Mathematical Model for Determining Preventive Maintenance Intervals and Equipment Quality Control Parameters with a Meta-Heuristic Approach
Keywords:
Integrated metaheuristic model, maintenance cost minimization, quality control, ventive maintenance intervals, Urmia Wastewater Treatment PlantAbstract
This study aimed to develop and optimize an integrated mathematical model for determining preventive maintenance intervals and equipment quality control parameters using a meta-heuristic approach. This applied and descriptive–analytical study was conducted at the Urmia Industrial City Wastewater Treatment Plant. Empirical data were collected from maintenance, quality, cost, and time records. Descriptive statistics, bivariate regression, paired t-test, and a metaheuristic mathematical optimization model with parameter sensitivity analysis were used. The four decision variables—sample size (n), sampling interval (h), control limit coefficient (k), and preventive maintenance interval (t_PM)—were optimized to minimize total cost per unit time. The model was solved using Maple software, and sensitivity analyses were conducted to validate robustness. The integrated model reduced total costs from 289.12 to 116 monetary units. The paired t-test confirmed a significant difference between costs before and after implementation (p<0.05). Sensitivity analysis indicated that machine failure rate and process quality variation had the greatest impact on the objective function. The independent quality control model produced a higher cost (341.8 units), confirming the superior efficiency of the integrated model. Integrating preventive maintenance and quality control policies significantly reduces overall costs, improves output quality, and enhances operational efficiency. The proposed model serves as a practical decision-support tool for industrial managers to optimize maintenance scheduling, minimize machine downtime, and enhance process reliability.
Downloads
References
Ben-Daya, M., & Duffuaa, S. O. (2020). Maintenance and Quality: The Missing Link. Journal of Quality in Maintenance Engineering(1), 20-26. https://doi.org/10.1108/13552519510083110
Ben-Daya, M., & Rahim, M. A. (2020). Effect of Maintenance on the Economic Design of x-Chart. European Journal of Operational Research, 131-143. https://doi.org/10.1016/S0377-2217(98)00379-8
Ben-Daya, M., & Rahim, M. A. (2023). Joint optimization of preventive maintenance and control charts under deteriorating processes. International Journal of Production Economics, 255, 108702.
Berrichi, A., Amodeo, L., Yalaoui, F., Châtelet, E., & Mezghiche, M. (2016). Bi-objective optimization algorithms for joint production and maintenance scheduling: application to the parallel machine problem. Journal of Intelligent Manufacturing, 389-400. https://doi.org/10.1007/s10845-008-0113-5
Black, J. J., & Mejabi, O. O. (2013). Simulation of complex manufacturing equipment reliability using object oriented methods. Reliability Engineering and System Safety. https://www.sciencedirect.com/science/article/abs/pii/095183209500008P
Brandolese, M., Francei, M., & Pozzetti, A. (2011). Production and Maintenance Integrated Planning. International Journal of Production Research(7), 2059-2075. https://doi.org/10.1080/00207549608905013
Chand, S. (2015). Lot Sizes and Setup Frequency with Learning in Setups and Process Quality. European Journal of Operations Research, 190-202. https://doi.org/10.1016/0377-2217(89)90321-4
Chen, S. L., & Chung, K. J. (2015). Determination of the optimal production run and the most profitable process mean for a production process. International Journal of Production Research(7), 2051-2058. https://doi.org/10.1080/00207549608905012
Cheng, T. C. E. (2016a). An Economic Order Quantity Model with Demand Dependent Unit Production Cost and Imperfect Production Processes. IIE Transactions(1), 23-28. https://doi.org/10.1080/07408179108963838
Cheng, T. C. E. (2016b). EPQ with Process Capability and Quality Assurance Considerations. Journal of the Operational Research Society(8), 713-720. https://doi.org/10.1057/jors.1991.137
Chiu, H. N., & Huang, B. S. (2016). The economic design of X-control chart under preventive maintenance policy. Journal of Quality in Maintenance Engineering, 13(1), 61-71. https://doi.org/10.1108/02656719610108323
Chiu, H. N., & Huang, B. S. (2017). The Economic Design of x and S2 Control Charts with Preventive Maintenance and Increasing Hazard Rate. Journal of Quality in Maintenance Engineering(4), 17-40. https://doi.org/10.1108/13552519510105188
Cruthis, E. N., & Rigdon, S. E. (2018). Comparing two estimates of variance to determine the stability of a process. Quality Engineering, 30(2), 190-198. https://www.researchgate.net/publication/233311436_Comparing_two_estimates_of_variance_to_determine_the_stability_of_a_process
Garg, A., & Deshmukh, S. G. (2015). Maintenance management: literature review and directions. Journal of Quality in Maintenance Engineering, 12(3), 205-238. https://doi.org/10.1108/13552510610685075
Garvin, D. A. (2017). Competing on the Eight Dimensions of Quality. Harvard business review(6), 101-109. https://hbr.org/1987/11/competing-on-the-eight-dimensions-of-quality
Goyal, S. K., Gunasekaran, A., & Martikainen, T. (2021). Integrated production, maintenance and quality models: A comprehensive review. European Journal of Operational Research, 292(2), 367-392.
Goyal, S. K., Gunasekaran, A., Martikainen, T., & Yli-Olli, P. (2011). Integrating production and quality control policies: A survey. European Journal of Operational Research, 1-13. https://www.sciencedirect.com/science/article/abs/pii/0377221793900852
Jeong, I. J., Leon, V. J., & Villalobos, J. R. (2017). Integrated decision-support system for diagnosis, maintenance planning, and scheduling of manufacturing systems. International Journal of Production Research, 45(2), 267-285. https://doi.org/10.1080/00207540600678896
Jones, L. A., Woodall, W. H., & Conerly, M. D. (2016). Exact Properties of Dermit Control Charts. Journal of Quality Technology. https://www.tandfonline.com/doi/abs/10.1080/00224065.1999.11979915
Keller, G., & Noori, H. (2020). Impact of Investing in the Quality Improvement on the Lot size Model. Omega International Journal of Management Science(6), 595-601. https://doi.org/10.1016/0305-0483(88)90033-3
Khouja, M., & Mehrez, A. (2017). Economic Production Lot Size Model with Variable Production Rate and Imperfect Quality. Journal of Operational Research Society(12), 1405-1417. https://doi.org/10.1057/jors.1994.217
Lee, H. L., & Rosenblatt, M. J. (2010). Economic Design and Control of Monitoring Mechanisms in Automated Production Systems. IIE Transactions(2), 201-209. https://doi.org/10.1080/07408178808966170
Leng, K., Ren, P., & Gao, L. (2016). A novel approach to integrated preventive maintenance planning and production scheduling for a single machine using the chaotic particle swarm optimization algorithm. Proceedings of the 6th World Congress on Intelligent Control and Automation, Dalian, China. https://ieeexplore.ieee.org/document/1713491/authors
Linderman, K., McKone-Sweet, K. E., & Anderson, J. C. (2015). An integrated systems approach to process control and maintenance. European Journal of Operational Research, 324-340. https://doi.org/10.1016/j.ejor.2003.11.026
Liou, M. J., Tseng, S. T., & Lin, T. M. (2012). The Effects of Inspection Errors to the Imperfect EMQ Model. IIE Transactions(2), 42-51. https://doi.org/10.1080/07408179408966595
Makis, V. (2016). Optimal Lot Sizing and Inspection Policy for an EMQ Model with Imperfect Inspections. Naval Research Logistics, 45(2), 165-186. https://doi.org/10.1002/(SICI)1520-6750(199803)45:2<165::AID-NAV3>3.0.CO;2-6
Panagiotidou, S., & Tagaras, G. (2017). Optimal preventive maintenance for equipment with two quality states and general failure time distributions. European Journal of Operational Research, 329-353. https://doi.org/10.1016/j.ejor.2006.04.014
Pandey, D., Kulkarni, M. S., & Vrat, P. (2017). Integrated production scheduling, quality, maintenance models: an overview. Proceedings of the International Conference on Recent Trends in Mechanical Engineering ICRTME, Ujjain, India.
Peters, M. H., Schneider, H., & Tang, K. (2016). Joint Determination of Optimal Inventory and Quality Control Policy. Management Science, 34(8), 991-1004. https://doi.org/10.1287/mnsc.34.8.991
Porteus, E. L. (2014). Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction. Operations Research, 34(1), 137-144. https://doi.org/10.1287/opre.34.1.137
Raafat, F. (2012). Survey of Literature of Continuously Deteriorating Inventory Models. Journal of the Operational Research Society, 27-37. https://doi.org/10.1057/jors.1991.4
Rahim, M. A. (2018). Joint Determination of Production Quantity, Inspection Schedule and Control Chart Design. IIE Transactions, 26(6), 2-11. https://doi.org/10.1080/07408179408966632
Rahim, M. A., & Ben-Daya, M. (2015). A Generalized Economic Model for Joint Determination of Production Run, Inspection Schedules and Control Chart Design. International Journal of Production Research, 277-289. https://doi.org/10.1080/002075498194047
Rahim, M. A., & Ben-Daya, M. (2018). A Joint Optimization of Production Quantity, Inspection Schedule and Quality Control for an Imperfect Process with deteriorating Products. Journal of Operations Research Society.
Rahmani, K. a.-D. (2022). Planning for Maintenance and Repairs. Foroozeesh Publications.
Rosenblatt, M. J., & Lee, H. L. (2010). Economic Production Cycles with Imperfect Production Process. IIE Transactions, 48-55. https://doi.org/10.1080/07408178608975329
Tagaras, G. (2000). An Integrated Cost Model for the Joint Optimization of Process Control and Maintenance. Journal of the Operational Research Society(8), 757-766. https://doi.org/10.1057/palgrave.jors.0390807
Taguchi, G. (2014). Introduction to Quality Engineering. Asian Productivity Organization. https://books.google.ca/books/about/Introduction_to_Quality_Engineering.html?id=1NtTAAAAMAAJ&redir_esc=y
Voros, J. (2019). Lot Sizing with Quality Improvement and Setup Time Reduction. European Journal of Operations Research, 568-574. https://doi.org/10.1016/S0377-2217(97)00447-5
Zhou, W. H., & Zhu, G. L. (2018). Economic design of integrated model of control chart and maintenance management. Mathematical and Computer Modeling(11-12), 1389-1395. https://doi.org/10.1016/j.mcm.2007.09.008
Zhou, Y., Li, X., & Zhang, Y. (2023). A hybrid grey wolf optimizer for maintenance scheduling and process quality control. Applied Soft Computing, 133, 109915.
Downloads
Published
Submitted
Revised
Accepted
Issue
Section
License
Copyright (c) 2025 سید جمال اشرفی سعادت, كمال الدين رحماني, سليمان ايران زاده , ناصر فقهی فرهمند, هوشنگ تقی زاده (نویسنده)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
