Multivariate monitoring of the process mean vector with sequential sampling

Journal of Quality Technology

Volumn 37, Issue 2, 2005, Pages 149-162

  Reynolds Jr , Marion R ^a,c   Kim, Keunpyo ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b PRA International USA   (Netherlands)

^c Depts of Statistics and Forestry   (United States)

Author keywords

Average Time to Signal; Multivariate Exponentially Weighted Moving Average Control Chart; Statistical Process Control; Variable Sample Size; Variable Sampling Rate

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; PROBLEM SOLVING; QUALITY CONTROL; SAMPLING; VECTORS;

MULTIVARIATE CONTROL CHARTS; MULTIVARIATE EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHARTS; VARIABLE SAMPLE SIZES; VARIABLE SAMPLING RATES;

STATISTICAL PROCESS CONTROL;

EID: 18144362924     PISSN: 00224065     EISSN: None     Source Type: Journal    
DOI: 10.1080/00224065.2005.11980313     Document Type: Article

References (44)

1. ANNADI, H. P.; KEATS, J. B.; RUNGER, G. C.; and MONTGOMERY, D. C. (1995). "An Adaptive Sample Size CUSUM Control Chart". International Journal of Production Research 33, pp. 1605-1616.
2. 2 Control Chart with Adaptive Sample Sizes". International Journal of Production Research 34, pp. 2853-2862.
3. 2 Control Chart with Variable Sampling Intervals". International Journal of Production Research 39, pp. 3127-3140.
4. 2 Control Charts with Variable Sampling Schemes as Opposed to MEWMA Chart". International Journal of Production Research 41, pp. 2169-2182.
5. ARNOLD, J. C. and REYNOLDS, M. R., JR. (2001). "CUSUM Control Charts with Variable Sample Sizes and Sampling Intervals". Journal of Quality Technology 33, pp. 68-81.
6. BAXLEY, R. V., JR. (1995). "An Application of Variable Sampling Interval Control Charts". Journal of Quality Technology 27, pp. 275-282.
7. BODDEN, K. M. and RIGDON, S. E. (1999). "A Program for Approximating the In-Control ARL for the MEWMA Chart". Journal of Quality Technology 31, pp. 120-123.
8. CAROT, V.; JABALOYES, J. M.; and CAROT, T. (2002). "Combined Double Sampling and Variable Sampling Interval X̄ Chart". International Journal of Production Research 40, pp. 2175-2186.
9. COSTA, A. F. B. (1994). "X̄ Charts with Variable Sample Size". Journal of Quality Technology 26, pp. 155-163.
10. COSTA, A. F. B. (1997). "X̄ Charts with Variable Sample Size and Sampling Intervals". Journal of Quality Technology 29, pp. 197-204.
11. CROASDALE, P. (1974). "Control Charts for a Double-Sampling Scheme Based on Average Production Run Lengths". International Journal of Production Research 12, pp. 585-592.
12. DAUDIN, J. J. (1992). "Double Sampling X̄ Charts". Journal of Quality Technology 24, pp. 78-87.
13. DUNCAN, A. J. (1986). Quality Control and Industrial Statistics, 5th ed. Irwin, Homewood, IL.
14. GHOSH, B. K. (1970). Sequential Tests of Statistical Hypotheses. Addison-Wesley, Reading, MA.
15. HE, D. (2002). "Development of Multivariate Double Sampling X̄ Control Charts". Presented at the INFORMS 2002 Annual Meeting, San Jose, CA.
16. HE, D.; GRIGORYAN, A.; and SIGH, M. (2002). "Design of Double- and Triple-Sampling X̄ Control Charts Using Genetic Algorithms". International Journal of Production Research 40, pp. 1387-1404.
17. HOTELLING, H. (1947). "Multivariate Quality Control-Illustrated by the Air Testing of Sample Bombsights" in Techniques of Statistical Analysis, edited by C. Eisenhart, M. W. Hastay, and W. A. Wallis, McGraw-Hill, New York, NY.
18. IRIANTO, D. and SHINOZAKI, N. (1998). "An Optimal Double Sampling X Control Chart". International Journal of Industrial Engineering - Theory Applications and Practice 5, pp. 226-234.
19. LOWRY, C. A.; WOODALL, W. H.; CHAMP, C. W.; and RIGDON, S. E. (1992). "A Multivariate Exponentially Weighted Moving Average Control Chart". Technometrics 34, pp. 46-53.
20. MASON, R. L. and YOUNG, J. C. (2002). Multivariate Statistical Process Control with Industrial Applications. ASA-SIAM, Philadelphia, PA.
21. MOLNAU, W. E.; RUNGER, G. C.; MONTGOMERY, D. C.; SKINNER, K. R.; LOREDO, E. N.; and PRABHU, S. S. (2001). "A Program for ARL Calculation for Multivariate EWMA Charts". Journal of Quality Technology 33, pp. 515-521.
22. MONTGOMERY, D. C. (2005). Introduction to Statistical Quality Control. 5th Ed. John Wiley & Sons, New York, NY.
23. PARK, C. and REYNOLDS, M. R., JR. (1999). "Economic Design of a Variable Sampling Rate X̄ Chart". Journal of Quality Technology 31, pp. 427-443.
24. PRABHU, S. S.; MONTGOMERY, D. C.; and RUNGER, G. C. (1994). "A Combined Adaptive Sample Size and Sampling Interval X̄ Control Scheme". Journal of Quality Technology 26, pp. 164-176.
25. PRABHU, S. S.; RUNGER, G. C.; and KEATS, J. B. (1993). "An Adaptive Sample Size X̄ Control Scheme". International Journal of Production Research 31, pp. 2895-2909.
26. REYNOLDS, M. R., JR. (1995). "Evaluating Properties of Variable Sampling Interval Control Charts". Sequential Analysis 14, pp. 59-97.
27. REYNOLDS, M. R., JR. (1996a). "Shewhart and EWMA Variable Sampling Interval Control Charts with Sampling at Fixed Times". Journal of Quality Technology 28, pp. 199-212.
28. REYNOLDS, M. R., JR. (1996b). "Variable Sampling Interval Control Charts with Sampling at Fixed Times". IIE Transactions 28, pp. 497-510.
29. REYNOLDS, M. R., JR.; AMIN, R. W.; and ARNOLD, J. C. (1990). "CUSUM Charts with Variable Sampling Intervals". Technometrics 32, pp. 371-384.
30. REYNOLDS, M. R., JR. and ARNOLD, J. C. (2001). "EWMA Control Charts with Variable Sample Sizes and Variable Sampling Intervals". IIE Transactions 33, pp. 511-530.
31. REYNOLDS, M. R., JR. and STOUMBOS, Z. G. (1998). "The SPRT Chart for Monitoring a Proportion". IIE Transactions 30, pp. 545-561.
32. REYNOLDS, M. R., JR. and STOUMBOS, Z. G. (2001). "Monitoring the Process Mean and Variance Using Individual Observations and Variable Sampling Intervals". Journal of Quality Technology 33, pp. 181-205.
33. REYNOLDS, M. R., JR. and STOUMBOS, Z. G. (2004). "Control Charts and the Efficient Allocation of Sampling Resources". Technometrics, 46, pp. 200-214.
34. RIGDON, S. E. (1995a). "An Integral Equation for the In-Control Average Run Length of a Multivariate Exponentially Weighted Moving Average Control Chart". Journal of Statistical Computation and Simulation 52, pp. 351-365.
35. RIGDON, S. E. (1995b). "A Double-Integral Equation for the Average Run Length of a Multivariate Exponentially Weighted Moving Average Control Chart". Statistics and Probability Letters 24, pp. 365-373.
36. RUNGER, G. C. and PRABHU, S. S. (1996). "A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart". Journal of the American Statistical Association 91, pp. 1701-1706.
37. STOUMBOS, Z. G. and REYNOLDS, M. R., JR. (1996). "Control Charts Applying a General Sequential Test at Each Sampling Point". Sequential Analysis 15, pp. 159-183.
38. STOUMBOS, Z. G. and REYNOLDS, M. R., JR. (1997). "Control Charts Applying a Sequential Test at Fixed Sampling Intervals". Journal of Quality Technology 29, pp. 21-40.
39. STOUMBOS, Z. G. and REYNOLDS, M. R., JR. (2001). "The SPRT Control Chart for the Process Mean with Samples Starting at Fixed Times". Nonlinear Analysis, Series B: Real-World Applications 2, pp. 1-34.
40. STOUMBOS, Z. G. and SULLIVAN, J. H. (2002). "Robustness to Non-Normality of the Multivariate EWMA Control Chart". Journal of Quality Technology 34, pp. 260-276.
41. SULLIVAN, J. H. and WOODALL, W. H. (1996). "A Comparison of Multivariate Control Charts for Individual Observations". Journal of Quality Technology 28, pp. 398-408.
42. SULLIVAN, J. H. and WOODALL, W. H. (1998). "Adapting Control Charts for the Preliminary Analysis of Multivariate Observations". Communications In Statistics - Simulation and Computation 27, pp. 953-979.
43. TAGARAS, G. (1998). "A Survey of Recent Developments in the Design of Adaptive Control Charts". Journal of Quality Technology 30, pp. 212-231.
44. ZIMMER, L. S.; MONTGOMERY, D. C.; and RUNGER, G. C. (1998). "Evaluation of a Three-State Adaptive Sample Size X̄ Control Chart". International Journal of Production Research 36, pp. 733-743.