Economic statistical design of adaptive control schemes for monitoring the mean and variance: An application to analyzers

Nonlinear Analysis: Real World Applications

Volumn 6, Issue 5, 2005, Pages 817-844

  Stoumbos, Zachary G ^a   Reynolds Jr , Marion R ^b  

^a RUTGERS BUSINESS SCHOOL   (United States)

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

Author keywords

Analyzers; Calibration; Economic design; EWMA control charts; Loss function; Markov chains; Shewhart control charts; Standards; Statistical process control; Stochastic optimization; Variable sampling interval control charts

Indexed keywords

CALIBRATION; CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; MARKOV PROCESSES; MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; RANDOM PROCESSES; STANDARDS; STATISTICAL PROCESS CONTROL;

CONTROL CHARTS; ECONOMIC DESIGN; ECONOMIC STATISTICAL DESIGN; EXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA); LOSS FUNCTION; SHEWHART CONTROL CHARTS; STOCHASTIC OPTIMIZATION; VARIABLE SAMPLING INTERVAL CONTROL CHARTS;

ADAPTIVE CONTROL SYSTEMS;

EID: 21144440746     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2005.05.002     Document Type: Article

References (57)

1. J. Abadie J. Carpentier Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints, in: R. Fletcher (Ed.), Optimization 1969 Academic Press New York, NY pp. 34-37
2. S.L. Albin L. Kang G. Shea An X and EWMA chart for individual observations J. Quality Technol. 29 1997 41-48
3. R.W. Amin R.A. Ethridge A note on individual and moving range control charts J. Quality Technol. 30 1998 70-74
4. M.S. Bazaraa H.D. Sherali C.M. Shetty Nonlinear Programming second ed. 1993 Wiley New York, NY
5. W. Boyes Instrumentation Reference Book third ed. 2003 Elsevier Science Burlington, MA
6. K.J. Clevett Process Analyzer Technology 1986 Wiley New York, NY
7. A.F.B. Costa M.A. Rahim Economic design of X̄ charts with variable parameters: A Markov chain approach J. Appl. Stat. 28 2001 875-885
8. S.V. Crowder A simple method for studying run-length distributions of exponentially weighted moving average charts Technometrics 29 1987 401-407
9. R. Domangue S.C. Patch Some omnibus exponentially weighted moving average statistical process monitoring schemes Technometrics 33 1991 299-313
10. A.J. Duncan The economic design of X̄ charts used to maintain current control of a process J. Am. Stat. Assoc. 51 1956 228-242
11. F.F. Gan Joint monitoring of process mean and variance using exponentially weighted moving average control charts Technometrics 37 1995 446-453
12. C. Ho K.E. Case Economic design of control charts: A literature review for 1981-1991 J. Quality Technol. 26 1994 39-53
13. R. Hooke T.A. Jeeves Direct search solution of numerical and statistical problems J. Assoc. Comput. Mach. 8 1961 212-229
14. J.B. Keats E. Del Castillo E. von Collani E.M. Saniga Economic modeling for statistical process control J. Quality Technol. 29 1997 144-147
15. T.L. Lai Sequential changepoint detection in quality control and dynamical systems (with discussion) J. Roy. Stat. Soc. Ser. B 57 1995 613-658
16. L.S. Lasdon A.D. Waren A. Jain M. Ranter Design and testing of generalized reduced gradient code for nonlinear programming ACM Trans. Math. Software 4 1978 34-50
17. E.L. Lehmann Testing Statistical Hypotheses second ed. 1985 Springer New York, NY
18. B.G. Liptak Analytical Instrumentation 1994 CRC Press Boca Raton, FL
19. T.J. Lorenzen L.C. Vance The economic design of control charts: A unified approach Technometrics 28 1986 3-10
20. J.M. Lucas M.S. Saccucci Exponentially weighted moving average control schemes: Properties and enhancements Technometrics 32 1990 1-12
21. D.G. Luenberger Linear and Nonlinear Programming second ed. 1989 Addison-Wesley Reading, MA
22. J.F. MacGregor T.J. Harris The exponentially weighted moving variance J. Quality Technol. 25 1993 106-118
23. D.C. Montgomery The economic design of control charts: A review and literature survey J. Quality Technol. 12 1980 75-87
24. D.C. Montgomery J.C. Torng J.K. Cochran F.P. Lawrence Statistically constrained economic design of EWMA control charts J. Quality Technol. 27 1995 250-256
25. M.C. Morais A. Pacheco On the performance of combined EWMA schemes for μ and σ: A Markovian approach Commun. Stat. Part B - Simulation Comput. 29 2000 153-174
26. L.S. Nelson Control charts for individual measurements J. Quality Technol. 14 1982 172-173
27. G.D. Nichols On-Line Process Analyzers 1988 Wiley New York, NY
28. E.S. Page Continuous inspection schemes Biometrika 41 1954 100-114
29. C. Park M.R. Reynolds Jr. Economic design of a variable sampling rate X̄ chart J. Quality Technol. 31 1999 427-443
30. S.S. Prabhu D.C. Montgomery G.C. Runger Economic-statistical design of an adaptive X̄ chart Int. J. Prod. Econom. 49 1997 1-15
31. M.R. Reynolds Jr. Optimal variable sampling interval control charts Sequential Anal. 8 1989 361-379
32. M.R. Reynolds Jr. Evaluating properties of variable sampling interval control charts Sequential Anal. 14 1995 59-97.
33. M.R. Reynolds Jr. Variable sampling interval control charts with sampling at fixed times IIE Trans. 28 1996 497-510.
34. M.R. Reynolds Jr. Z.G. Stoumbos The SPRT chart for monitoring a proportion IIE Trans. Quality Rel. Eng. 30 1998 545-561.
35. M.R. Reynolds Jr. Z.G. Stoumbos Monitoring the process mean and variance using individual observations and variable sampling intervals J. Quality Technol. 33 2001 181-205.
36. M.R. Reynolds Jr. Z.G. Stoumbos Individuals control schemes for monitoring the mean and variance of processes subject to drifts Stochast. Anal. Appl. 19 2001 863-892.
37. M.R. Reynolds Jr. Z.G. Stoumbos Control charts and the efficient allocation of sampling resources Technometrics 46 2004 200-214
38. M.R. Reynolds Jr. Z.G. Stoumbos Should observations be grouped for effective process monitoring? J. Quality Technol. 36 2004 343-366.
39. S.E. Rigdon E.N. Cruthis C.W. Champ Design strategies for individuals and moving range control charts J. Quality Technol. 26 1994 274-287.
40. S.W. Roberts Control charts based on geometric moving averages Technometrics 1 1959 239-250
41. K.C.B. Roes R.J.M.M. Does Y. Schurink Shewhart-type control charts for individual observations J. Quality Technol. 25 1993 188-198.
42. S.M. Ross Applied Probability Models with Optimization Applications 1970 Holden-Day San Francisco, CA
43. M.S. Saccucci R.W. Amin J.M. Lucas Exponentially weighted moving control schemes with variable sampling intervals Commun. Stat. - Simul. Comput. 21 1992 627-657
44. E.M. Saniga Economic statistical control charts design with an application to X̄ and R charts Technometrics 31 1989 313-321
45. S.E. Shamma R.W. Amin An EWMA quality control procedure for jointly monitoring the mean and variance Int. J. Quality Rel. Manage. 10 1993 58-67
46. W.A. Shewhart Economic Control of Quality of Manufactured Product 1931 Van Nostrand New York, NY
47. D. Siegmund Sequential Analysis 1985 Springer New York, NY
48. Z.G. Stoumbos J. Mittenthal G.C. Runger Steady-state-optimal adaptive control charts based on variable sampling intervals Stochast. Anal. Appl. 19 2001 1025-1057
49. Z.G. Stoumbos M.R. Reynolds Jr. Control charts applying a general sequential test at each sampling point Sequential Anal. 15 1996 159-183
50. Z.G. Stoumbos M.R. Reynolds Jr. Control charts applying a sequential test at fixed sampling intervals J. Quality Technol. 29 1997 21-40
51. Z.G. Stoumbos M.R. Reynolds Jr. Corrected diffusion theory approximations in evaluating properties of SPRT charts for monitoring a process mean Nonlinear Anal. - Theory, Methods Appl. 30 1997 3987-3996
52. Z.G. Stoumbos M.R. Reynolds Jr. Robustness to non-normality and autocorrelation of individuals control charts J. Stat. Comput. Simul. 66 2000 145-187
53. Z.G. Stoumbos M.R. Reynolds Jr. The SPRT control chart for the process mean with samples starting at fixed times Nonlinear Anal. - Real World Appl. 2 2001 1-34
54. Z.G. Stoumbos M.R. Reynolds Jr. T.P. Ryan W.H. Woodall The state of statistical process control as we proceed into the 21st century J. Am. Stat. Assoc. 95 2000 992-998
55. Z.G. Stoumbos M.R. Reynolds Jr. W.H. Woodall Control chart schemes for monitoring the mean and variance of processes subject to sustained shifts and drifts, in: C.R. Rao, R. Khattree (Eds.), Handbook of Statistics: Statistics in Industry vol. 22 2003 Elsevier Science Amsterdam, Netherlands pp. 553-571
56. G. Tagaras A survey of recent developments in the design of adaptive control charts J. Quality Technol. 30 1998 212-231
57. E. Yashchin Statistical control schemes: Methods, applications and generalizations Int. Stat. Rev. 61 1993 41-66