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Communications in Statistics - Simulation and Computation Volume 21, 1992 - Issue 4
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Original Articles

Evaluation of average run lengths of cumulative sum charts for an arbitrary data distribution

Douglas M Hawkins Department of Applied Statistics School Statistics, University of Minnesota, St Paul, MN, 55108
Pages 1001-1020 | Received 01 Nov 1991, Published online: 27 Jun 2007

Citations (43)

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Chunjie Wu, Zhijun Wang, Steven MacEachern & Jingjing Schneider. (2023) A robust latent CUSUM chart for monitoring customer attrition. Journal of Applied Statistics 50:7, pages 1477-1495.
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Emmanuel Yashchin. (2022) Gradient analysis of Markov-type control schemes and its applications. Communications in Statistics - Simulation and Computation 51:4, pages 1814-1836.
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Aya A. Aly, Nesma A. Saleh & Mahmoud A. Mahmoud. (2021) An adaptive exponentially weighted moving average control chart for poisson processes. Quality Engineering 33:4, pages 627-640.
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Douglas M. Hawkins & F. Lombard. (2017) Cusum control for data following the von Mises distribution. Journal of Applied Statistics 44:8, pages 1319-1332.
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M. A. A. Cox. (2015) Exact Average Run Lengths for Monitoring Poisson Counts. Communications in Statistics - Theory and Methods 44:22, pages 4757-4771.
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Guanfu Liu, Xiaolong Pu, Lei Wang & Dongdong Xiang. (2015) CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid. Journal of Applied Statistics 42:8, pages 1635-1644.
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Zhonghua Li, Changliang Zou, Zhen Gong & Zhaojun Wang. (2014) The computation of average run length and average time to signal: an overview. Journal of Statistical Computation and Simulation 84:8, pages 1779-1802.
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Lianjie Shu, Wenpo Huang, Yan Su & Kwok-Leung Tsui. (2013) Computation of the run-length percentiles of CUSUM control charts under changes in variances. Journal of Statistical Computation and Simulation 83:7, pages 1238-1251.
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Sven Knoth & Sebastian Steinmetz. (2013) EWMA p charts under sampling by variables. International Journal of Production Research 51:13, pages 3795-3807.
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RonaldD. Armstrong & MabelT. Kung. (2011) CUSUM Hypothesis Tests and Alternative Response Probabilities for Finite Poisson Trials. Communications in Statistics - Simulation and Computation 40:7, pages 1057-1073.
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John M. Dukich & Douglas M. Hawkins. (2010) Identifying shifts in spread using the Cauchy CUSUM: an application to the Japanese yen/US dollar exchange rate. Applied Financial Economics 20:5, pages 417-424.
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Douglas M. Hawkins & Qiqi Deng. (2009) Combined Charts for Mean and Variance Information. Journal of Quality Technology 41:4, pages 415-425.
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Zhang Wu, Jianxin Jiao & Ying Liu. (2008) A binomial CUSUM chart for detecting large shifts in fraction nonconforming. Journal of Applied Statistics 35:11, pages 1267-1276.
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Paul F. Zantek. (2008) A Markov-chain method for computing the run-length distribution of the self-starting cumulative sum scheme. Journal of Statistical Computation and Simulation 78:5, pages 463-473.
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RonaldA. Webster & AnthonyN. Pettitt. (2007) Stability of Approximations of Average Run Length of Risk-Adjusted CUSUM Schemes Using the Markov Approach: Comparing Two Methods of Calculating Transition Probabilities. Communications in Statistics - Simulation and Computation 36:3, pages 471-482.
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J. Y. Liu, M. Xie & T. N. Goh. (2006) CUSUM Chart with Transformed Exponential Data. Communications in Statistics - Theory and Methods 35:10, pages 1829-1843.
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P. E. Maravelakis, S. Bersimis, J. Panaretos & S. Psarakis. (2002) IDENTIFYING THE OUT OF CONTROL VARIABLE IN A MULTIVARIATE CONTROL CHART. Communications in Statistics - Theory and Methods 31:12, pages 2391-2408.
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Marion R. Reynolds$suffix/text()$suffix/text() & Zachary G. Stoumbos. (1999) A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously. Journal of Quality Technology 31:1, pages 87-108.
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William H. Woodall. (1997) Control Charts Based on Attribute Data: Bibliography and Review. Journal of Quality Technology 29:2, pages 172-183.
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Carolyn H. White & J. Bert Keats. (1996) ARLs and Higher-Order Run-Length Moments for the Poisson CUSUM. Journal of Quality Technology 28:3, pages 363-369.
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Douglas M. Hawkins. (1995) Discussion. Journal of Quality Technology 27:4, pages 324-327.
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F. F. Gan & K. P. Choi. (1994) Computing Average Run Lengths for Exponential CUSUM Schemes. Journal of Quality Technology 26:2, pages 134-143.
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Douglas M. Hawkins. (1993) Robustification of Cumulative Sum Charts by Winsorization. Journal of Quality Technology 25:4, pages 248-261.
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Articles from other publishers (20)

Zhifang Mu Mu & Xuemin Zi Zi. (2023) Two-phase control chart monitoring binomial high-dimensional data streams. Two-phase control chart monitoring binomial high-dimensional data streams.
Cornelis J. Potgieter, F. Lombard & Douglas M. Hawkins. 2022. Directional Statistics for Innovative Applications. Directional Statistics for Innovative Applications 425 447 .
Sven Knoth. 2021. Frontiers in Statistical Quality Control 13. Frontiers in Statistical Quality Control 13 25 44 .
Mohammad Aghaali, Amir Kavousi, Abbas Shahsavani & Seyed Saeed Hashemi Nazari. (2020) Performance of Bayesian outbreak detection algorithm in the syndromic surveillance of influenza‐like illness in small region. Transboundary and Emerging Diseases.
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Manuel Cabral Morais & Sven Knoth. (2020) Improving the ARL profile and the accuracy of its calculation for Poisson EWMA charts. Quality and Reliability Engineering International 36:3, pages 876-889.
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Dushyant Tyagi. (2019) Designing an Effective Combined Shewhart-CUSUM Control Scheme with Exponentially Distributed Data. International Journal of Mathematical, Engineering and Management Sciences 4:5, pages 1277-1286.
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Vasyl Golosnoy & Jan Roestel. (2018) REAL-TIME MONITORING OF THE US INFLATION EXPECTATION PROCESS. Macroeconomic Dynamics 23:06, pages 2221-2249.
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Subhabrata Chakraborti & Marien Alet Graham. 2019. Nonparametric Statistical Process Control. Nonparametric Statistical Process Control 413 424 .
Y. Lu & S. Chatterjee. (2014) Instability and change detection in exponential families and generalized linear models, with a study of Atlantic tropical storms. Nonlinear Processes in Geophysics 21:6, pages 1133-1143.
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Shervin Asadzadeh, Abdollah Aghaie & Seyed Taghi Akhavan Niaki. (2012) AFT regression-adjusted monitoring of reliability data in cascade processes. Quality & Quantity 47:6, pages 3349-3362.
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Thomas P. Ryan. 2011. Statistical Methods for Quality Improvement. Statistical Methods for Quality Improvement 261 307 .
Michael Höhle. 2010. Statistical Modelling and Regression Structures. Statistical Modelling and Regression Structures 377 397 .
Y. J. Ou, J. X. Jiao & Z. Wu. (2009) An advanced CUSUM chart for attributes. An advanced CUSUM chart for attributes.
Michael Höhle, Michaela Paul & Leonhard Held. (2009) Statistical approaches to the monitoring and surveillance of infectious diseases for veterinary public health. Preventive Veterinary Medicine 91:1, pages 2-10.
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Paul F. Zantek & Scott T. Nestler. (2009) Performance and properties of Q ‐Statistic monitoring schemes . Naval Research Logistics (NRL) 56:3, pages 279-292.
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Michael Höhle & Michaela Paul. (2008) Count data regression charts for the monitoring of surveillance time series. Computational Statistics & Data Analysis 52:9, pages 4357-4368.
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Sven Knoth. (2006) Computation of the ARL for CUSUM- schemes. Computational Statistics & Data Analysis 51:2, pages 499-512.
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R.A. Vesilo. (1998) Cumulative sum technique in ATM traffic management. Cumulative sum technique in ATM traffic management.
Douglas M. Hawkins & David H. OlwellDouglas M. Hawkins & David H. Olwell. 1998. Cumulative Sum Charts and Charting for Quality Improvement. Cumulative Sum Charts and Charting for Quality Improvement 231 242 .
Vasyl Golosnoy & Jan Roestel. (2015) Real Time Monitoring of the US Inflation Expectation Process. SSRN Electronic Journal.
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