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Original Articles

A a comparison of the markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts

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Pages 191-204 | Received 01 Apr 1990, Published online: 27 Jun 2007

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

Read on this site (19)

Piyatida Phanthuna, Yupaporn Areepong & Saowanit Sukparungsee. (2023) Run length distribution for a modified EWMA scheme fitted with a stationary AR(p) model. Communications in Statistics - Simulation and Computation 52:9, pages 4260-4279.
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Theodoros Perdikis, Stelios Psarakis, Philippe Castagliola, Athanasios C. Rakitzis & Petros E. Maravelakis. (2023) The EWMA sign chart revisited: performance and alternatives without and with ties. Journal of Applied Statistics 50:1, pages 170-194.
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Petros E. Maravelakis, Philippe Castagliola & Michael B. C. Khoo. (2019) Run length properties of run rules EWMA chart using integral equations. Quality Technology & Quantitative Management 16:2, pages 129-139.
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Amitava Mukherjee & Marco Marozzi. (2017) A distribution-free phase-II CUSUM procedure for monitoring service quality. Total Quality Management & Business Excellence 28:11-12, pages 1227-1263.
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Sven Knoth. (2017) ARL Numerics for MEWMA Charts. Journal of Quality Technology 49:1, pages 78-89.
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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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Wenpo Huang, Lianjie Shu & Yan Su. (2014) An accurate evaluation of adaptive exponentially weighted moving average schemes. IIE Transactions 46:5, pages 457-469.
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AlekseyS. Polunchenko, Grigory Sokolov & Wenyu Du. (2014) An Accurate Method for Determining the Pre-Change Run Length Distribution of the Generalized Shiryaev-Roberts Detection Procedure. Sequential Analysis 33:1, pages 112-134.
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Yougui Wu, Yiliang Zhu & Wei Wang. (2009) Effect of Inspection Error on Out-of-Control Average Run Length of CUSUM Charts. Communications in Statistics - Simulation and Computation 38:7, pages 1435-1445.
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M. H. Lee & MichaelB. C. Khoo. (2006) Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL. Communications in Statistics - Simulation and Computation 35:3, pages 831-847.
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Darrell Radson & AmyHancock Boyd. (2005) Graphical Representation of Run Length Distributions. Quality Engineering 17:2, pages 301-308.
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Kuoh How Ong, Craig M. Harvey, Randa L. Shehab, Jerry D. Dechert & Ashok Darisipudi. (2004) The effects of three statistical control charts on task performance. Production Planning & Control 15:3, pages 313-323.
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Chuen-Sheng Cheng & Sheng-Su Cheng. (2001) A CUSUM CONTROL SCHEME FOR CLUSTERED DEFECTS. Journal of the Chinese Institute of Industrial Engineers 18:6, pages 1-8.
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W. Matthew Carlyle, Douglas C. Montgomery & George C. Runger. (2000) Optimization Problems and Methods in Quality Control and Improvement. Journal of Quality Technology 32:1, pages 1-17.
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Kevin M. Bodden & Steven E. Rigdon. (1999) A Program for Approximating the In-Control ARL for the MEWMA Chart. Journal of Quality Technology 31:1, pages 120-123.
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GeorgeC. Runger & SharadS. Prabhu. (1996) A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart. Journal of the American Statistical Association 91:436, pages 1701-1706.
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S.A. Vander Wiel. (1996) Monitoring Processes That Wander Using Integrated Moving Average Models. Technometrics 38:2, pages 139-151.
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Marion R. Reynolds$suffix/text()$suffix/text(). (1995) Evaluating properties of variable sampling interval control charts. Sequential Analysis 14:1, pages 59-97.
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Articles from other publishers (43)

Phunsa Mongkoltawat, Yupaporn Areepong & Saowanit Sukparungsee. (2024) Average Run Length Computations of Autoregressive and Moving Average Process using the Extended EWMA Procedure. WSEAS TRANSACTIONS ON MATHEMATICS 23, pages 371-384.
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Wilasinee Peerajit. (2024) Approximating the ARL to Monitor Small Shifts in the Mean of an AR Fractionally Integrated with an exogenous variable Process Running on an EWMAControl Chart. WSEAS TRANSACTIONS ON SYSTEMS 23, pages 176-187.
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Zwelakhe Magagula, Jean-Claude Malela-Majika, Schalk William Human, Philippe Castagliola, Kashinath Chatterjee & Christos Koukouvinos. (2024) Closed-form expressions of the run-length distribution of the nonparametric double sampling precedence monitoring scheme. Computational Statistics.
Crossref
Yupaporn Areepong, Saowanit Sukparungsee & Tanapat Anusas-Amornkul. (2024) Efficient Monitoring of Autoregressive and Moving Average Process using HWMA Control Chart. WSEAS TRANSACTIONS ON SYSTEMS 23, pages 128-140.
Crossref
Suganya Phantu, Yupaporn Areepong & Saowanit Sukparungsee. (2024) Double Moving Average Control Chart for Time Series Data with Poisson INARCH(1). WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS 21, pages 694-707.
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Rapin Sunthornwat, Yupaporn Areepong & Saowanit Sukparungsee. (2024) Performance Evaluation of HWMA Control Chart based on AR(p) with Trend Model to Detect Shift Process Mean. WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS 21, pages 603-616.
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Wilasinee Peerajit. An integral equation approach for average run length of incorporation of exogenous variable in seasonal autoregressive fractionally integrated model. An integral equation approach for average run length of incorporation of exogenous variable in seasonal autoregressive fractionally integrated model.
Yupaporn Areepong & Saowanit Sukparungsee. Explicit formulas of average run lengths of moving average control chart for INARCH (1) Poisson counting processes. Explicit formulas of average run lengths of moving average control chart for INARCH (1) Poisson counting processes.
Rapin Sunthornwat, Saowanit Sukparungsee & Yupaporn Areepong. (2023) Analytical Explicit Formulas of Average Run Length of Homogenously Weighted Moving Average Control Chart Based on a MAX Process. Symmetry 15:12, pages 2112.
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Wilasinee Peerajit. (2023) Approximating the ARL of Changes in the Mean of a Seasonal Time Series Model with Exponential White Noise Running on a CUSUM Control Chart. WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 18, pages 370-381.
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Sittikorn Khamrod, Yupaporn Areepong, Saowanit Sukparungsee & Rapin Sunthornwat. (2023) Statistical Design for Monitoring Process Mean on Modified EWMA Control Chart based on Autocorrelated Data. WSEAS TRANSACTIONS ON COMPUTER RESEARCH 11, pages 450-464.
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Lili Zhang, Sujitta Suraphee & Piyapatr Busababodhin. (2023) Derivation of Explicit Formulae for Performance Measures of CUSUM Control Chart for SMA(Q)$${}_{\boldsymbol{s}}$$ Model with Exponential White Noise. Lobachevskii Journal of Mathematics 44:9, pages 3902-3913.
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Isaac Tranter-Entwistle, Corin Simcock, Tim Eglinton & Saxon Connor. (2023) Prospective cohort study of operative outcomes in laparoscopic cholecystectomy using operative difficulty grade-adjusted CUSUM analysis. British Journal of Surgery 110:9, pages 1068-1071.
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Wilasinee Peerajit & Yupaporn Areepong. (2023) Alternative to Detecting Changes in the Mean of an Autoregressive Fractionally Integrated Process with Exponential White Noise Running on the Modified EWMA Control Chart. Processes 11:2, pages 503.
Crossref
Korakoch Silpakob, Yupaporn Areepong, Saowanit Sukparungsee & Rapin Sunthornwat. (2023) A New Modified EWMA Control Chart for Monitoring Processes Involving Autocorrelated Data. Intelligent Automation & Soft Computing 36:1, pages 281-298.
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Kotchaporn Karoon, Yupaporn Areepong & Saowanit Sukparungsee. (2023) Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart. Computer Systems Science and Engineering 44:2, pages 1143-1160.
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Yupaporn Areepong & Wilasinee Peerajit. (2022) Integral equation solutions for the average run length for monitoring shifts in the mean of a generalized seasonal ARFIMAX(P, D, Q, r)s process running on a CUSUM control chart. PLOS ONE 17:2, pages e0264283.
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Y Areepong & C Chananet. (2021) Optimal parameters of EWMA Control Chart for Seasonal and Non-Seasonal Moving Average Processes. Journal of Physics: Conference Series 2014:1, pages 012005.
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Mehmet Necip Kurt, Yasin Ylmaz & Xiaodong Wang. (2021) Real-Time Nonparametric Anomaly Detection in High-Dimensional Settings. IEEE Transactions on Pattern Analysis and Machine Intelligence 43:7, pages 2463-2479.
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Gary A. DavisIndrajit ChatterjeeJingru Gao & John Hourdos. (2021) Traffic Density versus Rear-End Crash Risk on Freeways: Empirical Model, Mechanism Model, and Transfer to Automated Vehicles. Journal of Transportation Engineering, Part A: Systems 147:4.
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Amir Ahmadi-Javid & Mohsen Ebadi. (2020) Economic design of memory-type control charts: The fallacy of the formula proposed by Lorenzen and Vance (1986). Computational Statistics 36:1, pages 661-690.
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Piyatida Phanthuna, Yupaporn Areepong & Saowanit Sukparungsee. (2021) Exact Run Length Evaluation on a Two-Sided Modified Exponentially Weighted Moving Average Chart for Monitoring Process Mean. Computer Modeling in Engineering & Sciences 127:1, pages 23-41.
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Yadpirun Supharakonsakun, Yupaporn Areepong & Saowanit Sukparungsee. (2020) The performance of a modified EWMA control chart for monitoring autocorrelated PM2.5 and carbon monoxide air pollution data. PeerJ 8, pages e10467.
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Murat Caner Testik, Ozge Kara & Sven Knoth. (2020) An algorithmic approach to outlier detection and parameter estimation in Phase I for designing Phase II EWMA control chart. Computers & Industrial Engineering 144, pages 106440.
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Carlos Murguia & Justin Ruths. (2019) On model‐based detectors for linear time‐invariant stochastic systems under sensor attacks. IET Control Theory & Applications 13:8, pages 1051-1061.
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Kim Phuc Tran, Philippe Castagliola & Giovanni Celano. (2016) Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts. Statistical Papers 59:1, pages 387-413.
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Carlos Murguia & Justin Ruths. (2016) Characterization of a CUSUM model-based sensor attack detector. Characterization of a CUSUM model-based sensor attack detector.
Phuong Hanh Tran & Kim Phuc Tran. (2016) The efficiency of CUSUM schemes for monitoring the coefficient of variation. Applied Stochastic Models in Business and Industry 32:6, pages 870-881.
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Carlos Murguia & Justin Ruths. (2016) CUSUM and chi-squared attack detection of compromised sensors. CUSUM and chi-squared attack detection of compromised sensors.
Aleksey S. Polunchenko. (2016) A note on efficient performance evaluation of the Cumulative Sum chart and the Sequential Probability Ratio Test. Applied Stochastic Models in Business and Industry 32:5, pages 565-573.
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R. Noorossana, S. Fathizadan & M. R. Nayebpour. (2016) EWMA Control Chart Performance with Estimated Parameters under Non-normality. Quality and Reliability Engineering International 32:5, pages 1637-1654.
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Aleksey S. Polunchenko, Grigory Sokolov & Wenyu Du. (2014) Efficient performance evaluation of the generalized Shiryaev–Roberts detection procedure in a multi‐cyclic setup. Applied Stochastic Models in Business and Industry 30:6, pages 723-739.
Crossref
Thomas P. Ryan. 2011. Statistical Methods for Quality Improvement. Statistical Methods for Quality Improvement 261 307 .
Fong-Jung Yu, Yung-Yu Yang, Ming-Jaan Wang & Zhang Wu. (2011) Using EWMA control schemes for monitoring wafer quality in negative binomial process. Microelectronics Reliability 51:2, pages 400-405.
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Christopher A. Carolan, John F. Kros & Said E. Said. (2009) Economic design of Xbar control charts with continuously variable sampling intervals. Quality and Reliability Engineering International 26:3, pages 235-245.
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Giovanna Capizzi & Guido Masarotto. (2009) Evaluation of the run-length distribution for a combined Shewhart-EWMA control chart. Statistics and Computing 20:1, pages 23-33.
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Sven Knoth. 2010. Frontiers in Statistical Quality Control 9. Frontiers in Statistical Quality Control 9 3 18 .
Zhonghua Li, Zhaojun Wang & Zhang Wu. (2009) Necessary and sufficient conditions for non-interaction of a pair of one-sided EWMA schemes with reflecting boundaries. Statistics & Probability Letters 79:3, pages 368-374.
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Petros E. Maravelakis. (2007) The effect of measurement error on the performance of the CUSUM control chart. The effect of measurement error on the performance of the CUSUM control chart.
Sven Knoth. (2006) Computation of the ARL for CUSUM- schemes. Computational Statistics & Data Analysis 51:2, pages 499-512.
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Sven Knoth. (2005) Accurate ARL computation for EWMA-S2 control charts. Statistics and Computing 15:4, pages 341-352.
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James C. Fu, Fred A. Spiring & Hansheng Xie. (2002) On the average run lengths of quality control schemes using a Markov chain approach. Statistics & Probability Letters 56:4, pages 369-380.
Crossref
Thomas P. Ryan & Belinda J. Faddy. 2001. Frontiers in Statistical Quality Control 6. Frontiers in Statistical Quality Control 6 176 193 .

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