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Original Articles

Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed

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Pages 145-150 | Published online: 23 Mar 2012

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Read on this site (53)

Eralp Dogu & Muhammad Noor-ul-Amin. (2023) Monitoring exponentially distributed time between events data: self-starting perspective. Communications in Statistics - Simulation and Computation 52:3, pages 1104-1118.
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Nirpeksh Kumar, Subha Chakraborti & Philippe Castagliola. (2022) Phase II exponential charts for monitoring time between events data: performance analysis using exact conditional average time to signal distribution. Journal of Statistical Computation and Simulation 92:7, pages 1457-1486.
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Patrick D. Bourke. (2022) CUSUM design for detection of event-rate increases for a Poisson process. Quality Engineering 34:1, pages 36-51.
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Shu Wu, Philippe Castagliola & Giovanni Celano. (2021) A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data. Journal of Applied Statistics 48:3, pages 434-454.
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Vasileios Alevizakos & Christos Koukouvinos. (2020) A double exponentially weighted moving average chart for time between events. Communications in Statistics - Simulation and Computation 49:10, pages 2765-2784.
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Nirpeksh Kumar. (2020) Conditional analysis of Phase II exponential chart for monitoring times to an event. Quality Technology & Quantitative Management 17:3, pages 285-306.
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Dorra Rahali, Philippe Castagliola, Hassen Taleb & Michael B. C. Khoo. (2019) Evaluation of Shewhart time-between-events-and-amplitude control charts for several distributions. Quality Engineering 31:2, pages 240-254.
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Liang Qu, Shuguang He, Michael B. C. Khoo & Philippe Castagliola. (2018) A CUSUM chart for detecting the intensity ratio of negative events. International Journal of Production Research 56:19, pages 6553-6567.
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Liang Qu, Michael B.C. Khoo, Philippe Castagliola & Zhen He. (2018) Exponential cumulative sums chart for detecting shifts in time-between-events. International Journal of Production Research 56:10, pages 3683-3698.
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Yuan Cheng, Lirong Sun & Baocai Guo. (2018) Phase II synthetic exponential charts and effect of parameter estimation. Quality Technology & Quantitative Management 15:1, pages 125-142.
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N. Kumar, S. Chakraborti & A. C. Rakitzis. (2017) Improved Shewhart-Type Charts for Monitoring Times Between Events. Journal of Quality Technology 49:3, pages 278-296.
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Yuan Cheng, Amitava Mukherjee & Min Xie. (2017) Simultaneously monitoring frequency and magnitude of events based on bivariate gamma distribution. Journal of Statistical Computation and Simulation 87:9, pages 1723-1741.
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Nirpeksh Kumar & Subha Chakraborti. (2017) Bayesian Monitoring of Times Between Events: The Shewhart t-Chart. Journal of Quality Technology 49:2, pages 136-154.
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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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Jun Yang, Huan Yu, Yuan Cheng & Min Xie. (2015) Design of exponential control charts based on average time to signal using a sequential sampling scheme. International Journal of Production Research 53:7, pages 2131-2145.
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Saylisse Dávila, George Runger & Eugene Tuv. (2014) Public health surveillance with ensemble-based supervised learning. IIE Transactions 46:8, pages 770-789.
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Liang Qu, Zhang Wu, Michael B. C. Khoo & Abdur Rahim. (2014) Time-Between-Event Control Charts for Sampling Inspection. Technometrics 56:3, pages 336-346.
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Yu Liu & X. Rong Li. (2013) Performance Analysis of Sequential Probability Ratio Test. Sequential Analysis 32:4, pages 469-497.
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Wenpo Huang, Lianjie Shu, Wei Jiang & Kwok-Leung Tsui. (2013) Evaluation of run-length distribution for CUSUM charts under gamma distributions. IIE Transactions 45:9, pages 981-994.
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Eduardo Santiago & Joel Smith. (2013) Control Charts Based on the Exponential Distribution: Adapting Runs Rules for the t Chart. Quality Engineering 25:2, pages 85-96.
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Yujuan Xie, Min Xie & Thong Ngee Goh. (2011) Two MEWMA Charts for Gumbel's Bivariate Exponential Distribution. Journal of Quality Technology 43:1, pages 50-65.
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Yafen Liu, Zhen He, M. Shamsuzzaman & Zhang Wu. (2010) A combined control scheme for monitoring the frequency and size of an attribute event. Journal of Applied Statistics 37:12, pages 1991-2013.
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Marianne Frisén. (2009) Optimal Sequential Surveillance for Finance, Public Health, and Other Areas. Sequential Analysis 28:3, pages 310-337.
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Zhang Wu, Jianxin Jiao & Zhen He. (2009) A control scheme for monitoring the frequency and magnitude of an event. International Journal of Production Research 47:11, pages 2887-2902.
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C. W. Zhang, M. Xie, J. Y. Liu & T. N. Goh. (2007) A control chart for the Gamma distribution as a model of time between events. International Journal of Production Research 45:23, pages 5649-5666.
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Ji Ying Liu, Min Xie, Thong Ngee Goh & L. Y. Chan. (2007) A study of EWMA chart with transformed exponential data. International Journal of Production Research 45:3, pages 743-763.
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Cai Wen Zhang, Min Xie & Thong Ngee Goh. (2006) Design of exponential control charts using a sequential sampling scheme. IIE Transactions 38:12, pages 1105-1116.
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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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William H. Woodall. (2006) The Use of Control Charts in Health-Care and Public-Health Surveillance. Journal of Quality Technology 38:2, pages 89-104.
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Yoon-Dong Lee. (2005) Unified Solutions of Integral Equations of SPRT for Exponential Random Variables. Communications in Statistics - Theory and Methods 33:1, pages 65-74.
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Connie M Borror, J. Bert Keats & Douglas C Montgomery. (2003) Robustness of the time between events CUSUM. International Journal of Production Research 41:15, pages 3435-3444.
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PatrickD. Bourke. (2001) The geometric CUSUM chart with sampling inspection for monitoring fraction defective. Journal of Applied Statistics 28:8, pages 951-972.
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F. F. Gan & T. C. Chang. (2000) Computing Average Run Lengths of Exponential EWMA Charts. Journal of Quality Technology 32:2, pages 183-187.
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Seven Knoth & Seven Knoth. (1998) Exact average run lengths of cusum schemes for erlang distributions. Sequential Analysis 17:2, pages 173-184.
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F. F. Gan. (1998) Designs of One- and Two-Sided Exponential EWMA Charts. Journal of Quality Technology 30:1, pages 55-69.
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G. Geoffrey Vining & Marion R. Reynolds$suffix/text()$suffix/text(). (1997) Multi-Level Sampling Interval Approach to Control Charts. Journal of Quality Technology 29:4, pages 418-428.
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JAMESR. BUCK, JOSEPHJ. PIGNATIELLO$suffix/text()$suffix/text() & TZVI RAZ. (1995) Bayesian Poisson rate estimation using parameter maps. IIE Transactions 27:3, pages 405-412.
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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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F. F. Gan. (1994) Design of Optimal Exponential CUSUM Control Charts. Journal of Quality Technology 26:2, pages 109-124.
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Giovanni Radaelli. (1994) Poisson and negative binomial dynamics for counted data under CUSUM-type charts. Journal of Applied Statistics 21:5, pages 347-356.
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Chi-Hyuck Jun & Moon Soo Choi. (1993) Simulating the average run length for cusum schemes using variance reduction techniques. Communications in Statistics - Simulation and Computation 22:3, pages 877-887.
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Douglas M Hawkins. (1992) Evaluation of average run lengths of cumulative sum charts for an arbitrary data distribution. Communications in Statistics - Simulation and Computation 21:4, pages 1001-1020.
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Patrick D. Bourke. (1991) Detecting a Shift in Fraction Nonconforming Using Run-Length Control Charts with 100% Inspection. Journal of Quality Technology 23:3, pages 225-238.
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Yaakov Mevorach & Moshe Pollak. (1991) A Small Sample Size Comparison of the Cusum and Shiryayev-Roberts Approaches: Changepoint Detection. American Journal of Mathematical and Management Sciences 11:3-4, pages 277-298.
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W. J. Padgett & John D. Spurrier. (1990) Shewhart-Type Charts for Percentiles of Strength Distributions. Journal of Quality Technology 22:4, pages 283-288.
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AMYHANCOCK BOYD & GARYD. HERRIN. (1988) A Minimum Cost Sequential Test to Monitor Injury Incidence on an Operation. IIE Transactions 20:3, pages 269-279.
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William H. Woodall. (1986) The Design of CUSUM Quality Control Charts. Journal of Quality Technology 18:2, pages 99-102.
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JamesM. Lucas. (1985) Counted Data CUSUM's. Technometrics 27:2, pages 129-144.
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Mohammadreza Mirzaei Novin & Amirhossein Amiri. Simultaneous monitoring of multivariate time between events and their magnitude using multivariate marked Hawkes point process. Quality Technology & Quantitative Management 0:0, pages 1-21.
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