Fuzzy-based functional capability indices for simple linear profile

Document Type : Research Paper

Author

Khorasan Razavi Agricultural and Natural Resources Research and Education Center, AREEO, Mashhad, Iran

Abstract

The quality of some processes is defined by a simple linear function between a response and an explanatory variable, which is named a simple linear profile. Various capability indices have been introduced in the literature for these processes. Some of them are functional, that use all domain of the explanatory variable instead of its levels values. Therefore, these methods may fail to account capability of the process and overstate it. This paper applies fuzzy logic to deal with the explanatory variable domain and introduces two capability indices. Then, investigates and compares the performance of the proposed indices and some existing ones, using a simulation study. Results show that one of the new proposed indices has the best performance based on the mean square error and mean absolute error criteria.

Keywords

Main Subjects

References

1] Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2016). A class of process capability indices for asymmetric tolerances. Quality Engineering, 28 (4), 441-454. https://doi.org/10.1080/08982112.2016.1168524
[2] Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2016). Assessing process performance with incapability index based on fuzzy critical value. Iranian Journal of Fuzzy Systems, 13 (5), 21-34. https://doi.org/10.22111/ijfs.2016.2731
[3] Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2020). On the non-parametric multivariate control charts in fuzzy environment. Iranian Journal of Fuzzy Systems, 17 (1), 185-205. https://doi.org/10.22111/ijfs.2020.5119
[4] Abbasi Ganji, Z., & Sadeghpour Gildeh, B. (2021). A new process capability index for simple linear pro le. Communications in Statistics - Theory and Methods. https://doi.org/10.1080/03610926.2021.1980804
[5] Albassam, M., & Aslam, M. (2023). Product evaluation using uncertainty-based process capability index. Ain Shams Engineering Journal, 14 (4), 1011947. https://doi.org/10.1016/j.asej.2022.101947
[6] Draper, N. R., & Smith, H. (2011). Applied Regression Analysis. Third Edition, John Wiley & Sons, Inc. https://onlinelibrary.wiley.com/doi/book/10.1002/9781118625590
[7] Ebadi, M., & Amiri, A. (2012). Evaluation of process capability in multivariate simple linear pro les. Scientia Iranica, Transactions E: Industrial Engineering, 19 (6), 1960-1968. https://doi.org/10.1016/j.scient.2012.09.010
[8] Ebadi, M. and Shahriari, H. A process capability index for simple linear pro le, International Journal of Advanced Manufacturing Technology 2013; 64: 857-865. https://doi.org/10.1007/s00170-012-4066-7
[9] Hosseinifard, S. Z., & Abbasi, B. (2012a). Evaluation of process capability indices of linear pro les. International Journal of Quality & Reliability Management, 29 (2), 161-176. https://doi.org/10.1108/02656711211199892
[10] Hosseinifard, S. Z., & Abbasi, B. (2012b). Process capability analysis in non normal linear regression pro les. Communication in Statistics - Simulation and Computation, 41 (10), 1761-1784. https://doi.org/10.1080/03610918.2011.611313
[11] Kang, L., & Albin, S. L. (2000). On-line monitoring when the process yields a linear pro le. Journal of Quality Technology, 32 (4), 418-426. https://doi.org/10.1080/00224065.2000.11980027
[12] Karakaya, K. (2024). A general novel process capability index for normal and non-normal measurements. Ain Shams Engineering Journal, 15 (6), 102753. https://doi.org/10.1016/j.asej.2024.102753
[13] Kim, S., & Kim, H. (2016). A new metric of absolute percentage error for intermittent demand forecasts. International Journal of Forecasting, 32, 669-679. https://doi.org/10.1016/j.ijforecast.2015.12.003
[14] Kunter, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear statistical models, Boston: McGraw-Hill. https://www.amazon.com/Applied-Linear-Statistical-Models-Michael/dp/007310874X
[15] Nemati Keshteli, R., Baradaran Kazemzadeh, R., Amiri. A., & Noorossana, R. (2014). Developing functional process capability indices for simple linear pro le. Scientia Iranica, 21 (3), 1044-1050. https://scientiairanica.sharif.edu/article_3545.html
[16] Pakzad, A., Razavi, H., & Sadeghpour Gildh, B. (2022). Developing loss-based functional process capability indices for simple linear pro le. Journal of Statistical Computation and Simulation. 92 (1), 115-144. https://doi.org/10.1080/00949655.2021.1933486
[17] Sardesai, S., & Klingebiel, K. (2023). Maintaining viability by rapid supply chain adaptation using a process capability index. Omega. 115, 102778. https://doi.org/10.1016/j.omega.2022.102778
[18] Sedighi Maman, Z., Wade Murphy, W., Maghsoodloo, S., Haji Ahmadi, F., & Megahed, F. M. (2016). A short note on the e ect of sample size on the estimation error in Cp. Quality Engineering, 28 (4), 455-466. http://dx.doi.org/10.1080/08982112.2016.1172091
[19] Shahriari, H., & Sarra an, M. (2009). Assessment of process capability in linear pro les. Proceedings of the 16th Iran International Industrial Engineering Conference, Tehran, Iran (in Farsi).
[20] Shi, L., Chen, W., & Fu Lu, L. (2014). An approach for simple linear pro le gauge R&R studies. Discrete Dynamics in Nature and Society, Article ID 816980, https://doi.org/10.1155/2014/816980.
[21] Wang, F. K. (2014a). A process yield for simple linear pro les. Quality Engineering, 26, 311-318. https://doi.org/10.1080/08982112.2013.830739
[22] Wang, F. K. (2014b). Measuring the process yield for simple linear pro les with onesided speci cation. Quality and Reliability Engineering International, 30 (8), 1145-1151. https://doi.org/10.1002/qre.1537
[23] Wu, X. F. (2015). An assessment approach for process capability in simple linear pro le. In: Qi E., Shen J., Dou R. (eds). Proceedings of the 22nd International Conference on Industrial Engineering and Engineering Management, Atlantis Press, Paris, p. 613-620. https://doi.org/10.2991/978-94-6239-180-2_59
[24] Wu, C. W., & Wang, Z. H. (2024). A cost-e ective skip-lot sampling scheme using lossbased capability index for product acceptance determination. International Journal of Production Economics, 273, 109281 https://doi.org/10.1016/j.ijpe.2024.109281
[25] Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
[26] Zimmermann, H. J. (2001). Fuzzy set theory- and its applications. Fourth edition, Springer Science + Business Media, New York. https://link.springer.com/book/10.1007/978-94-010-0646-0

Files

History

  • Receive Date: 21 January 2025
  • Revise Date: 12 April 2025
  • Accept Date: 20 May 2025

Share

How to cite

Statistics