Computing the run length probability distribution for CUSUM charts

Journal of Quality Technology

Volumn 34, Issue 2, 2002, Pages 209-215

  Luceño, Alberto ^a   Puig Pey, Jaime ^a  

^a UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

Cumulative sum control charts; Statistical process control

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; PROBABILITY DISTRIBUTIONS; QUALITY CONTROL;

CUMULATIVE SCORE CHARTS; CUMULATIVE SUM CHART;

STATISTICAL PROCESS CONTROL;

EID: 0442315278     PISSN: 00224065     EISSN: None     Source Type: Journal    
DOI: 10.1080/00224065.2002.11980147     Document Type: Article

References (21)

1. Barnard, G. A. (1959). "Control Charts and Stochastic Processes". Journal of the Royal Statistical Society Series B 21, pp. 239-271.
2. Bissell, A. F. (1969). "Cusum Techniques for Quality Control". Applied Statistics 18, pp. 1-30.
3. Box, G. E. P. and Luceño, A. (1997). Statistical Control by Monitoring and Feedback Adjustment. John Wiley, New York, NY.
4. Box, G. E. P. and Ramírez, J. (1992). "Cumulative Score Charts". Quality and Reliability Engineering International 8, pp. 17-27.
5. Brook, D. and Evans, D. A. (1972). "An Approach to the Probability Distribution of Cusum Run Length". Biometrika 59, pp. 539-549.
6. Ewan, W. D. and Kemp, K. W. (1960). "Sampling Inspection of Continuous Processes with No Autocorrelation Between Successive Results". Biometrika 47, pp. 363-380.
7. Fellner, W. H. (1990). "Algorithm AS 258: Average Run Lengths for Cumulative Sum Schemes". Applied Statistics 39, pp. 402-412.
8. Gan, F. F. (1993). "The Run Length Distribution of a Cumulative Sum Control Chart". Journal of Quality Technology 25, pp. 205-215.
9. 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 13, pp. 221-230.
10. Hawkins, D. M. and Olwell, D. H. (1998). Cumulative Sum Charts and Charting for Quality Improvement. Springer, New York, NY.
11. Lenth, R. V. (1989). "Algorithm AS 243: Cumulative Distribution Function of the Non-central t-Distribution". Applied Statistics 38, pp. 185-189.
12. Luceño, A. (1999). "Average Run Lengths and Run Length Probability Distributions for Cuscore Charts to Control Normal Mean". Computational Statistics and Data Analysis 32, pp. 177-195.
13. Luceño, A. and Box, G. E. P. (2000). "Influence of the Sampling Interval, Decision Limit, and Autocorrelation on the Average Run Length in Cusum Charts". Journal of Applied Statistics 27, pp. 177-183.
14. Luceño, A. and Puig-Pey, J. (2000). "Evaluation of the Run Length Probability Distribution for CUSUM Charts: Assessing Chart Performance". Technometrics 42, pp. 411-416.
15. Owen, D. B. (1968). "A Survey of Properties and Applications of the Noncentral t-Distribution". Technometrics 10, pp. 445-478.
16. Page, E. S. (1954). "Continuous Inspection Schemes". Biometrika 41, pp. 100-115.
17. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; and Flannery, B. P. (1992). Numerical Recipes. Cambridge University Press, Cambridge, UK.
18. Vance, L. C. (1986). "Average Run Lengths of Cumulative Sum Control Charts for Controlling Normal Means". Journal of Quality Technology 18, pp. 189-193.
19. Wilks, S. S. (1962). Mathematical Statistics. John Wiley, New York, NY.
20. Woodall, W. H. (1983). "The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables". Technometrics 25, pp. 295-301.
21. Yashchin, E. (1985). "On the Analysis and Design of CUSUM-Shewhart Control Schemes". IBM Journal of Research and Development 29, pp. 377-391.