Control chart, Ratio, Compositional data, EWMA, CUSUM, Shewhart, Measurement errors, VSI, Statistical process control.
Abstract :
[en] The ratio of two normal variables and compositional Data (CoDa) are two common types of process data in industrial and manufacturing applications. Control charts are powerful tools in statistical process control for monitoring these types of data, as they allow for the detection of process changes and improvement in process quality. In this chapter, we provide a comprehensive analysis of the existing literature on control charts for monitoring the ratio of two normal variables and CoDa and offer a perspective on the strengths and limitations of these methods, as well as potential areas for future research. Specifically, the review is organized into two main categories: control charts for monitoring the ratio of two normal variables and control charts for monitoring CoDa. In this comprehensive analysis, we examine 87 research studies, comprising 68 that focus on the ratio of two normal variables and 19 that delve into CoDa. This extensive review aims to furnish crucial insights into the application of control charts for monitoring these distinct data types. Moreover, it offers practical recommendations for practitioners on choosing suitable methods and incorporating machine learning techniques to enhance monitoring efficiency. This guidance is particularly pertinent for monitoring industrial processes within the context of Industry 5.0, reflecting the evolving needs and complexities of modern manufacturing environments.
Disciplines :
Quantitative methods in economics & management
Author, co-author :
Nguyen, Thi Thuy Van ; Université de Liège - ULiège > HEC Liège : UER > UER Opérations
Nguyen, Thi Hien; Laboratoire AGM, UMR CNRS 8088, CY Cergy Paris University, France
Tran, Kim Duc; IAD, Dong A University, Danang, Vietnam.
Heuchenne, Cédric ; Université de Liège - ULiège > HEC Liège : UER > UER Opérations : Statistique appliquée à la gestion et à l'économie
Tran, Kim Phuc; ENSAIT, GEMTEX, University of Lille, France
Language :
English
Title :
Monitoring the Ratio of Two Normal Variables and Compositional Data: A Literature Review and Perspective
Publication date :
15 December 2024
Main work title :
Computational Techniques for Smart Manufacturing in Industry 5.0: Methods and Applications
Editor :
Tran, Kim Phuc; ENSAIT, GEMTEX, University of Lille, France
G. Celano, P. Castagliola, A. Faraz, and S. Fichera. Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of two Normal Variables. Quality and Reliability Engineering International, 30(8):1361-1377, 2014.
J. Aitchison. The Statistical Analysis of Compositional Data (Monographs on Statistics and Applied Probability). Chapman & Hall Ltd., London, (Reprinted in 2003 with additional material by The Blackburn Press), 1986.
D.C. Montgomery. Statistical Quality Control: a Modern Introduction. Wiley, New York, 2009.
G. Celano and P. Castagliola. Design of a Phase II Control Chart for Monitoring the Ratio of two Normal Variables. Quality and Reliability Engineering International, 32, 2014.
A.W. Spisak. A Control Chart for Ratios. Journal of Quality Technology, 22(1):34-37, 1990.
D. Oksoy, E. Boulos, and L.D. Pye. Statistical Process Control by the Quotient of two Correlated Normal Variables. Quality Engineering, 6(2): 179-194, 1994.
G. Celano and P. Castagliola. A Synthetic Control Chart for Monitoring the Ratio of Two Normal Variables. Quality and Reliability Engineering International, 2015.
K.P. Tran, P. Castagliola, and G. Celano. Monitoring the ratio of two normal variables using Run Rules type control charts. International Journal of Production Research, ahead-of-print:1-19, 2015.
Kim Phuc Tran, Philippe Castagliola, and G. Celano. Monitoring the ratio of two normal variables using ewma type control charts. Quality and Reliability Engineering, 10 2015.
Kim Phuc Tran and Sven Knoth. Steady-state arl analysis of arl-unbiased ewma-rz control chart monitoring the ratio of two normal variables. Quality and Reliability Engineering, 34, 11 2017.
Kim Phuc Tran, Philippe Castagliola, and G. Celano. Monitoring the ratio of population means of a bivariate normal distribution using cusum type control charts. Statistical Papers, 59, 03 2018.
Huu Du Nguyen, Kim Phuc Tran, and Thong Ngee Goh. Variable sampling interval control charts for monitoring the ratio of two normal variables. Journal of Testing and Evaluation, 48, 12 2019.
Huu Du Nguyen, Kim Phuc Tran, and Cédric Heuchenne. Monitoring the ratio of two normal variables using variable sampling interval exponentially weighted moving average control charts. Quality and Reliability Engineering International, 35(1):439-460, 2019.
Huu Du Nguyen, Kim Phuc Tran, and Henri L. Heuchenne. Cusum control charts with variable sampling interval for monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 36(2):474-497, 2020.
Kim Phuc Tran, Philippe Castagliola, and G. Celano. The performance of the shewhart-rz control chart in the presence of measurement error. International Journal of Production Research, 54, 05 2016.
Huu-Du Nguyen and Kim Phuc Tran. Effect of the measurement errors on two one-sided shewhart control charts for monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 36, 05 2020.
H.D. Nguyen, K.P. Tran, and K.D. Tran. The effect of measurement errors on the performance of the Exponentially Weighted Moving Average control charts for the Ratio of Two Normally Distributed Variables. European Journal of Operational Research, 293(1):203-218, 2021.
Sani Salihu Abubakar, Michael B. C. Khoo, Sa jal Saha, Adamu Abubakar Umar, and Wai Chung Yeong. Run sum ratio chart when measurement errors are present. Quality and Reliability Engineering International, 38 (8):4049-4072, 2022.
V. Pawlowsky-Glahn, J. J. Egozcue, and R. Tolosana-Delgado. Modeling and Analysis of Compositional Data. John Wiley & Sons, 2015.
J. J. Egozcue, V. Pawlowsky-Glahn, G. Mateu-Figueras, and C. Barceló-Vidal. Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3):279-300, 2003.
J.J. Egozcue and V. Pawlowsky-Glahn. Groups of Parts and Their Balances in Compositional Data analysis. Mathematical Geology, 37(7):795-828, 2005.
R. A. Boyles. Using the chi-square statistic to monitor compositional process data. Journal of Applied Statistics, 24(5):589-602, 1997.
R. Guevara, J. Vargas, and D. Linero Segrera. Profile monitoring for compositional data. Revista Colombiana de Estadística, 37:159, 07 2014.
M. Vives-Mestres, J. Daunis-I-Estadella, and J.A. Martin-Fernandez. Out-of-Control Signals in Three-Part Compositional T 2 Control Chart. Quality and Reliability Engineering International, 30(3):337-346, 2014.
M. Vives-Mestres, J. Daunis-I-Estadella, and J.A. Martin-Fernandez. Individual T 2 Control Chart for Compositional Data. Journal of Quality Technology, 46(2):127-139, 2014.
K. P. Tran, P. Castagliola, G. Celano, and Michael B.C. Khoo. Monitoring compositional data using multivariate exponentially weighted moving average scheme. Quality and Reliability Engineering International, 34(3): 391-402, 2018.
M. Imran, J. Sun, F.S. Zaidi, Z. Abbas, and H.Z. Nazir. Multivariate cumulative sum control chart for compositional data with known and estimated process parameters. Quality and reliability engineering international, 38(5), 2022-07. ISSN 0748-8017.
T.T.V. Nguyen, C. Heuchenne, and K.P. Tran. Anomaly detection for compositional data using vsi mewma control chart. IFAC-PapersOnLine, 55(10):1533-1538, 2022. ISSN 2405-8963. 10th IFAC Conference on Manufacturing Modelling, Management and Control MIM 2022.
M. Imran, J. Sun, F.S. Zaidi, Z. Abbas, and H.Z. Nazir. On designing efficient multivariate exponentially weighted moving average control chart for compositional data using variable sample size. Journal of Statistical Computation and Simulation, 93(10):1622-1643, 2023.
C.A. Lowry, W.H. Woodall, C.W. Champ, and S.E. Rigdon. A Multivariate Exponentially Weighted Moving Average Control Chart. Technometrics, 34(1):pp. 46-53, 1992. ISSN 00401706.
F.S. Zaidi, P. Castagliola, K.P. Tran, and M.B.C. Khoo. Performance of the hotelling t2 control chart for compositional data in the presence of measurement errors. Journal of Applied Statistics, 46(14):2583-2602, 2019.
F.S. Zaidi, PY. Castagliola, K.P. Tran, and M.B.C. Khoo. Performance of the mewma-coda control chart in the presence of measurement errors. Quality and Reliability Engineering International, 36(7):2411-2440, 2020.
M. Imran, J. Sun, F.S. Zaidi, Z. Abbas, and H.Z. Nazir. Effect of measurement error on the multivariate cusum control chart for compositional data. CMES-Computer Modeling in Engineering & Sciences, 136(2), 2023.
M. Imran, J. Sun, F.S Zaidi, Z. Abbas, and H.Z. Nazir. Evaluating the performance of variable sampling interval hotelling t2 charting scheme for compositional data in the presence of measurement error. Quality and Reliability Engineering International, 2023.
F.S. Zaidi, H.L. Dai, M. Imran, and K.P. Tran. Monitoring autocorrelated compositional data vectors using an enhanced residuals hotelling t2 control chart. Computers & Industrial Engineering, 181:109280, 2023.
M. Vives-Mestres, J. Daunis-i Estadella, and J. A. Martin-Fernandez. Signal interpretation in hotelling's t 2 control chart for compositional data. IIE Transactions, 48(7):661-672, 2016.
M. Imran, J. Sun, X. Hu, F.S. Zaidi, and A. Tang. Investigating zerostate and steady-state performance of mewma-coda control chart using variable sampling interval. Journal of Applied Statistics, pages 1-22, 2023.
C.H. Weiß. Ordinal compositional data and time series. Statistical Modelling, page 1471082X231190971, 2023.
F.S. Zaidi, H.L. Dai, M. Imran, and K.P. Tran. Analyzing abnormal pattern of hotelling t2 control chart for compositional data using artificial neural networks. Computers & Industrial Engineering, 180:109254, 2023.
M. Imran, H.L. Dai, F.S. Zaidi, X. Hu, K.P. Tran, and J. Sun. Analyzing out-of-control signals of t2 control chart for compositional data using artificial neural networks. Expert Systems with Applications, page 122165, 2023.
J. Schmidhuber, S. Hochreiter, et al. Long short-term memory. Neural Comput, 9(8):1735-1780, 1997.
C.K.I. Williams and C.E. Rasmussen. Gaussian processes for machine learning, volume 2. MIT press Cambridge, MA, 2006.
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A.N. Gomez, L. Kaiser, and I. Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017.
J. Wang and L. Liu. A new multivariate control chart based on the isolation forest algorithm. Quality Engineering, pages 1-17, 2023.
H.D. Nguyen, A.A. Nadi, K.D. Tran, P. Castagliola, G. Celano, and K.P. Tran. The shewhart-type rz control chart for monitoring the ratio of autocorrelated variables. International Journal of Production Research, 61(20):6746-6771, 2023.
G.A. Pugh. Synthetic neural networks for process control. Computers & industrial engineering, 17(1-4):24-26, 1989.
R.S. Guh. Real-time recognition of control chart patterns in autocorrelated processes using a learning vector quantization network-based approach. International Journal of Production Research, 46(14):3959-3991, 2008.
T. Li, S. Hu, Z.Y. Wei, Z.Q. Liao, et al. A framework for diagnosing the out-of-control signals in multivariate process using optimized support vector machines. Mathematical Problems in Engineering, 2013, 2013.
D.D. Diren, S. Boran, and I. Cil. Integration of machine learning techniques and control charts in multivariate processes. 2020.
V. Vapnik, I. Guyon, and T. Hastie. Support vector machines. Machine Learning, 20(3):273-297, 1995.
S.Y. Lin, R.S. Guh, and Y.R. Shiue. Effective recognition of control chart patterns in autocorrelated data using a support vector machine based approach. Computers & Industrial Engineering, 61(4):1123-1134, 2011.
C.S. Cheng. A neural network approach for the analysis of control chart patterns. International Journal of Production Research, 35(3):667-697, 1997.
A. Addeh, A. Khormali, and N.A. Golilarz. Control chart pattern recognition using rbf neural network with new training algorithm and practical features. ISA transactions, 79:202-216, 2018.
P.H. Tran, A. Ahmadi Nadi, T.H. Nguyen, K.D. Tran, and K.P. Tran. Application of machine learning in statistical process control charts: A survey and perspective. In Control charts and machine learning for anomaly detection in manufacturing, pages 7-42. Springer, 2022.
S.T.A. Niaki and B. Abbasi. Fault diagnosis in multivariate control charts using artificial neural networks. Quality and reliability engineering international, 21(8):825-840, 2005.
C.S. Cheng and H.P. Cheng. Identifying the source of variance shifts in the multivariate process using neural networks and support vector machines. Expert Systems with Applications, 35(1-2):198-206, 2008.
R.S. Guh and Y.R. Shiue. An effective application of decision tree learning for on-line detection of mean shifts in multivariate control charts. Computers & Industrial Engineering, 55(2):475-493, 2008.
