Journal of Quality Engineering and Management

Statistical-economic design of control charts RNLMVSIT2

Document Type : Original Article

Authors

Asghar Seif 1
Mitra Abdolmohammadi 2

1 Department of Statistics, Faculty of Basic Sciences, Bu-Ali Sina University, Hamedan, Iran.

2 Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

https://doi.org/10.48313/jqem.2024.214759
Abstract
Purpose: In many industrial processes, there are situations where simultaneous monitoring and control of two or more dependent variables are necessary. In such cases, univariate control of quality characteristics can be misleading when considered independently. In the classical approach, when a quality characteristic falls outside the specified technical limits, the quality loss is regarded as a cost. All products within the technical limits of the quality characteristic are assumed to have similar quality, regardless of the deviation of the quality characteristic from its target value. However, it is essential to distinguish between products that fall within the technical limits of the quality characteristic, as any deviation from the target value incurs a proportional loss.
Methodology: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated. In summary, this study focuses on the statistical-economic design of a multivariate T²-Hotelling control chart with multivariate variable sampling intervals in the presence of a reflected normal multivariate loss function (RNLMVSIT²). Additionally, a sensitivity analysis is conducted to examine the effects of time and cost parameters on the design parameters and the average cost.
Findings: The results demonstrate the satisfactory performance of the proposed models.
Originality/Value: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated.

Keywords

Statistical-economic design؛ T²
؛ -hotelling control chart؛ Markov chain؛ Reflected normal multivariate loss function
[1]     Montgomery, D. C. (1980). The economic design of control charts: A review and literature survey. Journal of quality technology, 12(2), 75–87. https://doi.org/10.1080/00224065.1980.11980940
[2]     Saniga, E. M. (1989). Economic statistical control-chart designs with an application to and r charts. Technometrics, 31(3), 313–320. https://doi.org/10.1080/00401706.1989.10488554
[3]     Woodall, W. H. (1986). Weaknesses of the economic design of control charts. Technometrics, 28(4), 408–409. https://doi.org/10.1080/00401706.1986.10488171
[4]     Aparisi, F., & and Haro, C. L. (2003). A comparison of T 2 control charts with variable sampling schemes as opposed to MEWMA chart. International journal of production research, 41(10), 2169–2182. https://doi.org/10.1080/0020754031000138655
[5]     Faraz, A., R. B., K., & and Saniga, E. (2010). Economic and economic statistical design of T 2 control chart with two adaptive sample sizes. Journal of statistical computation and simulation, 80(12), 1299–1316. https://doi.org/10.1080/00949650903062574
[6]     Seif, A., Alireza, F., & and Saniga, E. (2015). Economic statistical design of the VP control charts for monitoring a process under non-normality. International journal of production research, 53(14), 4218–4230. https://doi.org/10.1080/00207543.2014.986298
[7]     Seif, A., Alireza, F., Erwin, S., & and Heuchenne, C. (2016). A statistically adaptive sampling policy to the Hotelling’s T2 control chart: Markov chain approach. Communications in statistics-theory and methods, 45(13), 3919–3929. https://doi.org/10.1080/03610926.2014.911910
[8]     Seif, A. (2018). Multi-objective genetic algorithm for economic statistical design of the T2 control chart with variable sample size: The updated markov chain approach. Journal of testing and evaluation, 46(3), 1209–1219. https://doi.org/10.1520/JTE20160647
[9]     Bai, D. S., & Lee, K. T. (1998). An economic design of variable sampling interval X̄ control charts. International journal of production economics, 54(1), 57–64. https://doi.org/10.1016/S0925-5273(97)00125-4
[10]   Saadatmelli, A., M. Bameni, M., Asghar, S., & and Faraz, A. (2019). Economic design of X‾ control charts with multiple assignable causes under Burr XII shock model. Communications in statistics-theory and methods, 48(3), 500–522. https://doi.org/10.1080/03610926.2017.1414262
[11]   Naderi, M. H., Seif, A., & Bameni Moghadam, M. (2018). Constrained optimal design of X‾ control chart for correlated data under weibull shock model with multiple assignable causes and taguchi loss function. Srtc-jsri, 15(1), 1–44. http://dx.doi.org/10.29252/jsri.15.1.1
[12]   Abolmohammadi, M., Seif, A., Behzadi, M. H., & B. Moghadam, M. (2021). Economic statistical design of adaptive ̄ X X¯ control charts based on quality loss functions. Operational research, 21(2), 1041-1080.. https://doi.org/10.1007/s12351-019-00467-3
[13]   Taguchi, G., Taguchi, G., Elsayed, E. A., & Hsiang, T. C. (1989). Quality engineering in production systems. McGraw-Hill companies. https://b2n.ir/tp9621
[14]   Chou, C. Y., Liu, H. R., Huang, X. R., & Chen, C. H. (2002). Economic-statistical design of multivariate control charts using quality loss function. The international journal of advanced manufacturing technology, 20(12), 916–924. https://doi.org/10.1007/s001700200215
[15]   Serel, D. A. (2009). Economic design of EWMA control charts based on loss function. Mathematical and computer modelling, 49(3), 745–759. https://doi.org/10.1016/j.mcm.2008.06.012
[16]   Chiu, W. K. (1975). Economic design of attribute control charts. Technometrics, 17(1), 81–87. https://doi.org/10.1080/00401706.1975.10489275
[17]   Spiring, F. A. (1993). The reflected normal loss function. Canadian journal of statistics, 21(3), 321–330. https://doi.org/10.2307/3315758
Journal of Quality Engineering and Management
Volume 14, Issue 2
Summer 2024
Pages 162-176

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