-007-9016-8     Document Type: Review

References (63)

1. L. A. Aerne, C. W. Champ, and S. E. Rigdon, "Evaluation of control charts under linear trend," Communications in Statistics. Theory and Methods vol. 20 pp. 3341-3349, 1991.
2. L. C. Alwan, C. W. Champ, and H. D. Maragah, "Study of the average run lengths for supplementary runs rules in the presence of autocorrelation," Communications in Statistics. Theory and Methods vol. 23 pp. 373-391, 1994.
3. R. W. Amin and W. G. H. Letsinger, "Improved switching rules in control procedures using variable sampling intervals," Communications in Statistics. Simulation and Computation vol. 20 pp. 205-230, 1991.
4. D. L. Antzoulakos and A. Rakintzis, "The Modified r m Control Chart for Detecting Small Process Average Shifts," (preprint) 2006.
5. 2 control chart with supplementary run rules," Quality Engineering vol. 16 pp. 359-368, 2004.
6. N. Balakrishnan and M. V. Koutras, Runs and Scans with Applications, Wiley: New York, 2002.
7. A. F. Bissel, "An attempt to unify the theory of quality control procedures," Bulletin in Applied Statistics vol. 5 pp. 113-128, 1978.
8. P. D. Bourke, "Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection," Journal of Quality Technology vol. 23 pp. 225-238, 1991.
9. C. W. Champ, "Steady-state run length analysis of a Shewhart quality control chart with supplementary runs rules," Communications in Statistics. Theory and Methods vol. 21 pp. 765-777, 1992.
10. C. W. Champ and W. H. Woodall, "Exact results for Shewhart control charts with supplementary runs rules," Technometrics vol. 29 pp. 393-399, 1987.
11. C. W. Champ and W. H. Woodall, "A program to evaluate the run length distribution of a Shewhart control chart with supplementary runs rules," Journal of Quality Technology vol. 22 pp. 68-73, 1990.
12. C. W. Champ and W. H. Woodall, "Signal probabilities of runs rules supplementing a Shewhart control chart," Communications in Statistics. Simulation and Computation vol. 26 pp. 1347-1360, 1997.
13. T. K. Das and V. Jain, "An economic design model for x-bar charts with random sampling policies," IIE Transactions vol. 29 pp. 507-518, 1997.
14. T. K. Das, V. Jain, and A. Gosavi, "Economic design of dual-sampling-interval sampling policies for x-bar charts with and without run rules," IIE Transactions vol. 30 pp. 515-523, 1997.
15. R. B. Davis and T. C. Krehbiel, "Shewhart and zone control chart performance under linear trend," Communications in Statistics. Simulation and Computation vol. 31 pp. 91-96, 2002.
16. R. B. Davis and W. H. Woodall, "Performance of the control chart trend rule under linear shift," Journal of Quality Technology vol. 20 pp. 260-262, 1990.
17. R. B. Davis and W. H. Woodall, "Evaluating and improving the synthetic control chart," Journal of Quality Technology vol. 34 pp. 200-207, 2002.
18. R. B. Davis A. Homer, and W. H. Woodall, "Performance of the zone control chart," Communications in Statistics. Theory and Methods vol. 19 pp. 1581-1587, 1990.
19. R. B. Davis, J. Chun, and Y. Y. Guo, "Improving the performance of the zone control chart," Communications in Statistics. Theory and Methods vol. 23 pp. 3557-3565, 1994.
20. C. Derman and S. M. Ross, Statistical Aspects of Quality Control, Academic: San Diego, CA, 1997.
21. J. J. Divoky and E. W. Taylor, "Detecting process drift with combinations of trend and zonal supplementary runs rules," International Journal of Quality and Reliability Management vol. 12 pp. 60-71, 1995.
22. B. P. Dudding and W. J. Jannet, Quality Control Charts, B.S. 600 R. London: B.S.I., 1942.
23. J. C. Fu and W. Y. W. Lou, Distribution Theory of Runs and Patterns and its Applications: A Finite Markov Chain Imbedding Approach, World Scientific: New Jersey, 2003.
24. J. C. Fu, G. Shmueli, and Y. M. Chang, "A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules," Statistics and Probability Letters vol. 65 pp. 457-466, 2003.
25. J. C. Fu, F. A. Spiring, and H. S. Xie, "On the average run lengths of quality control schemes using a Markov chain approach," Statistics and Probability Letters vol. 56 pp. 369-380, 2002.
26. J. Glaz, J. Naus, and S. Wallenstein, Scan Statistics, Springer: Berlin Heidelberg New York, 2001.
27. A. M. Hurwitz, and M. A. Mathur, "Very simple set of process control rules," Quality Engineering vol. 1 pp. 21-29, 1992.
28. A. H. Jaehn, "Zone control charts - SPC made easy," Quality vol. 26 pp. 51-53, 1987.
29. A. H. Jaehn, "Zone control charts find new applications," ASQC Quality Congress Transactions pp. 890-895, 1989.
30. M. B. C. Khoo, "Design of runs rules schemes," Quality Engineering vol. 16 pp. 27-43, 2003.
31. 2 control charts," Quality Engineering vol. 15 pp. 671-675, 2003.
32. M. Klein, "Modified Shewhart-EWMA control charts," IIE Transactions vol. 29 pp. 1051-1056, 1997.
33. M. Klein, "Two alternatives to the Shewhart x-bar control chart," Journal of Quality Technology vol. 32 pp. 427-431, 2000.
34. M. V. Koutras, S. Bersimis, and D. L. Antzoulakos, "Improving the performance of the chi-square control chart via runs rules," Methodology and Computing in Applied Probability vol. 8 pp. 409-426, 2006.
35. V. Kuralmani, M. Xie, T. N. Goh, and F. F. Gan, "A conditional decision procedure for high yield processes," IIE Transactions vol. 34 pp. 1021-1030, 2002.
36. A. C. Lowry, C. W. Champ, and W. H. Woodall, "The performance of control charts for monitoring process variation," Communications in Statistics. Simulation and Computation vol. 24 pp. 409-437, 1995.
37. D. C. Montgomery, Introduction to Statistical Quality Control, Wiley: New York, 2001.
38. P. G. Moore, "Some properties of runs in quality control procedures," Biometrika vol. 45 pp. 89-95, 1958.
39. F. Mosteller, "Note on application of runs to quality control charts," Annals of Mathematical Statistics vol. 12 pp. 228-231, 1941.
40. L. S. Nelson, "The Shewhart control chart - test for special causes," Journal of Quality Technology vol. 16 pp. 237-239, 1984.
41. L. S. Nelson, "Interpreting Shewharts x-bar chart," Journal of Quality Technology vol. 17 pp. 114-116, 1985.
42. P. R. Nelson and P. L. Stephenson, "Runs tests for group control charts," Communications in Statistics. Theory and Methods vol. 25 pp. 2739-2765, 1996.
43. E. S. Page, "Continuous inspection schemes," Biometrika vol. 41 pp. 100-115, 1954.
44. E. S. Page, "Control charts with warning lines," Biometrics vol. 42 pp. 243-257, 1955.
45. A. C. Palm, "Tables of run length percentiles for determining the sensitivity of Shewhart control charts for averages with supplementary runs rules," Journal of Quality Technology vol. 22 pp. 289-298, 1990.
46. C. P. Quesenberry, "SPC Q charts for a binomial parameter p: Short or long runs," Journal of Quality Technology vol. 23 pp. 239-246, 1991.
47. S. W. Roberts, "Properties of control chart zone tests," Bell System Technical Journal vol. 37 pp. 83-114, 1958.
48. S. W. Roberts, "Control charts based on geometric moving averages," Technometrics vol. 1 pp. 239-250, 1959.
49. W. A. Shewhart, Economic Control of Quality of Manufactured Products, Macmillan: New York, 1931.
50. G. Shmueli and A. Cohen, "Run-length distribution for control charts with runs and scans rules," Communication in Statistics. Theory and Methods vol. 32 pp. 475-495, 2003.
51. E. Walker, J. W. Philpot, and J. Clement, "False signal rates for the Shewhart control chart with supplementary runs tests," Journal of Quality Technology vol. 23 pp. 247-252, 1991.
52. H. Weiler, "The use of runs to control the mean in quality control," Annals of Mathematical Statistics vol. 48 pp. 816-825, 1953.
53. Western Electric, Statistical Quality Control Handbook, Western Electric Corporation, Indianapolis, Ind., 1956.
54. J. A. Westgard and T. Groth, "Power functions for statistical control rules," Clinical Chemistry vol. 25 pp. 863-869, 1979.
55. J. A. Westgard, P. L. Barr, M. R. Hunt, and T. Groth, "A multi-run Shewhart chart for quality control in clinical chemistry," Clinical Chemistry vol. 27 pp. 493-501, 1981.
56. D. J. Wheeler, "Detecting a shift in process average: Tables of the power function for x-bar charts," Journal of Quality Technology vol. 15 pp. 155-170, 1983.
57. P. S. Wludyka and S. L. Jacobs, "Runs rules and p -charts for multi-stream binomial processes," Communication in Statistics. Simulation and Computation vol. 31 pp. 97-142, 2002.
58. J. Wolfowitz, "On the theory of runs with some applications to quality control," Annals of Mathematical Statistics vol. 14 pp. 280-284, 1943.
59. W. H. Woodall, "Controversies and contradictions in statistical process control," Journal of Quality Technology vol. 32 pp. 341-350, 2000.
60. Z. Wu and T. A. Spedding, "Synthetic control chart for detecting small shifts in the proces mean," Journal of Quality Technology vol. 32 pp. 32-38, 2000 (a).
61. Z. Wu and T. A. Spedding, "Implementing synthetic control charts," Journal of Quality Technology vol. 32 pp. 74-78, 2000 (b).
62. Z. Wu and S. H. Yeo, "Implementing synthetic control chart for attributes," Journal of Quality Technology vol. 33 pp. 112-114, 2001.
63. Z. Wu, S. H. Yeo, and T. A. Spedding, "A synthetic control chart for detecting fraction nonconforming increases," Journal of Quality Technology vol. 33 pp. 104-111, 2001.