Advanced search
Publication Cover
Journal of Quality Technology
A Quarterly Journal of Methods, Applications and Related Topics
Volume 38, 2006 - Issue 2
Submit an article Journal homepage
205
Views
92
CrossRef citations to date
0
Altmetric
Articles

A Markov Chain Model for the Adaptive CUSUM Control Chart

Lianjie ShuUniversity of Macau, MacauView further author information
&
Wei JiangStevens Institute of Technology, Hoboken, NJ07030View further author information
Pages 135-147 | Published online: 05 Feb 2018

Citations (92)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (39)

Poune Ghasemian & Rassoul Noorossana. (2024) The Inertial properties of EWMA control charts. Communications in Statistics - Theory and Methods 53:12, pages 4542-4555.
Read now
Zameer Abbas, Hafiz Zafar Nazir, Saddam Akber Abbasi, Muhammad Riaz & Dongdong Xiang. (2023) On designing efficient memory-type charts using multiple auxiliary-information. Journal of Statistical Computation and Simulation 93:4, pages 646-670.
Read now
O. Arda Vanli & Rupert Giroux. (2022) An adaptive cumulative sum method for monitoring integer-valued time-series data. Quality Engineering 34:2, pages 230-247.
Read now
Muhammad Noor-ul-Amin & Afshan Riaz. (2021) Performance of adaptive exponentially weighted moving average control chart in the presence of measurement error. Journal of Statistical Computation and Simulation 91:11, pages 2328-2343.
Read now
Saba Abbasi & Abdul Haq. (2020) New adaptive CUSUM charts for process mean. Communications in Statistics - Simulation and Computation 49:11, pages 2944-2962.
Read now
Saba Abbasi & Abdul Haq. (2019) Enhanced adaptive CUSUM charts for process mean. Journal of Statistical Computation and Simulation 89:13, pages 2562-2582.
Read now
Saba Abbasi & Abdul Haq. (2019) Optimal CUSUM and adaptive CUSUM charts with auxiliary information for process mean. Journal of Statistical Computation and Simulation 89:2, pages 337-361.
Read now
Aya A. Aly, Ramadan M. Hamed & Mahmoud A. Mahmoud. (2017) Optimal design of the adaptive exponentially weighted moving average control chart over a range of mean shifts. Communications in Statistics - Simulation and Computation 46:2, pages 890-902.
Read now
Tianhua Wang & Shuguang Huang. (2016) An adaptive multivariate CUSUM control chart for signaling a range of location shifts. Communications in Statistics - Theory and Methods 45:16, pages 4673-4691.
Read now
Jiujun Zhang, Zhonghua Li, Qin Zhou & Zhaojun Wang. (2016) An Adaptive Shiryaev–Roberts Procedure for Signalling Varying Location Shifts. Communications in Statistics - Simulation and Computation 45:7, pages 2511-2527.
Read now
Wenpo Huang, Lianjie Shu & Wei Jiang. (2016) A Gradient Approach to the Optimal Design of CUSUM Charts Under Unknown Mean-Shift Sizes. Journal of Quality Technology 48:1, pages 68-83.
Read now
Honghao Zhao, Lianjie Shu & Kwok-Leung Tsui. (2015) A window-limited generalized likelihood ratio test for monitoring Poisson processes with linear drifts. Journal of Statistical Computation and Simulation 85:15, pages 2975-2988.
Read now
Yanjing Ou, Zhang Wu, Michael B. C. Khoo & Nan Chen. (2015) A rational sequential probability ratio test control chart for monitoring process shifts in mean and variance. Journal of Statistical Computation and Simulation 85:9, pages 1765-1781.
Read now
Nan Chen & Shiyu Zhou. (2015) CUSUM Statistical Monitoring of M/M/1 Queues and Extensions. Technometrics 57:2, pages 245-256.
Read now
J. Kim, K.N. Al-Khalifa, M.K. Jeong, A.M.S. Hamouda & E.A. Elsayed. (2014) Multivariate statistical process control charts based on the approximate sequential χ2 test. International Journal of Production Research 52:18, pages 5514-5527.
Read now
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.
Read now
Zhonghua Li & Peihua Qiu. (2014) Statistical Process Control Using a Dynamic Sampling Scheme. Technometrics 56:3, pages 325-335.
Read now
Qin Zhou, Wenpo Huang & Lianjie Shu. (2014) A comparison of weighted CUSUM procedures for monitoring process proportions with varying sample sizes. International Journal of Production Research 52:11, pages 3225-3238.
Read now
Peihua Qiu & Dongdong Xiang. (2014) Univariate Dynamic Screening System: An Approach For Identifying Individuals With Irregular Longitudinal Behavior. Technometrics 56:2, pages 248-260.
Read now
Liu Liu, Fugee Tsung & Jian Zhang. (2014) Adaptive nonparametric CUSUM scheme for detecting unknown shifts in location. International Journal of Production Research 52:6, pages 1592-1606.
Read now
Xin Zhang & Jiujun Zhang. (2013) CUSUM Procedures for Monitoring Process Mean and Variability. Communications in Statistics - Simulation and Computation 42:7, pages 1455-1471.
Read now
J. Kim, K.N. Al-Khalifa, M. Park, M.K. Jeong, A.M.S. Hamouda & E.A. Elsayed. (2013) Adaptive cumulative sum charts with the adaptive runs rule. International Journal of Production Research 51:15, pages 4556-4569.
Read now
Marion R. Reynolds$suffix/text()$suffix/text(), Jianying Lou, Jaeheon Lee & Sai Wang. (2013) The Design of GLR Control Charts for Monitoring the Process Mean and Variance. Journal of Quality Technology 45:1, pages 34-60.
Read now
Michael B. C. Khoo, V.H. Wong, Zhang Wu & Philippe Castagliola. (2012) Optimal design of the synthetic chart for the process mean based on median run length. IIE Transactions 44:9, pages 765-779.
Read now
Mei Yang, Zhang Wu, Ka Man Lee & Michael B.C. Khoo. (2012) The X control chart for monitoring process shifts in mean and variance. International Journal of Production Research 50:3, pages 893-907.
Read now
R. S. Sparks, T. Keighley & D. Muscatello. (2011) Optimal exponentially weighted moving average (EWMA) plans for detecting seasonal epidemics when faced with non-homogeneous negative binomial counts. Journal of Applied Statistics 38:10, pages 2165-2181.
Read now
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.
Read now
Ross S. Sparks, Tim Keighley & David Muscatello. (2010) Early warning CUSUM plans for surveillance of negative binomial daily disease counts. Journal of Applied Statistics 37:11, pages 1911-1929.
Read now
Zhonghua Li, Yunzhao Luo & Zhaojun Wang. (2010) Cusum of Q chart with variable sampling intervals for monitoring the process mean. International Journal of Production Research 48:16, pages 4861-4876.
Read now
Jong-Hyun Ryu, G Wan & Sujin Kim. (2010) Optimal Design of a CUSUM Chart for a Mean Shift of Unknown Size. Journal of Quality Technology 42:3, pages 311-326.
Read now
Marion R. Reynolds$suffix/text()$suffix/text() & Jianying Lou. (2010) An Evaluation of a GLR Control Chart for Monitoring the Process Mean. Journal of Quality Technology 42:3, pages 287-310.
Read now
Zhonghua Li & Zhaojun Wang. (2010) Adaptive CUSUM of the Q chart. International Journal of Production Research 48:5, pages 1287-1301.
Read now
Lianjie Shu, Hang-Fai Yeung & Wei Jiang. (2010) An Adaptive CUSUM Procedure for Signaling Process Variance Changes of Unknown Sizes. Journal of Quality Technology 42:1, pages 69-85.
Read now
Zhang Wu, Jianxin Jiao, Mei Yang, Ying Liu & Zhaojun Wang. (2009) An enhanced adaptive CUSUM control chart. IIE Transactions 41:7, pages 642-653.
Read now
Wei Jiang, Lianjie Shu & DanielW. Apley. (2008) Adaptive CUSUM procedures with EWMA-based shift estimators. IIE Transactions 40:10, pages 992-1003.
Read now
Lianjie Shu, Wei Jiang & Kwok-Leung Tsui. (2008) A Weighted CUSUM Chart for Detecting Patterned Mean Shifts. Journal of Quality Technology 40:2, pages 194-213.
Read now
Abdul Haq & Michael B. C. Khoo. Weighted adaptive CUSUM mean chart with variable sample size and sampling interval. Communications in Statistics - Simulation and Computation 0:0, pages 1-19.
Read now
Zhengcheng Mou, Jyun-You Chiang, Sihong Chen & Guojun Liu. A likelihood-based adaptive CUSUM for monitoring linear drift of Poisson rate with time-varying sample sizes. Journal of Statistical Computation and Simulation 0:0, pages 1-26.
Read now
FuPeng Xie, Philippe Castagliola, AnAn Tang, XueLong Hu & JinSheng Sun. The performance of the one-sided truncated exponentially weighted moving average control chart in the presence of measurement errors. Journal of Statistical Computation and Simulation 0:0, pages 1-25.
Read now

Articles from other publishers (53)

Zameer Abbas, Hafiz Zafar Nazir, Dongdong Xiang & Jianqing Shi. (2024) Nonparametric adaptive cumulative sum charting scheme for monitoring process location. Quality and Reliability Engineering International.
Crossref
Muhammad Atif Sarwar, Muhammad Noor-ul-Amin, Imad Khan, Emad A. A. Ismail, Wojciech Sumelka & Muhammad Nabi. (2023) A Weibull process monitoring with AEWMA control chart: an application to breaking strength of the fibrous composite. Scientific Reports 13:1.
Crossref
Afshan Riaz, Muhammad Noor-ul-Amin, Walid Emam, Yusra Tashkandy, Uzma Yasmeen & Javed Rahimi. (2023) Adaptive EWMA control chart for monitoring the coefficient of variation under ranked set sampling schemes. Scientific Reports 13:1.
Crossref
Liyan Xie, George V. Moustakides & Yao Xie. (2023) Window-Limited CUSUM for Sequential Change Detection. IEEE Transactions on Information Theory 69:9, pages 5990-6005.
Crossref
Zameer Abbas, Hafiz Zafar Nazir, Muhammad Riaz, Jianqing Shi & Atomsa Gemechu Abdisa. (2023) An unbiased function‐based Poisson adaptive EWMA control chart for monitoring range of shifts. Quality and Reliability Engineering International.
Crossref
Babar Zaman, Muhammad Hisyam Lee, Muhammad Riaz, Mu’azu Ramat Abujiya, Rashid Mehmood & Nasir Abbas. (2022) Adaptive Memory Control Charts Constructed on Generalized Likelihood Ratio Test to Monitor Process Location. Arabian Journal for Science and Engineering 47:11, pages 15049-15081.
Crossref
Tailin Zhou, Kaishun Xiahou, L.L. Zhang & Q. H. Wu. (2021) Real-Time Detection of Cyber-Physical False Data Injection Attacks on Power Systems. IEEE Transactions on Industrial Informatics 17:10, pages 6810-6819.
Crossref
Muhammad Noor-ul-Amin, Afshan Riaz & Amer Ibrahim Al-Omari. (2021) Adaptive Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean Under Ranked Set Sampling Schemes. Iranian Journal of Science and Technology, Transactions A: Science 45:5, pages 1777-1787.
Crossref
Ishaq Adeyanju Raji, Muhammad Hisyam Lee, Muhammad Riaz, Mu'azu Ramat Abujiya & Nasir Abbas. (2021) A robust multivariate Shewhart chart for contaminated normal environments. Quality and Reliability Engineering International 37:6, pages 2665-2684.
Crossref
Niloufar Khodahemmati & Mohsen Shahandashti. (2020) Diagnosis and Quantification of Postdisaster Construction Material Cost Fluctuations. Natural Hazards Review 21:3.
Crossref
Qifa Xu, Shixiang Lu, Zhongping Zhai & Cuixia Jiang. (2020) Adaptive fault detection in wind turbine via RF and CUSUM. IET Renewable Power Generation 14:10, pages 1789-1796.
Crossref
Yulong Qiao, Xuelong Hu, Jinsheng Sun & Qin Xu. (2019) Optimal Design of One-Sided Exponential EWMA Charts With Estimated Parameters Based on the Median Run Length. IEEE Access 7, pages 76645-76658.
Crossref
Nasir Abbas, Ishaq A. Raji, Muhammad Riaz & Khalid Al-Ghamdi. (2018) On Designing Mixed EWMA Dual-CUSUM Chart With Applications in Petro-Chemical Industry. IEEE Access 6, pages 78931-78946.
Crossref
M. Mujiya Ulkhaq & Favian Dewanta. Original observations-based control charts for monitoring the mean of auto-correlated processes: A comparison among modified Shewhart, modified EWMA, and ARMAST charts. Original observations-based control charts for monitoring the mean of auto-correlated processes: A comparison among modified Shewhart, modified EWMA, and ARMAST charts.
M. Shamsuzzaman, M. B. C. Khoo, S. Haridy & I. Alsyouf. (2016) An optimization design of the combined Shewhart-EWMA control chart. The International Journal of Advanced Manufacturing Technology 86:5-8, pages 1627-1637.
Crossref
Ross Sparks. (2016) Detecting Periods of Significant Increased Communication Levels for Subgroups of Targeted Individuals. Quality and Reliability Engineering International 32:5, pages 1871-1888.
Crossref
Bhupesh K. Lad, Divya Shrivastava & Makarand S. Kulkarni. 2016. Machine Tool Reliability. Machine Tool Reliability 277 295 .
Jianhua Ran, Maozhu Jin & Xingli Gan. (2016) A new RAIM algorithm based on multivariate cumulative sum and its improvement. Neurocomputing 171, pages 113-117.
Crossref
Ross Sparks. (2014) Spatio‐Temporal Surveillance Using CUSUM of Order Statistics. Quality and Reliability Engineering International 31:8, pages 1743-1760.
Crossref
Hai Yu Wang. (2014) Small Shifts Quality Control Schemes under MMSE Feedback Adjustment. Advanced Materials Research 915-916, pages 1471-1475.
Crossref
Lianjie Shu, Wenpo Huang & Wei Jiang. (2014) A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts. Naval Research Logistics (NRL) 61:3, pages 223-237.
Crossref
Feng He, Lianjie Shu & Kwok-Leung Tsui. (2014) Adaptive CUSUM charts for monitoring linear drifts in Poisson rates. International Journal of Production Economics 148, pages 14-20.
Crossref
Yanjing Ou, Zhang Wu, Ka Man Lee & Kan Wu. (2012) An Adaptive CUSUM Chart with Single Sample Size for Monitoring Process Mean and Variance. Quality and Reliability Engineering International 29:7, pages 1027-1039.
Crossref
Pei-Hsi Lee, Yi-Hsien Huang, Tsen-I Kuo & Ching-Cheng Wang. (2011) The effect of the individual chart with variable control limits on the river pollution monitoring. Quality & Quantity 47:4, pages 1803-1812.
Crossref
M. Daniel Docmac, Eduardo I. Silva & Agustín J. González. (2013) Evaluación de algoritmos para la estimación del Round-Trip Delay Time y una propuesta de mejora. Revista Iberoamericana de Automática e Informática Industrial RIAI 10:1, pages 62-72.
Crossref
Yanjing Ou, Zhang Wu, Ka Man Lee & Songlin Chen. (2012) An optimal design algorithm of the SPRT chart for minimizing weighted ATS. International Journal of Production Economics 139:2, pages 564-574.
Crossref
Jae-Heon Lee. (2012) Optimal Design of a EWMA Chart to Monitor the Normal Process Mean. Korean Journal of Applied Statistics 25:3, pages 465-470.
Crossref
Li Li. (2012) The GLR Chart for Poisson Process with Individual Observations. Advanced Materials Research 542-543, pages 42-46.
Crossref
Yanjing Ou, Zhang Wu & Fugee Tsung. (2012) A comparison study of effectiveness and robustness of control charts for monitoring process mean. International Journal of Production Economics 135:1, pages 479-490.
Crossref
Nan Chen, Yuan Yuan & Shiyu Zhou. (2011) Performance analysis of queue length monitoring of M/G/1 systems. Naval Research Logistics (NRL) 58:8, pages 782-794.
Crossref
Jiujun Zhang, Changliang Zou & Zhaojun Wang. (2011) An adaptive Shiryaev-Roberts procedure for monitoring dispersion. Computers & Industrial Engineering 61:4, pages 1166-1172.
Crossref
Yi Dai, Yunzhao Luo, Zhonghua Li & Zhaojun Wang. (2010) A new adaptive CUSUM control chart for detecting the multivariate process mean. Quality and Reliability Engineering International 27:7, pages 877-884.
Crossref
Yanjing Ou, Zhang Wu & Thong Ngee Goh. (2011) A new SPRT chart for monitoring process mean and variance. International Journal of Production Economics 132:2, pages 303-314.
Crossref
Pei-Hsi Lee. (2011) Adaptive charts with variable parameters. Computational Statistics & Data Analysis 55:5, pages 2003-2010.
Crossref
Giovanna Capizzi & Guido Masarotto. (2010) Linear profile monitoring using an adaptive EWMA control chart. Linear profile monitoring using an adaptive EWMA control chart.
Yanjing Ou, Zhang Wu, Songlin Chen & Ka Man Lee. (2010) An improved SPRT control chart for monitoring process mean. The International Journal of Advanced Manufacturing Technology 51:9-12, pages 1045-1054.
Crossref
Zhang Wu, Yafen Liu, Zhen He & Michael B. C. Khoo. (2009) A Cumulative Sum scheme for monitoring frequency and size of an event. Quality and Reliability Engineering International 26:6, pages 541-554.
Crossref
Zhang Wu, ZhaoJun Wang & Wei Jiang. (2010) A generalized Conforming Run Length control chart for monitoring the mean of a variable. Computers & Industrial Engineering 59:2, pages 185-192.
Crossref
Zhang Wu, Mei Yang, Michael B.C. Khoo & Fong-Jung Yu. (2010) Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance. European Journal of Operational Research 205:1, pages 136-150.
Crossref
Qin Zhou, Yunzhao Luo & Zhaojun Wang. (2010) A control chart based on likelihood ratio test for detecting patterned mean and variance shifts. Computational Statistics & Data Analysis 54:6, pages 1634-1645.
Crossref
Zhen He, Yafen Liu & Min Zhang. (2010) A CUSUM Chart for Monitoring an Attribute Event. A CUSUM Chart for Monitoring an Attribute Event.
Fujee Tsung & Kaibo Wang. 2010. Frontiers in Statistical Quality Control 9. Frontiers in Statistical Quality Control 9 19 35 .
R. S. Sparks, T. Keighley & D. Muscatello. (2009) Improving EWMA Plans for Detecting Unusual Increases in Poisson Counts. Journal of Applied Mathematics and Decision Sciences 2009, pages 1-16.
Crossref
Yafen Liu, Zhen He, Lianjie Shu & Zhang Wu. (2009) Statistical computation and analyses for attribute events. Computational Statistics & Data Analysis 53:9, pages 3412-3425.
Crossref
Zhang Wu, Jianxin Jiao & Zhen He. (2009) A single control chart for monitoring the frequency and magnitude of an event. International Journal of Production Economics 119:1, pages 24-33.
Crossref
Yunzhao Luo, Zhonghua Li & Zhaojun Wang. (2009) Adaptive CUSUM control chart with variable sampling intervals. Computational Statistics & Data Analysis 53:7, pages 2693-2701.
Crossref
Zhang Wu, Penghui Wang & Qinan Wang. (2008) A loss function-based adaptive control chart for monitoring the process mean and variance. The International Journal of Advanced Manufacturing Technology 40:9-10, pages 948-959.
Crossref
Zhang Wu & Mei Yang. (2008) An adaptive CUSUM chart with exponential of mean shift. An adaptive CUSUM chart with exponential of mean shift.
L. J. Shu, W. Jiang & Z. Wu. (2008) Markov chain approximation to the performance of adaptive CUSUM procedures. Markov chain approximation to the performance of adaptive CUSUM procedures.
Jun Du, Zhang Wu & Roger J. Jiao. (2008) An improved adaptive CUSUM control chart for monitoring process mean. An improved adaptive CUSUM control chart for monitoring process mean.
Lianjie Shu, Wei Jiang & Zhang Wu. (2008) Adaptive CUSUM procedures with Markovian mean estimation. Computational Statistics & Data Analysis 52:9, pages 4395-4409.
Crossref
V. N. A. Naikan. 2008. Handbook of Performability Engineering. Handbook of Performability Engineering 187 201 .
M. Shamsuzzaman & Z. Wu. (2006) Control chart design for minimizing the proportion of defective units. Journal of Manufacturing Systems 25:4, pages 269-278.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.