On moving average based location charts under modified successive sampling

Year 2024, , 506 - 523, 23.04.2024

Tahir Mahmood , Mehvish Hyder , Syed Muhammad Muslim Raza , Muhammad Moeen , Muhammad Riaz

https://doi.org/10.15672/hujms.1223709

Cited By: 2

Abstract

Ceramics are made up of water, clay, and powders. These are categorized as non-metallic and inorganic materials. It is revealed in the literature that Longquan celadon glaze had irregular cracks in glaze layers due to the relatively high content of $Na_{2}O$. Therefore, it is necessary to monitor the influence of $Na_{2}O$ in the ceramic process. Control charts are a possible tool to monitor the changes in the ceramic process. For single event issues, simple random sampling strategy is utilized; however, modified successive sampling is preferred as the favored sampling strategy at regular intervals of time when the quality of any product is evaluated. Hence, this paper is designed to propose moving average $M{A_{MSS\left( S \right)}}$ and double moving average $DM{A_{MSS\left( S \right)}}$ based control charts to detect small to moderate location shifts using the modified successive sampling technique. We have highlighted the performance evaluations of designed control charts with respect to run-length metrics, and their comparison has been made with the existing $Shewhar{t_{MSS\left( S \right)}}\;$control chart. The results revealed that the $DM{A_{MSS\left( S \right)}}$ performs more efficiently as compared to the $Shewhar{t_{MSS\left( S \right)}}$ and $M{A_{MSS\left( S \right)}}\;$control charts. Further, to demonstrate the application of the designed charts, a dataset of the chemical composition of the ceramic is also utilized.

Keywords

Ceramics, control charts, moving average, quality control, statistical process monitoring

References

• [1] T. Abbas, T. Mahmood, M. Riaz and M. Abid, Improved linear profiling methods under classical and Bayesian setups: An application to chemical gas sensors, Chemometr Intell Lab Syst 196, 103908, 2020.
• [2] T. Abbas, F. Rafique, T. Mahmood and M. Riaz, Efficient Phase II Monitoring Methods for Linear Profiles Under the Random Effect Model, IEEE Access 7, 148278- 148296, 2019.
• [3] N. Abbas, M. Riaz, and T. Mahmood, An improved S 2 control chart for cost and efficiency optimization, IEEE Access 5, 19486-19493, 2017.
• [4] M. Abujiya, M.H. Lee and M. Riaz, Improving the performance of exponentially weighted moving average control charts, Qual. Reliab. Eng. 30 (4), 571-590, 2014.
• [5] M. Abujiya and A. Ramat, New cumulative sum control chart for monitoring Poisson processes, IEEE Access 5, 14298-14308, 2017.
• [6] L. Ahmad, M. Aslam, and C.H. Jun, The design of a new repetitive sampling control chart based on process capability index, Trans. Inst. Meas. Control. 38 (8), 971-980, 2016.
• [7] V. Alevizakos, K. Chatterjee, C. Koukouvinos and A. Lappa, A double moving average control chart: discussion, Commun. Stat. Simul. Comput. 51 (10), 6043-6057. 2022.
• [8] M. Amin, T. Mahmood and S. Kinat, Memory type control charts with inverse- Gaussian response: An application to yarn manufacturing industry, Trans. Inst. Meas. Control. 43 (3), 656-678, 2021.
• [9] M.W. Amir, M. Rani, Z. Abbas, H.Z. Nazir, M. Riaz and N. Akhtar, Increasing the efficiency of double moving average chart using auxiliary variable, J. Stat. Comput. Simul. 91 (14), 2880-2898, 2021.
• [10] Y. Areepong, Statistical design of double moving average scheme for zero inflated binomial process, Int. j. appl. phys. mathe. 6 (4), 185-193, 2016.
• [11] B. Chen and X.L. Luo, Incipient fault detection benefited from voting fusion strategy on analysis of process variation, Chemometr Intell Lab Syst 215, 104347, 2021.
• [12] I.D. Czabak-Górska, D. Frczek, A. Kuciska-Landwójtowicz, M. Lorenc, M. Rzsa and M. Czabak, Monitoring of location and dispersion parameters of production processes using hybrid control charts, Comput Ind Eng 162, 107707, 2021.
• [13] S. Durowaye, O. Sekunowo, G. Lawal and I. Raheem, Thermal and tribological characterizations of millscale-particles-reinforced ceramic matrix composites, J. Taibah Univ. Sci. 12 (2), 218-229, 2018.
• [14] R. Goedhart, M. Schoonhoven and R.J. Does, Guaranteed in-control performance for the Shewhart X and X control charts, J. Qual. Technol. 49 (2), 155-171, 2017.
• [15] Z. He, M. Zhang and H. Zhang, Data-driven research on chemical features of Jingdezhen and Longquan celadon by energy dispersive X-ray fluorescence, Ceram. Int. 42 (4), 5123-5129, 2016.
• [16] S. Hussain, T. Mahmood, M. Riaz and H.Z. Nazir, A new approach to design median control charts for location monitoring, Commun. Stat. Simul. Comput. 51 (7), 3553- 3577, 2022.
• [17] M. Hyder, T. Mahmood, M.M. Butt, S.M.M. Raza and N. Abbas, On the locationbased memory type control charts under modified successive sampling scheme, Qual. Reliab. Eng. 38 (4), 2200-2217, 2021.
• [18] M. Hyder, S.M.M. Raza, T. Mahmood and N. Abbas, Enhanced Dispersion Monitoring Structures Based on Modified Successive Sampling: Application to Fertilizer Production Process, Symmetry 15 (5), 1108, 2023.
• [19] A. Jamal, T. Mahmood, M. Riaz and H.M. Al-Ahmadi,GLM-based flexible monitoring methods: an application to real-time highway safety surveillance, Symmetry 13 (2), 362, 2021.
• [20] R.J. Jessen, Statistical investigation of a sample survey for obtaining farm facts, Iowa State University. 1943.
• [21] D. Karagöz, Robust X-bar control chart for monitoring the skewed and contaminated process, Hacettepe J. Math. Stat. 47 (1), 223-242, 2018.
• [22] M.B. Khoo and V. Wong, A double moving average control chart, Commun. Stat. Simul. Comput. 37 (8), 1696-1708, 2008.
• [23] S. Kinat, M. Amin and T. Mahmood, GLM-Based control charts for the inverse- Gaussian distributed response variable, Qual. Reliab. Eng. 36 (2), 765-783, 2019.
• [24] T. Mahmood, Generalized linear model based monitoring methods for highyield processes, Qual. Reliab. Eng. 36 (5), 1570-1591, 2020.
• [25] T. Mahmood and A. Erem, A bivariate exponentially weighted moving average control chart based on exceedance statistics, Comput Ind Eng 175, 108910, 2023.
• [26] R. Mehmood, M.H. Lee, A. Iftikhar and R. Muhammad, Comparative analysis between FAR and ARL based control charts with runs rules, Hacettepe J. Math. Stat. 50 (1), 275-288, 2021.
• [27] D.C. Montgomery, Introduction to statistical quality control. John Wiley & Sons, 2007.
• [28] H. Muttlak and W. Al-Sabah, Statistical quality control based on ranked set sampling, J. Appl. Stat. 30 (9), 1055-1078, 2003.
• [29] T. Nawaz and D. Han, Monitoring the process location by using new ranked set sampling-based memory control charts, Qual Technol Quant Manag 17 (3), 255-284, 2020.
• [30] T. Nawaz, M.A. Raza and D. Han, A new approach to design efficient univariate control charts to monitor the process mean, Qual. Reliab. Eng. Int. 34 (8), 1732- 1751, 2018.
• [31] M. Riaz, T. Mahmood, N. Abbas and S.A. Abbasi, On improved monitoring of linear profiles under modified successive sampling, Qual. Reliab. Eng. Int. 35 (7), 2202-2227, 2019.
• [32] M. Riaz, T. Mahmood, S.A. Abbasi, N. Abbas and S. Ahmad, Linear profile monitoring using EWMA structure under ranked set schemes, Int. J. Adv. Manuf. Technol. 91 (5-8), 2751-2775, 2017.
• [33] S. Roberts, Control chart tests based on geometric moving averages, Technometrics 42 (1), 97-101, 2000.
• [34] S. Roberts, A comparison of some control chart procedures, Technometrics 8 (3), 411-430, 1966.
• [35] P. Robinson and T.Y. Ho, Average run lengths of geometric moving average charts by numerical methods, Technometrics 20 (1), 85-93, 1978.
• [36] J.L. Rodríguez-Álvarez, R. López-Herrera, I.E. Villalon-Turrubiates, R.D. Molina- Arredondo, J.L.G. Alcaraz and Ó.D. Hernández-Olvera, Analysis and control of the paper moisture content variability by using fuzzy and traditional individual control charts, Chemometr Intell Lab Syst 208, 104211, 2021.
• [37] R. Salazar and A. Sinha, Control chart X based on ranked set sampling, Comunicacion Tecica 1 (9), 1997.
• [38] Y. Shangchen and K. Mohammad, On the boundary crossing problem in memoryless models, Hacettepe J. Math. Stat. 52 (3), 785 - 794. 2023.
• [39] H.E. Tekşen and A.S. Anagün, Interval type-2 fuzzy c-control charts using ranking methods, Hacettepe J. Math. Stat. 48 (2), 510-520, 2019.
• [40] F. Touqeer, T. Mahmood, M. Riaz and N. Abbas, On developing linear profile methodologies: a ranked set approach with engineering application, J. Eng. Res. 8 (2), 203- 225, 2020.
• [41] H. Wong, F. Gan,and T. Chang, Designs of moving average control chart, J. Stat. Comput. Simul. 74 (1), 47-62, 2004.
• [42] M. Yaqub, N. Abbas, M. Riaz and J. Shabbir, On modified successive sampling based control charting schemes, Qual. Reliab. Eng. Int. 32 (7), 2491-2497, 2016.
• [43] L. Zhang, C. Lai, K. Govindaraju and M. Bebbington, A note on average run lengths of moving average control charts, Stoch. Qual. Control. 19 (1), 23-27, 2004.