Abstract
Software for CUSUM design calculations is available from many sources. Yashchin (1986) describes an APL2 package with the capability of solving many design and ARL problems. At the time of this writing, this software is available on request from the author (yashchi@watson.ibm.com) and is scheduled to be put onto a Web site.
Keywords
- Control Chart
- Apply Statistics
- Royal Statistical Society
- Quality Technology
- Sequential Probability Ratio Test
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alwan, Layth C. (1986) CUSUM Quality Control — Multivariate Approach. Communications in Statistics B. Vol. 15. No. 12. 3531–3543.
Alt, Frank B. (1985) Multivariate Quality Control. Encyclopedia of the Statistical Sciences. Ed N. L. Johnson, S. Kotz and C. R. Read. Vol. 6. 111–122.
Alt, Frank. B., Heikes,R. G., and Montgomery, Douglas C. (1986) Economic Design of Chi-Square Control Chart for Multivariate Processes. Presented paper, Annual meetings of the American Statistical Association. Chicago.
Assaf, David, and Ritov, Ya’acov. (1989) Dynamic sampling procedures for detecting a change in the drift of Brownian motion: A non-Bayesian model. The Annals of Statistics. Vol. 17. 793–800.
Bagshaw, Michael, and Richard A. Johnson. (1975) The effect of serial correlation on the performance of CUSUM tests II. Technometrics. Vol. 17. 73–80.
Bagshaw, Michael, and Johnson, Richard A. (1975) The influence of reference values and estimated variance on the ARL of CUSUM tests. Journal of the Royal Statistical Society, Series B, Methodological. Vol. 37. 413–420.
Banzai, R. K. and Papantoni-Kazakos, P. (1986) An algorithm for detecting a change in a stochastic process. IEEE Transactions on Information Theory. Vol. IT-32. 227–235.
Barnard, George A. (1959) Control Charts and Stochastic Processes. Journal of the Royal Statistical Society, Series B. Vol. 21. No. 2. 239–257.
Basseville, M. and Nikiforov, I. (1993) Detection of Abrupt Changes. Englewood Cliffs, NJ: Prentice Hall.
Bather, John A. (1963) Control Charts and Minimization of Costs. Journal of the Royal Statistical Society, (B). Vol. 25.
Bauer, Peter, and Hackl, Peter. (1978) The use of MOSUMs for quality control. Technometrics. Vol. 20. 431–436.
Bauer, Peter, and Hackl, Peter. (1980) An extension of the MOSUM technique for quality control. Technometrics. Vol. 22. 1–7.
Baxter, L. A., Coutts, S. M., and Ross, G. A. (1980) Applications of linear models in motor insurance. Proceedings of the 21st International Congress of Actuaries. Zurich. 11–29.
Bissell, Alfred F. (1969) CUSUM techniques for quality control (with discussion). Applied Statistics. Vol. 18. 1–30.
Bissell, A. F. (1973) Process monitoring with variable element sizes. Applied Statistics. Vol. 22. 226–238.
Bissell, Alfred F. (1973) Process monitoring with variable element sizes. Applied Statistics. Vol. 22. 226–238.
Bissell, Alfred F. (1979) A semi-parabolic mask for CUSUM charts (Corr: V30 p77). The Statistician. Vol. 28. 1–8.
Bissell, A. F. (1984) The performance of control charts and cusums under linear trend. Applied Statistics. Vol. 33. 145–151.
Bissell, Alfred F. (1984) The performance of control charts and cusums under linear trend. Applied Statistics. Vol. 33. 145–151.
Bissell, Alfred F. (1984) Estimation of linear trend from a CUSUM chart or tabulation. Applied Statistics. Vol. 33. 152–157.
Bourke, Patrick D. (1991) Detecting a shift in fraction nonconforming using run-length control charts with 100 percent inspection. Journal of Quality Technology. Vol. 23. 225–238.
Bourke, Patrick D. (1992) Performance of cumulative sum schemes for monitoring low count-level processes. Metrika. Vol. 39. 365–384.
Box, George E. P. and Jenkins, G. M. (1976) Time Series Analysis: Forecasting and Control 2nd ed. San Francisco: Holden-Day.
Box, George E. P. and Kramer, T. (1992) Statistical Process Monitoring and Feedback Adjustment — A discussion. Technometrics. Vol. 34. 51–267.
Box, George E. P., and Ramirirez, J. (1992) Cumulative score charts. Quality and Reliability Engineering International. Vol. 8. 17–27.
Brook D., and Evans, D. A. (1972) An approach to the probability distribution of CUSUM run length. Biometrika Vol. 59. 539–549.
Brown, R. L., Durbin, J. and Evans, J. M. (1975) Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society, Series B, Methodological Vol. 37. 149–192.
Champ, Charles W. and Woodall, William H. (1987) Exact results for Shewhart control charts with supplementary runs rules. Technometrics. Vol. 29. 393–399.
Chhikara, R. S. and Folks, J. L. (1977) The Inverse Gaussian Distribution as a Lifetime Model. Technometrics Vol. 19. No. 4. 461–468.
Chhikara, R. S. and Folks, J. L. (1989) The Inverse Gaussian Distribution. New York: Marcel Dekker.
Chiu, W. K. (1974) The economic design of CUSUM charts for controlling normal means. Applied Statistics. Vol. 23. 420–433.
Chiu, W. K. (1974) The economic design of CUSUM charts for controlling normal means. Applied Statistics. Vol. 23. 420–433.
Crosier, Ronald B. (1986) A new two-sided cumulative sum quality control scheme (Corr: V31 p503). Technometrics. Vol. 28. 187–194.
Crosier, Ronald B. (1988) Multivariate Generalizations of Cumulative Sum Quality-Control Schemes. Technometrics Vol. 30. No. 3. 291–303.
Dawid, A. P. (1979) Conditional Independence in Statistical Theory. Journal of the Royal Statistical Society, Series B, Methodological. Vol. 41. 1–15.
Desmond, A. F. and Chapman, G. R. (1993) Modeling Task Completion Data with Inverse Gaussian Mixtures. Applied Statistics. Vol. 42. No. 4. 603–613.
Doganaksoy, Necip, Faltin, Frederick W., and Tucker, William T. (1991) Identification of Out of Control Quality Characteristics in a Multivariate Manufacturing Environment. Communications in Statistics B: Theory and Methods. Vol. 20. No. 9. 2774–2790.
Doob, J. L. (1953) Stochastic Processes. New York: Wiley.
Duncan, A. J. (1986). Quality Control and Industrial Statistics. 5 ed. Chicago: Irwin.
Dupuy, Trevor N. (1987) Can We Rely Upon Computer Combat Simulations? Armed Forces Journal International. August. 58–63
Edgeman, Rick. (1996) SPRT and CUSUM Results for Inverse Gaussian Processes, unpublished manuscript.
Fellner, William H. (1990) AS 258 Average run length for cumulative sum scheme. Applied Statistics Vol. 39. 402–412.
Ferguson, T.S. (1967) Mathematical Statistics. New York: Academic.
Flury, B., and Riedwyl, H. (1988) Multivariate Statistics A Practical Approach. London: Chapman and Hall.
Galpin, Jacqueline S., and Hawkins, Douglas M. (1984) The use of recursive residuals in checking model fit in linear regression. The American Statistician. Vol. 38. 94–105.
Gan, F. F. (1989) Combined cumulative sum and Shewhart variance charts. Journal of Statistical Computation and Simulation. Vol. 32. 149–163.
Gan, F. F. (1991) An optimal design of CUSUM quality control charts. Journal of Quality Technology. Vol. 23. 279–286.
Gan, F. F. (1992a) Exact run length distributions for one-sided exponential CUSUM schemes. Statistica Sinica. Vol. 2. 197–312.
Gan, F. F. (1992b) CUSUM control charts under linear drift. The Statistician Vol. 41. 71–84.
Gan, F. F. (1993a), An optimal design of CUSUM control charts for binomial counts. Journal of Applied Statistics. Vol. 20. 445–460.
Gan, F. F. (1993b) The run length distribution of a cumulative sum control chart. Journal of Quality Technology. Vol. 25. 205–215.
Gan, F. F., and Choi, K. P. (1994) Computing average run lengths for exponential CUSUM schemes. Journal of Quality Technology. Vol. 26. 134–143.
Goel, A. L. (1982) Cumulative sum control charts. Encyclopedia of Statistical Sciences. Vol. 2. 233–241.
Goel, A. L., and Wu, S. M. (1971). Determination of A.R.L. and a contour nomogram for CUSUM charts to control normal mean. Technometrics. Vol. 13. 221–230.
Gold, Morris S. (1989) The geometric approximation to the CUSUM run length distribution. Biometrika. Vol. 76. 725–733.
Goldsmith, P. L., and Whitfield, H. (1961) Average run lengths in cumulative chart quality control schemes (Corr: V3 p442). Technometrics. Vol. 3. 11–20.
Goodman, Alan L. (1982) Cumulative sum control and continuous processes. Proceedings of the ASQC Technical Conference. 270–274.
Gordon, Louis, and Pollak, Moshe. (1994) An efficient sequential nonparametric scheme for detecting a change of distribution. The Annals of Statistics. Vol. 22. 763–804.
Hawkins, Douglas M. (1981) A CUSUM for a scale parameter. Journal of Quality Technology. Vol.13. 228–231.
Hawkins, Douglas M. (1987) Self-starting cusums for location and scale. The Statistician Vol. 36. 299–315.
Hawkins, Douglas M.(1991) Multivariate quality control using regression adjusted variables. Technometrics. Vol. 33. 61–75.
Hawkins, Douglas M. (1991) Diagnostics for use with regression recursive residuals. Technometrics. Vol. 33. 221–234.
Hawkins, Douglas M. (1992) Evaluation of the average run length of cumulative sum charts for an arbitrary data distribution. Communications in Statistics, series B Vol. 21. 1001–1020.
Hawkins, Douglas M. (1993) Robustification of cumulative sum charts by Winsorization, Journal of Quality Technology. Vol. 25. 248–261.
Healy, J. D. (1987) A note on Multivariate CUSUM procedures. Technometrics. Vol. 29. 409–412.
Hoel, Paul G., Port, Sidney G., and Stone, Charles J. (1972) Introduction to Stochastic Processes. Prospect Heights, III: Waveland.
Hotelling, H. (1947) Multivariate quality control — illustrated by the air testing of sample bomb sights. Techniques of Statistical Analysis Ed. C. Eisenhart, M. W. Hastay and W. A. Wallis. New York: McGraw Hill.
Jackson, J. Edward, and Mudholkar, G. S. (1979) Control procedures for residuals associated with principal component analysis. Technometrics. Vol. 21. 341–349.
Jackson, J. Edward. (1985) Multivariate quality control. Communications in Statistics Vol. 14. 2657–2688.
Jackson, J. Edward. (1991) A User’s Guide to Principal Components. New York: John Wiley and Sons.
Johnson, Norman L. (1961) A Simple Theoretical Approach to Cumulative Sum Control Charts. Journal of the American Statistical Association. Vol. 56. 835–840.
Johnson, Norman L. (1963) Cumulative sum control charts for the folded normal distribution. Technometrics. Vol. 5. 451–458.
Johnson, Norman L. (1966) Cumulative sum control charts and the Weibull distribution, Technometrics, Vol. 8. 481–491.
Johnson, Norman L. and Leone, Fred C. (1962a) Cumulative Sum Control Charts: Mathematical principles applied to their construction and use. Part I. Industrial Quality Control Vol. 18, No. 12. 15–21.
Johnson, Norman L. and Leone, Fred C. (1962b) Cumulative Sum Control Charts: Mathematical principles applied to their construction and use. Part II. Industrial Quality Control. Vol. 19. No. 1. 29–36.
Johnson, Norman L. and Leone, Fred C. (1962c) Cumulative Sum Control Charts: Mathematical principles applied to their construction and use. Part III. Industrial Quality Control. Vol. 19. No. 2. 22–28.
Johnson, Norman L., and Kotz, Samuel. (1969) Discrete Distributions. Boston MA: Houghton Mifflin.
Johnson, Richard A., and Bagshaw, Michael. (1974) The effect of serial correlation on the performance of CUSUM tests. Technometrics. Vol. 16. 103–112.
Jorgensen, B. (1982) Lecture Notes in Statistics: Statistical Properties of the Generalized Inverse Gaussian Distribution. New York: Springer-Verlag.
Jun, Chi-Hyuck and Choi, Moon Soo. (1993) Simulating the Average Run Length for CUSUM Schemes using Variance Reduction Techniques. Communications in Statistics B: Simulation. Vol. 22. No. 3. 877–887.
Kemp, Kenneth W. (1967) A simple procedure for determining upper and lower limits for the average sample run length of a cumulative sum scheme. Journal of the Royal Statistical Society, Series B, Methodological Vol. 29. 263–265.
Khan, Rasul A. (1981) A note on Page’s two-sided cumulative sum procedure. Biometrika. Vol. 68. 717–719.
Lai, T. L. (1995) Sequential changepoint detection in quality control and dynamical systems. Journal of the Royal Statistical Society, Series B, Methdological. Vol. 57. 613–642.
Lange, K. L., Little, R. J. A., and Taylor, J. G. (1989) Robust statistical modeling using the distribution. Journal of the American Statistical Association. Vol. 84. 881–895.
Lawless, J. R. (1982) Statistical Models and Methods for Lifetime Data. New York: Wiley.
Lorden, G. (1971) Procedures for reacting to a change in distribution. Annals of Mathematical Statistics. Vol. 42. 1897–1908.
Lowry, Cynthia A., Woodall, William H., Champ, Charles W., and Rigdon, Stephen E. (1992) A Multivariate exponentially weighted moving average control chart. Technometrics. Vol. 34. 46–53.
Lucas, James M. (1976) The design and use of V-mask control schemes. Journal of Quality Technology Vol. 8. 1–11.
Lucas, James M. (1982) Combined Shewhart-CUSUM quality control schemes, Journal of Quality Technology Vol. 14. 51–59.
Lucas, James M. (1985) Counted data CUSUMS. Technometrics. Vol. 28. 129–144.
Lucas, James M. (1989) Control schemes for low count levels. Journal of Quality Technology. Vol. 21. 199–201.
Lucas, James M., and Crosier, Ronald B. (1982a) Robust CUSUM. Communications in Statistics A Vol. 11. 2669–2687.
Lucas, James M., and Crosier, Ronald B. (1982b) Fast Initial Response for CUSUM Quality Control Schemes: Give your CUSUM a Head Start. Technometrics. Vol. 24. No. 3. 199–205.
Mandel, B. J. (1969) The regression control chart. Journal of Quality Technology Vol. 1. 1–9.
McGilchrist, C. A., and Woodyer, K. D. (1975) Note on a distributionfree CUSUM technique. Technometrics. Vol. 17. 321–325.
Montgomery, Douglas C. (1991) Introduction to Statistical Process Control. 2nd Ed. New York: Wiley.
Montgomery, Douglas C., Keats, J. Bert, Runger, George C., and Messina, William S. (1994) Integrating statistical process control and engineering process control. Journal of Quality Technology. Vol. 26. 79–87.
Montgomery, Douglas C, and Mastrangelo, Christina M. Some statistical process control methods for autocorrelated data Journal of Quality Technology. Vol. 23. 179–204.
Moustakides, G. V. (1986) Optimal stopping times for detecting changes in distributions. Annals of Statistics. Vol. 14. 1379–1387.
Munford, A. G. (1980) A control chart based on cumulative scores. Applied Statistics. Vol. 29. 252–258.
Murphy, B. J. (1987) Selecting out-of-control variables with the T Multivariate quality control procedures. The Statistician. Vol. 36. 571–583.
Nabar, S. P. and Bilgi, Shobar. (1994) Cumulative Sum Control Chart for the inverse Gaussian distribution. Journal of the Indian Statistical Association. Vol. 32. 9–14.
Ncube, Matoteng M., and Amin, Raid W. (1990) Two parameter cuscore quality control procedures. Communications in Statistics, Part A-Theory and Methods. Vol. 19. 2191–2205.
Ncube, Matoteng M., and Woodall, William H. (1984) A combined Shewhart-cumulative score quality control chart. Applied Statistics. Vol. 33. 259–265.
Olwell, David H. (1996) Topics in Statistical Process Control Ann Arbor: University Microfilms.
Olwell, David H. (1997a) Statistical Process Control of Low Frequency Events. Proceedings of the 5th Annual USMA-ARL Technical Conference. West Point, NY: USMA.
Olwell, David H. (1997b) Managing Misconduct: Statistical Process Control applied to sexual harassment. 1991 Proceedings of the Section on Quality and Productivity. Alexandria, VA: American Statistical Association.
Page, E. S. (1954) Continuous inspection schemes. Biometrika. Vol. 41. 100–115.
Person, Ron (1996) Special Edition, Using Windows 1995. Indianapolis: Que.
Pignatiello, Joseph J. Jr. and Runger, George C. (1990) Comparisons of Multivariate CUSUM Charts. Journal of Quality Technology. Vol. 22 No. 3. 173–186.
Pollak, Moshe, and Siegmund, David. (1985) A diffusion process and its applications to detecting a change in the drift of Brownian motion. Biometrika. Vol. 72. 267–280.
Quesenberry, Charles P. (1991) SPC Q charts for start-up processes and short or long runs, Journal of Quality Technology Vol. 23. 213–224.
Quesenberry, Charles P. (1995) On properties of Poisson Q charts for Attributes. Journal of Quality Technology. Vol. 27. No. 4. 293–303.
Regula, Gary A. (1976) Optimal Cumulative Sum Procedures to Detect a Change in Distribution for the Gamma Family. Ph.D. Dissertation, Case Western Reserve University.
Reynolds, Marion R., Jr. (1975) Approximations to the average run length in cumulative sum control charts. Technometrics. Vol. 17. 65–71.
Reynolds, Marion R., Jr. (1989) Optimal variable sampling interval control charts. Sequential Analysis. Vol. 8. 361–379.
Reynolds, Marion R., Jr, Amin, Raid W., and Arnold, Jesse C. (1990) CUSUM charts with variable sampling intervals (C/R: p385-396). Technometrics. Vol. 32. 371–384.
Ritov, Ya’acov. (1990) Decision Theoretic Optimally of the CUSUM Procedure. Annals of Statistics Vol. 18. No. 3. 1464–1469.
Rocke, David M. (1989) Robust control charts. Technometrics. Vol. 31. 173–184.
Ross, S. M. (1971) Quality Control under Markovian Deterioration. Management Science. Vol. 17.
Ross, Sheldon M. (1990) Variance reduction in simulation via random hazards. Probability in the Engineering and Informational Sciences. Vol. 4. 299–309.
Rowlands, R. J., Nix, A. B. J., Abdollahian, M. A., and Kemp, Kenneth W. (1982) Snub-nosed V-mask control schemes. The Statistician. Vol. 31. 133–142.
Ryan, Thomas P. (1989) Statistical Methods for Quality Improvement. New York: Wiley.
Srivastava, M. S. and Worsley, K. J. (1986) Likelihood ratio tests for a change in the multivariate normal mean. Journal of the American Statistical Association Vol. 81 199–204.
Shewhart, Walter A. (1931) Economic Control of Quality of Manufactured Product. New York: Van Nostrand.
Siegmund, David. (1985) Sequential Analysis Tests and Confidence Intervals. New York: Springer-Verlag.
Siegmund, David. (1995) Using the generalized likelihood ratio statistic for sequential detection of a change-point. Annals of Statistics. Vol. 23. 255–271.
Taylor, Howard M. (1968) The economic design of cumulative sum control charts. Technometrics. Vol. 10. 479–488.
Tierney, Luke. (1990) LISP-STAT: An Object Oriented Environment for Statistical Computing and Dynamic Graphics. New York: Wiley.
Tracy, N. D., Young, J. C., and Mason, F. L. (1992) Multivariate control charts for individual observations. Journal of Quality Technology. Vol. 24. 88–95.
Vance, Lonnie. (1986). Average run lengths of cumulative sum control charts for controlling normal mean. Journal of Quality Technology. Vol. 18. 189–193.
Van Dobben de Bruyn, C. S. (1968), Cumulative Sum Tests: Theory and Practice. London: Griffin.
Vander Wiel, Scott A., Tucker, William T., Faltin, Frederick W., and Doganaksoy, Necip. (1992) Algorithmic statistical process control: Concepts and an application. Technometrics. Vol. 34. 286–297.
Vardeman, Stephen, and Ray, Di-ou. (1985) Average run lengths for CUSUM schemes when observations are exponentially distributed, Technometrics Vol. 27. 145–150.
Wade, M. R., and Woodall, W. M. (1992) A review of causeselecting control charts. Unpublished manuscript.
Wald, Abraham. (1944) On Cumulative Sums of Random Variables. Annals of Mathematical Statistics. Vol. 15.
Wald, Abraham (1945) Sequential Tests of Statistical Hypotheses. Annals of Mathematical Statistics. Vol. 16.
Wald, Abraham. (1947) Sequential Analysis. New York: Wiley.
Wald, Abraham, and Wolfowitz, Jacob. (1948) Optimum character of the sequential probability ratio test. Annals of Mathematical Statistics. Vol. 19. 326–339.
Waldmann, K. H. (1986) Bounds for the distribution of the run length of one-sided and two-sided CUSUM quality control schemes. Technometrics. Vol. 28. 61–67.
Westgard, J. O., Groth, T., Aronson, T., and de Verdier, C. (1977) Combined Shewhart-CUSUM control chart for improved quality control in clinical chemistry. Clinical Chemistry. Vol. 23. No. 10. 1881–1887.
Wetherill, G. Barrie. (1975) Sequential Methods in Statistics. London: Chapman and Hall.
Woodall, William H. (1983) The distribution of run-length of onesided CUSUM procedures for continuous random variables. Technometrics Vol. 25. 295–301.
Woodall, William H. (1984) On the Markov chain approach to the two-sided CUSUM procedure. Technometrics. Vol. 26. 41–46.
Woodall, William H. (1986) The Design of CUSUM Quality Control Charts. Journal of Quality Technology Vol. 18. No. 2. 99–102.
Woodall, William H., and Ncube, Matoteng M. (1985) Multivariate CUSUM quality-control procedures. Technometrics Vol. 27. 285–292.
Worsley, Keith J., (1979) On the likelihood ratio test for a shift in location of normal populations. Journal of the American Statistical Association Vol. 74. 365–367.
Worsley, Keith J. (1986) Confidence regions and tests for a changepoint in a sequence of exponential family random variables. Biometrika Vol. 73. 91–104.
Xiao, H. (1992) A cumulative score control scheme. Applied Statistics. Vol. 41. 47–54.
Yashchin, Emmanuel. (1985a) On a unified approach to the analysis of two-sided cumulative sum control schemes with head starts. Advances in Applied Probability. Vol. 17. 562–593.
Yashchin, Emmanuel. (1985b) On the analysis and design of CUSUM-Shewhart control schemes. IBM Journal of Research and Development. Vol. 29. 377–391.
Yashchin, Emmanuel. (1989) Weighted cumulative sum technique. Technometrics. Vol. 31. 321–338. Correction: Vol. 32. p. 469.
Yashchin, Emmanuel. (1992) Analysis of CUSUM and other Markovtype control schemes by using empirical distributions. Technometrics. Vol. 34. 54–63.
Yashchin, Emmanuel. (1993a) Statistical Control Schemes: Methods, Applications, and Generalizations. International Statistical Review Vol. 61. No. 1. 41–66.
Yashchin, Emmanuel. (1993b) Performance of CUSUM control schemes for serially correlated observations. Technometrics. Vol. 35. 37–52.
Yashchin, Emmanuel. (1995) Estimating the current mean of a process subject to abrupt change. Technometrics. Vol. 37. 311–323.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hawkins, D.M., Olwell, D.H. (1998). References. In: Cumulative Sum Charts and Charting for Quality Improvement. Statistics for Engineering and Physical Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1686-5_11
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1686-5_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7245-8
Online ISBN: 978-1-4612-1686-5
eBook Packages: Springer Book Archive