The Revised m-of-k Runs Rule Based on Median Run Length

References

• Antzoulakos , D. L. , Rakitzis , C. A. ( 2008 ). The revised m-of-k runs rule . Quality Engineering 20 ( 1 ): 175 – 81 .
   Google Scholar
• Barnard , G. A. ( 1959 ). Control charts and stochastic processes . Journal of the Royal Statistical Society, Series B 21 ( 2 ): 239 – 271 .
   Web of Science ®Google Scholar
• Bissell , A. F. ( 1969 ). CUSUM techniques for quality control . Journal of the Royal Statistical Society, Series C 18 ( 1 ): 1 – 30 .
   Web of Science ®Google Scholar
• Brook , D. , Evans , D. A. ( 1972 ). An approach to the probability distribution of CUSUM run length . Biometrika 59 ( 3 ): 539 – 549 .
   Web of Science ®Google Scholar
• DeVor , R. E. , Chang , T. , Sutherland , J. W. ( 1992 ). Statistical Quality Design and Control . New York : Macmillan .
   Google Scholar
• Fu , J. C. , Koutras , M. V. ( 1994 ). Distribution theory of runs: A Markov chain approach . Journal of the American Statistical Association 89 ( 427 ): 1050 – 1058 .
   Web of Science ®Google Scholar
• Gan , F. F. ( 1992 ). An optimal design of cumulative sum control charts based on median run length. Research Report No. 536. Lee Kong Chian Center for Mathematical Research, Singapore .
   Google Scholar
• Gan , F. F. ( 1993a ). An optimal design of EWMA control charts based on median run length . Journal of Statistical Computation and Simulation 45 ( 3&4 ): 169 – 184 .
   Web of Science ®Google Scholar
• Gan , F. F. (1993b). The run length distribution of a cumulative sum control chart. Journal of Quality Technology 25(3):205–215.
   Web of Science ®Google Scholar
• Gan , F. F. ( 1994 ). An optimal design of cumulative sum control chart based on median run length . Communications in Statistics – Simulation and Computation 23 ( 2 ): 485 – 503 .
   Web of Science ®Google Scholar
• Khoo , M. B. C. ( 2003 ). Design of runs rules schemes . Quality Engineering 16 ( 1 ): 27 – 43 .
   Google Scholar
• Khoo , M. B. C. ( 2004 ). Performance measures for the Shewhart control chart . Quality Engineering 16 ( 4 ): 585 – 590 .
   Google Scholar
• Khoo , M. B. C. , Ariffin , K. N. ( 2006 ). Two improved runs rules for the Shewhart control chart . Quality Engineering 18 ( 2 ): 173 – 178 .
   Google Scholar
• Klein , M. ( 2000 ). Two alternatives to the Shewhart control chart . Journal of Quality Technology 32 ( 4 ): 427 – 431 .
   Web of Science ®Google Scholar
• Koutras , M. V. , Bersimis , S. , Maravelakis , P. E. ( 2007 ). Statistical process control using Shewhart control charts with supplementary runs rules . Methodology and Computing in Applied Probability 9 ( 2 ): 207 – 224 .
   Web of Science ®Google Scholar
• Montgomery , D. C. ( 2009 ). Introduction to Statistical Quality Control, ed. , 6th New York : John Wiley & Sons .
   Google Scholar
• Waldmann , K.-H. ( 1986a ). Bounds for the distribution of the run length of geometric moving average charts . Journal of the Royal Statistical Society, Series C 35 ( 2 ): 151 – 158 .
   Web of Science ®Google Scholar
• Waldmann , K.-H. ( 1986b ). Bounds for the distribution of the run length of one-sided and two-sided CUSUM quality control schemes . Technometrics 28 ( 1 ): 61 – 67 .
   Web of Science ®Google Scholar
• Western Electric. ( 1956 ). Statistical Quality Control Handbook . Indianapolis , IN : Western Electric Corporation .
   Google Scholar
• Woodall , W. H. ( 1983 ). The distribution of the run length of one-sided CUSUM procedures for continuous random variables . Technometrics 25 ( 3 ): 295 – 301 .
   Web of Science ®Google Scholar
• Zhang , L. , Chen , G. , Castagliola , P. ( 2009 ). On t and EWMA t charts for monitoring changes in the process mean . Quality and Reliability Engineering International 25 ( 8 ): 933 – 945 .
   Web of Science ®Google Scholar