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Design and Optimization of c-Control Chart Using a Triple Sampling Scheme

  • José Jorge Muñoz ORCID logo , Manuel J. Campuzano ORCID logo EMAIL logo and Verónica Deibe-Blanco ORCID logo
Published/Copyright: July 25, 2023
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Abstract

In this paper, a c-control chart using a triple sampling scheme (TS-c) is studied. The chart design, procedure, and a bi-objective optimization model are given to optimize the TS-c-chart. The Average Run Length for in-control and out-of-control ( ARL 1 ), and Average Sample Number metrics are calculated. A Comparison among TS-c, Fixed parameters c (FP-c), VSS-c, EWMA-c, and Double Sampling c (DS-c) control charts are carried out in terms of ARL 1 . The proposed TS-c-chart has lower ARL 1 values for detecting small and moderate shifts in the mean number of non-conformities in control compared with FP-c, VSS-c, EWMA-c, and DS-c.

MSC 2020: 62P30

Funding statement: This work was fully supported by the Universidad del Magdalena, Santa Marta, Colombia.

References

[1] I. Ahmed, I. Sultana, S. K. Paul and A. Azeem, Performance evaluation of control chart for multiple assignable causes using genetic algorithm, Int. J. Adv. Manuf. Technol. 70 (2013), 1889–1902. 10.1007/s00170-013-5412-0Search in Google Scholar

[2] A. Amiri and A. Namin, Evaluating multi-objective economic-statistical design of attribute c-control charts for monitoring the number of non-conformities, Int. J. Qual. Eng. Technol. 5 (2015), 10.1504/IJQET.2015.071653. 10.1504/IJQET.2015.071653Search in Google Scholar

[3] G. Atalik and S. Senturk, Intuitionistic fuzzy c-control charts based on intuitionistic fuzzy ranking method for TIFNs, Soft. Comp. 26 (2022), 11403–11407. 10.1007/s00500-022-07438-5Search in Google Scholar

[4] M. Bashiri, A. Amiri, M. H. Doroudyan and A. Asgari, Multi-objective genetic algorithm for economic statistical design of (X)overbar control chart, Sci. Iran. 20 (2013), 909–918. Search in Google Scholar

[5] C. M. Borror, C. W. Champ and S. E. Rigdon, Poisson EWMA control charts, J. Qual. Technol. 30 (1998), no. 4, 352–361. 10.1080/00224065.1998.11979871Search in Google Scholar

[6] M. J. Campuzano, A. Carrion and J. Mosquera, Characterization and optimal design of a new double sampling c chart, Eur. J. Ind. Eng. 13 (2019), no. 6, 775–793. 10.1504/EJIE.2019.104312Search in Google Scholar

[7] P. Charongrattanasakul and W. Bamrungsetthapong, mixed control chart design using the integration of genetic algorithm and Monte Carlo simulation, Thai J. Math. 18 (2020), 651–667. Search in Google Scholar

[8] P. Charongrattanasakul and A. Pongpullponsak, Minimizing the cost of integrated systems approach to process control and maintenance model by EWMA control chart using genetic algorithm, Expert Syst. Appl. 38 (2011), 5178–5186. 10.1016/j.eswa.2010.10.044Search in Google Scholar

[9] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comp. 6 (2002), 182–197. 10.1109/4235.996017Search in Google Scholar

[10] E. K. Epprecht and A. F. B. Costa, Adaptive sample size control charts for attributes, Qual. Eng. 13 (2001), no. 3, 465–473. 10.1080/08982110108918675Search in Google Scholar

[11] E. K. Epprecht, A. F. B. Costa and F. C. T. Mendes, Adaptive control charts for attributes, IIE Trans. 35 (2003), no. 6, 567–582. 10.1080/07408170304427Search in Google Scholar

[12] E. K. Epprecht, B. F. Simoes and F. C. Mendes, A variable sampling interval EWMA chart for attributes, Int. J. Adv. Manuf. Technol. 49 (2010), no. 1, 281–292. 10.1007/s00170-009-2390-3Search in Google Scholar

[13] A. Faraz and E. Saniga, Multiobjective genetic algorithm approach to the economic statistical design of control charts with an application to X-bar and S-2 charts, Qual. Reliab. Eng. Int. 29 (2013), 407–415. 10.1002/qre.1390Search in Google Scholar

[14] B. C. Franco, A. F. B. Costa and M. A. G. Machado, Economic-statistical design of the X-bar chart used to control a wandering process mean using genetic algorithm, Expert Syst. Appl. 39 (2012), no. 17, 12961–12967. 10.1016/j.eswa.2012.05.034Search in Google Scholar

[15] L. J. Gu and Q. G. Tang, Economic design of the special VSSI T-2 chart with genetic algorithms based on Markov chain, Proceedings of the 3rd Annual International Conference on Management, Economics and Social Development (ICMESD), Atlantis Press, Amsterdam (2017), 94–99. Search in Google Scholar

[16] D. He, A. Grigoryan and M. Sigh, Design of double- and triple-sampling X-bar control charts using genetic algorithms, Int. J. Prod. Res. 40 (2002), no. 6, 1387–1404. 10.1080/00207540110118415Search in Google Scholar

[17] R. Inghilleri, T. Lupo and G. Passannanti, An effective double sampling scheme for the c control char, Qual. Reliab. Eng. Int. 31 (2013), no. 2, 205–216. 10.1002/qre.1572Search in Google Scholar

[18] A. Iziy, B. Sadeghpour and E. Monabbati, Comparison between the economic-statistical design of double and triple sampling control charts, Stoch. Qual. Control. 32 (2017), 9–61. 10.1515/eqc-2017-0005Search in Google Scholar

[19] S. Joekes and E. Barbosa, An improved attribute control chart for monitoring non-conforming proportion in high quality processes, Control Eng. Prac. 21 (2013), no. 4, 407–412. 10.1016/j.conengprac.2012.12.005Search in Google Scholar

[20] S. N. Lin, C. Y. Chou, S. L. Wang and H. R. Liu, Economic design of autoregressive moving average control chart using genetic algorithms, Expert Syst. Appl. 39 (2012), 1793–1798. 10.1016/j.eswa.2011.08.073Search in Google Scholar

[21] M. R. Maleki, A. Salmasnia and S. S. Yarmohammadi, The performance of triple sampling control chart with measurement errors, Qual. Technol. Quant. Manag. 19 (2022), 587–604. 10.1080/16843703.2022.2040702Search in Google Scholar

[22] F. N. Mim, M. B. C. Khoo, S. Saha and P. Castagliola, Revised triple sampling control charts for the mean with known and estimated process parameters, Int. J. Prod. Res. 60 (2022), 4911–4935. 10.1080/00207543.2021.1943035Search in Google Scholar

[23] D. C. Montgomery, Introduction to Statistical Quality Control, 7th ed., Hoboken, New York, 2012. Search in Google Scholar

[24] J. J. Munoz, M. J. Campuzano and J. Mosquera, Optimized np attribute control chart using triple sampling, Mathematics 10 (2022), 10.3390/math10203791. 10.3390/math10203791Search in Google Scholar

[25] S. T. A. Niaki and M. J. Ershadi, A parameter-tuned genetic algorithm for statistically constrained economic design of multivariate CUSUM control charts: A Taguchi loss approach, Int. J. Syst. Sci. 43 (2012), 2275–2287. 10.1080/00207721.2011.570878Search in Google Scholar

[26] S. T. A. Niaki, M. J. Ershadi and M. Malaki, Economic and economic-statistical designs of MEWMA control charts—A hybrid Taguchi loss, Markov chain, and genetic algorithm approach, Int. J. Adv. Manuf. Technol. 48 (2009), 283–296. 10.1007/s00170-009-2288-0Search in Google Scholar

[27] S. T. A. Niaki, F. M. Gazaneh and J. Karimifar, Economic design of x-bar control chart with variable sample size and sampling interval under non-normality assumption: A genetic algorithm, Econ. Comput. Econ. Cybern. Stud. Res. 46 (2012), 159–182. Search in Google Scholar

[28] S. T. A. Niaki, F. M. Gazaneh and M. A. Toosheghanian, Parameter-tuned genetic algorithm for economic-statistical design of variable sampling interval x-bar control charts for non-normal correlated samples, Comm. Statist. Simulation Comput. 43 (2013), 1212–1240. 10.1080/03610918.2012.732176Search in Google Scholar

[29] P. C. Oprime, N. J. da Costa, C. I. Mozambani and C. L. Gonçalves, X-bar control chart design with asymmetric control limits and triple sampling, Int. J. Adv. Manuf. Technol. 104 (2018), 3313–3326. 10.1007/s00170-018-2640-3Search in Google Scholar

[30] E. Perez, A. Carrion, J. Jabaloyes and F. Aparisi, Optimization of the new DS-u control chart: An application of genetic algorithms, Proceedings of the 9th WSEAS International Conference on Applications of Electrical Engineering (AEE ’10), ACM, New York (2010), 105–109. Search in Google Scholar

[31] T. P. Ryan and N. C. Schwertman, Optimal limits for attributes control charts, J. Qual. Technol. 29 (1997), 86–98. 10.1080/00224065.1997.11979728Search in Google Scholar

[32] A. Saghaei, S. M. T. Fatemi and S. Jaberi, Economic design of exponentially weighted moving average control chart based on measurement error using genetic algorithm, Qual. Reliab. Eng. Int. 30 (2013), 1153–1163. 10.1002/qre.1538Search in Google Scholar

[33] A. Seif, Multi-objective genetic algorithm for economic statistical design of the t-2 control chart with variable sample size: The updated Markov chain approach, J. Test. Eval. 46 (2018), 1209–1219. 10.1520/JTE20160647Search in Google Scholar

[34] A. Seif and M. Sadeghifar, Non-dominated sorting genetic algorithm (NSGA-II) approach to the multi-objective economic statistical design of variable sampling interval T-2 control charts, Hacet. J. Math. Stat. 44 (2015), 203–214. 10.15672/HJMS.201497460Search in Google Scholar

[35] S. Sevil, Construction of fuzzy c control charts based on fuzzy rule method, Anadolu Univ. J. Sci. Technol. A 10 (2017), no. 3, 563–572. Search in Google Scholar

[36] W. A. Shewhart, Quality control charts, Bell Sys. Tech. J. 5 (1926), no. 4, 593–603. 10.1002/j.1538-7305.1926.tb00125.xSearch in Google Scholar

[37] R. Suich, The c control chart under inspection error, J. Qual. Technol. 20 (1988), no. 4, 263–266. 10.1080/00224065.1988.11979119Search in Google Scholar

[38] M. Tavana, Z. Li, M. Mobin, M. Komaki and E. Teymourian, Multi-objective control chart design optimization using NSGA-III and MOPSO enhanced with DEA and TOPSIS, Expert Syst. Appl. 50 (2016), 17–39. 10.1016/j.eswa.2015.11.007Search in Google Scholar

[39] H. Trautmann, D. Steuer and O. Mersmann, Package “mco‘”: Multiple criteria optimization algorithms and related functions, 2020, https://cran.r-project.org/web/packages/mco/mco.pdf. Search in Google Scholar

[40] A. A. Umar, M. B. C. Khoo, S. Saha and A. Haq, Effect of measurement errors on triple sampling X-bar chart, Qual. Reliab. Eng. Int. 38 (2022), 1886–1908. 10.1002/qre.3061Search in Google Scholar

[41] S. Yanık, C. Kahraman and H. Yılmaz, Intelligent process control using control charts—II, control charts for attributes, Intelligent Decision Making in Quality Management, Springer, Cham (2015), 71–100. 10.1007/978-3-319-24499-0_3Search in Google Scholar

[42] M. Zandieh, A. H. Hosseinian and R. Derakhshani, A hybrid NSGA-II-DEA method for the economic-statistical design of the C-control charts with multiple assignable causes, Int. J. Qual. Eng. Technol. 7 (2019), no. 3, 222–255. 10.1504/IJQET.2019.104871Search in Google Scholar

[43] M. J. Zhao and A. R. Driscoll, The c-chart with bootstrap adjusted control limits to improve conditional performance, Qual. Reliab. Eng. Int. 32 (2016), no. 8, 2871–2881. 10.1002/qre.1971Search in Google Scholar

Received: 2023-03-28
Accepted: 2023-06-22
Published Online: 2023-07-25
Published in Print: 2023-12-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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