Statistical Methods in Optimizing Industrial Systems
Abstract
Optimizing industrial energy systems is vital for achieving sustainability goals, reducing costs, and improving operational performance. This paper examines the integration of advanced statistical methods, such as regression analysis, time-series forecasting, Monte Carlo simulations, and machine learning, into industrial energy management. These approaches enable predictive maintenance, accurate energy demand forecasting, and efficient resource allocation, while machine learning models in particular enhance reliability by predicting failures, minimizing downtime, and extending asset life. Statistical techniques also strengthen risk assessment and process control under uncertainty, supporting proactive energy management. Despite these advantages, challenges such as data quality, model scalability, and system complexity remain. Addressing these requires advances in data integration, algorithm interpretability, and interdisciplinary collaboration. By synthesizing statistical approaches with emerging technologies like artificial intelligence and the Internet of Things, this paper underscores the transformative role of statistically informed optimization in building resilient, cost-effective, and sustainable industrial energy systems.
References
Akhiyar D, Nofriadiman. Study of energy management and efficiency in industrial processes: Analysis of implementation and its impact on productivity. J Tek dan Teknol Tepat Guna. 2024;3(2). https://doi.org/10.62357/j-t3g.v3i2.347
Alam MS, Rahman MM, Chowdhury S. ARIMA-based forecasting of solar energy output for smart grid applications. Energy Rep. 2023;9:1123-35. doi:10.1016/j.egyr.2023.01.045.
Aldahmani E, Alzubi A, Iyiola K. Demand Forecasting in Supply Chain Using Uni-Regression Deep Approximate Forecasting Model. Appl Sci. 2024;14(18):8110. https://doi.org/10.3390/app14188110
Almeida FA, Silva RM, Costa JM. Application of SPC tools in food packaging: A case study in fill-level control. J Qual Maint Eng. 2023;29(1):45-60. doi:10.1108/JQME-03-2022-0015.
Aly NA, Murti G. Statistical process control (SPC) implementation: A step–by–step program. Int J Mater Prod Technol. 1991;6(1):1–8. https://doi.org/10.1504/IJMPT.1991.036644
Andersen J. Practical problems of statistical learning. arXiv:2306.06518 [stat.ME]. 2023. https://doi.org/10.48550/arXiv.2306.06518
Anoune K, Ghazi M, Ghazouani M, Nasiri B, Zebraoui O. Empowering industry through energy auditing: A case study of savings and sustainability. Int J Appl Power Eng. 2024;13(4):952–962. https://doi.org/10.11591/ijape.v13.i4.pp952-962
Antony J. Design of experiments for engineers and scientists. Oxford: Elsevier; 2006.
Antony J. Six Sigma vs Lean: Some perspectives from leading academics and practitioners. Int J Product Perform Manag. 2011;60(2):185-90. doi:10.1108/17410401111101494.
Archana K, Kumar S. Enhancing manufacturing quality through statistical process control. J Adv Sci Technol. 2023;20(2):176–181. https://doi.org/10.29070/3xd2x680
Arinze CA, Jacks BS. A comprehensive review on AI-driven optimization techniques enhancing sustainability in oil and gas production processes. Eng Sci Technol J. 2024;5(3):962–973. https://doi.org/10.51594/estj.v5i3.950
Batool A, Dai Y, Ma H, Yin S. Industrial Machinery Components Classification: A Case of D-S Pooling. Symmetry. 2023;15(4):935. https://doi.org/10.3390/sym15040935
Bazaraa MS, Shetty CM. Foundations of optimization. Vol. 122. Springer Science & Business Media; 2012.
Bengtsson L. Statistics. In: Electrical Measurement Techniques. Singapore: Springer; 2024. https://doi.org/10.1007/978-981-99-8187-8_13
Bestle D. Optimization processes for automated design of industrial systems. In: Nachbagauer K, Held A, editors. Optimal Design and Control of Multibody Systems. IUTAM 2022. Vol. 42. Cham: Springer; 2024. https://doi.org/10.1007/978-3-031-50000-8_1
Briand L, Bianculli D, Nejati S, Pastore F, Sabetzadeh M. The case for context-driven software engineering research: Generalizability is overrated. IEEE Softw. 2017;34(5):72–75. https://doi.org/10.1109/MS.2017.3571562
Cerda-Flores SC, Rojas-Punzo AA, Nápoles-Rivera F. Applications of Multi-Objective Optimization to Industrial Processes: A Literature Review. Processes. 2022;10(1):133. https://doi.org/10.3390/pr10010133
Chaurasia AK, Aggarwal A, Khanna P. Mathematical modelling for prediction of angular distortion in the MIG welded Aluminium 6101 plates. Mater Today Proc. 2023 Apr 25.
Chaurasia AK, Aggarwal A, Khanna P. Mathematical modelling to predict bead geometry in MIG welded aluminium 6101 plates. Mater Today Proc. 2024;113:152–158.
Chen Y, Wang H, Li X. Real-time SPC integration with IoT-based manufacturing systems. Procedia CIRP. 2020;93:112-7. doi:10.1016/j.procir.2020.03.019.
Chen Y, Zhang H, Liu Q. Hybrid ARIMA and LSTM model for predictive maintenance in manufacturing. J Intell Manuf. 2022;33(4):987-1002. doi:10.1007/s10845-021-01800-9.
Costa I, Fernandes G, Tereso A. Integration of project management with NPD process: A metalworking company case study. In: 2017 Int Conf Eng Technol Innov (ICE/ITMC); 2017. p. 1191–1200. https://doi.org/10.1109/ICE.2017.8280016
Das T. Productivity optimization techniques using industrial engineering tools: A review. Int J Sci Res Arch. 2024;12(1):375–385. https://doi.org/10.30574/ijsra.2024.12.1.0820
Dass N, Kumar A, Sungroya M. Optimizing real-time systems with parallel computing: Techniques and challenges. In: Futuristic Trends in Information Technology. Vol. 3. IIP Series; 2024. p. 246–258. https://doi.org/10.58532/V3BBIT1P2CH7
Deeb A, Khokhlovskiy V, Prokofiev V, Shkodyrev V. Optimizing multi-level industrial systems through archive-based data-driven configuration. In: Proc 2024 Int Russ Autom Conf (RusAutoCon). IEEE; 2024. p. 252–259. https://doi.org/10.1109/RusAutoCon61949.2024.10694339
DelSole T, Tippett M. Basic concepts in probability and statistics. In: Statistical Methods for Climate Scientists. Cambridge University Press; 2022. p. 1–29. https://doi.org/10.1017/9781108659055.002
Deman V, Ciantar M, Naudin L, Castera P, Beignon A-S. Combining Zhegalkin polynomials and SAT solving for context-specific Boolean modeling of biological systems. IEEE/ACM Trans Comput Biol Bioinform. 2024. https://doi.org/10.1109/TCBB.2024.3456302
Deprez M, Robinson EC. Regression. In: Machine Learning for Biomedical Applications: With Scikit-Learn and PyTorch. Elsevier; 2024. p. 67–86. https://doi.org/10.1016/B978-0-12-822904-0.00008-X
Desouky O, Al Hamidi YM, Khraisheh MK. Student-led multi-disciplinary approach for the design of experiments in engineering: A methodology. Presented at the 2024 ASEE Annu Conf Exposition; 2024 Jun; Portland, Oregon. https://doi.org/10.18260/1-2--48023
DiRenzo GV, Hanks E, Miller DAW. A practical guide to understanding and validating complex models using data simulations. Methods Ecol Evol. 2023;14(1):203–217. https://doi.org/10.1111/2041-210X.14030
Echempati R, Mahajerin E, Sala A. Effective integration of mathematical and CAE tools in engineering. In: 2008 ASEE Annu Conf Exposition; 2008. p. 13–467.
Eckel F, Stampa J, Timkó M, Vecsey L. Data quality and availability tests of public seismometer data in Europe. In: EGU Gen Assem 2023 (EGU23-7852); 2023 Apr 24–28; Vienna, Austria. https://doi.org/10.5194/egusphere-egu23-7852
Edmonds B. Complexity and context-dependency. Found Sci. 2013;18(4):745–755. https://doi.org/10.1007/s10699-012-9303-x
Fang D, Varshney KR, Wang J, Ramamurthy KN, Mojsilovic A, Bauer JH. Quantifying and recommending expertise when new skills emerge. In: 2013 IEEE 13th Int Conf Data Min Worksh. IEEE; 2013. p. 672–679. https://doi.org/10.1109/ICDMW.2013.33
Filipić B, Tušar T. Challenges of applying optimization methodology in industry. In: Proc 15th Annu Conf Companion Genet Evol Comput. ACM; 2013. p. 1103–1104. https://doi.org/10.1145/2464576.2482688
Fitriyanti D, Wrasiati LP, Hartiati A. Penerapan metode Statistical Process Control (SPC) pada kemasan produk kopi bubuk di CV. Dewi Starindo. J Rekayasa dan Manajemen Agroindustri. 2024;12(1):78–92. https://doi.org/10.24843/JRMA.2024.v12.i01.p08
Gehrmann J, Beyan O. Data quality in medical real-world data – An oncological use case. Stud Health Technol Inform. 2024;316:9–13. https://doi.org/10.3233/SHTI240332
Grossmann IE. Challenges in the application of mathematical programming in the enterprise-wide optimization of process industries. Theor Found Chem Eng. 2014;48(5):555–573. https://doi.org/10.1134/S0040579514050182
Gurcan F, Sevik S. Expertise roles and skills required by the software development industry. In: 2019 1st Int Informatics Softw Eng Conf (UBMYK). IEEE; 2019. p. 1–4. https://doi.org/10.1109/UBMYK48245.2019.8965571
Heim HP. The statistical regression calculation in plastics processing: Process analysis, optimization, and monitoring. Macromol Mater Eng. 2002;287(11):773–783. https://doi.org/10.1002/mame.200290006
Hensel M, Bier H. Interdisciplinary data-integrated approaches. SPOOL. 2022;9(1):3–4. https://doi.org/10.47982/spool.2022.1.00
Hintermüller M, Kunisch K, Leugering G, Rocca E. Challenges in optimization with complex PDE-systems. Oberwolfach Rep. 2021;18(1):419–506. https://doi.org/10.4171/OWR/2021/9
Hou A, Gomaa A, Mita T. Comprehensive steam system optimization: A key element for carbon emissions reduction and energy efficiency. Abu Dhabi Int Pet Exhib Conf. 2023 Oct. https://doi.org/10.2118/216260-MS
Igarashi H. Optimization methods. In: Topology optimization and AI-based design of power electronic and electrical devices: Principles and methods. Elsevier; 2024. p. 127–179. https://doi.org/10.1016/B978-0-32-399166-7.00011-9
Ishola CY, Olabode AS. Fuzzy approach for determining statistical process control (SPC) tools location on the production floor. Data Sci J Comput Appl Inform. 2024;8(1):25–36. https://doi.org/10.32734/jocai.v8.i1-17137
Ito T, Fujita J, Tada A, Matsuzaki H. Industrial machinery and control method thereof (United States Patent No. US 11,256,229). Shibaura Machine Co., Ltd; 2022.
Jha A. Application of statistical process control in automotive manufacturing. Int J Res Appl Sci Eng Technol (IJRASET). 2024;12(IX):345–349. https://doi.org/10.22214/ijraset.2024.64176
Jiang Y. Research on improving production efficiency in smart manufacturing using IoT. In: Proc 4th Int Conf Mach Learn Intell Syst Eng (MLISE); 2024. p. 450–454. https://doi.org/10.1109/MLISE62164.2024.10674615
Kalita JK, Bhattacharyya DK, Roy S. Regression. In: Fundamentals of data science: Theory and practice. Elsevier; 2024. p. 69–89. https://doi.org/10.1016/B978-0-32-391778-0.00012-0
Kroese DP, Brereton T, Taimre T, Botev ZI. Why the Monte Carlo method is so important today. Wiley Interdiscip Rev Comput Stat. 2014;6(6):386-92. doi:10.1002/wics.1314.
Krzywański J, Sosnowski M, Grabowska K, Zylka A, Lasek L, Kijo-Kleczkowska A. Advanced computational methods for modeling, prediction and optimization a review. Materials. 2024 Jul 16;17(14):3521.
Kumar R, Singh A, Sharma P. Enhancing process capability through SPC: A review of recent industrial applications. Int J Product Perform Manag. 2021a;70(4):923-40. doi:10.1108/IJPPM-06-2020-0294.
Kumar R, Singh A, Sharma P. Monte Carlo simulation for risk assessment in industrial investment planning. Comput Ind Eng. 2021a;159:107594. doi:10.1016/j.cie.2021.107594.
Kutner MH, Nachtsheim CJ, Neter J, Li W. Applied linear statistical models. 5th ed. Boston (MA): McGraw-Hill Irwin; 2005.
Liu R, Vakharia V. Optimizing supply chain management through BO-CNN-LSTM for demand forecasting and inventory management. J Organ End User Comput. 2024;36(1):1–25. https://doi.org/10.4018/JOEUC.335591
Manea D-I, Țiţan E, Șerban RR, Mihai M. Statistical applications of optimization methods and mathematical programming. Proc Int Conf Appl Stat. 2020;1(1).
Martínez EC. The statistical simplex method for experimental optimization with process data. Comput Aided Chem Eng. 2005;20:31–36. https://doi.org/10.1016/S1570-7946(05)80127-0
Montgomery DC. Design and analysis of experiments. 9th ed. Hoboken (NJ): John Wiley & Sons; 2017.
Montgomery DC. Introduction to statistical quality control. 8th ed. Hoboken (NJ): John Wiley & Sons; 2019.
Montgomery DC. Opportunities and challenges for industrial statisticians. J Appl Stat. 2001;28(3–4):427–439. https://doi.org/10.1080/02664760120034153
Mosleuzzaman M, Arif I, Siddiki A. Design and development of a smart factory using Industry 4.0 technologies. Acad J Bus Adm Innov Sustain. 2024;4(04):89–108. https://doi.org/10.69593/ajbais.v4i04.131
Murari A, Lungaroni M, Rossi R, Spolladore L, Gelfusa M. Development of information theoretic model selection criteria for the analysis of experimental data. Complexity. 2022. https://doi.org/10.1155/2022/9518303
Myers RH, Montgomery DC, Anderson-Cook CM. Response surface methodology: Process and product optimization using designed experiments. 4th ed. Hoboken (NJ): John Wiley & Sons; 2016.
Nachappa MN, Faujdar PK, Agarwal P. Industrial systems optimization from combining Internet of Things and cloud computing. In: Proc 2024 Int Conf Optim Comput Wireless Commun (ICOCWC). IEEE; 2024. p. 1–7. https://doi.org/10.1109/ICOCWC60930.2024.10470880
Nwabueze MO, Aliyu A, Adegbo KJ, Ikemefuna CD. Enhancing machine optimization through AI-driven data analysis and gathering: Leveraging integrated systems and hybrid technology for industrial efficiency. World J Adv Res Rev. 2024;23(03):1919–1943. https://doi.org/10.30574/wjarr.2024.23.3.2882
Parashare GR, translator. AI-enabled statistical process control for semiconductor manufacturing quality improvement. Int J Sci Res Manag. 2025 Jun;13(06):2279-00. Available from: https://doi.org/10.18535/ijsrm/v13i06.ec07
Pauji NI, Dewi, Nugraha. Peningkatan kualitas kemeja menggunakan metode statistical process control (SPC). Bandung Conf Ser Ind Eng Sci. 2024;4(2):776–786. https://doi.org/10.29313/bcsies.v4i2.14689
Perez HD, Grossmann IE. Recent advances in computational models for the discrete and continuous optimization of industrial process systems. In: Quintela Estévez P, Coll B, Crujeiras RM, Durany J, Escudero L, editors. Advances on links between mathematics and industry. Vol. 15. Springer, Cham; 2021. p. 1–31. https://doi.org/10.1007/978-3-030-59223-3_1
Ponnusamy V, Nallarasan V, Rajasegar RS, Arivazhagan N, Gouthaman P. Modern real-world applications using data analytics and machine learning. In: Singh P, Mishra AR, Garg P, editors. Data analytics and machine learning. Vol. 145. Studies in Big Data. Springer, Singapore; 2024. https://doi.org/10.1007/978-981-97-0448-4_11
Prasad S. Regression. In: Advanced statistical methods. Springer, Singapore; 2024. p. 1–29. https://doi.org/10.1007/978-981-99-7257-9_1
Qiao H, Lin J, Guo Z, Gao L, Ye J, Xu J. Equipment system optimization method based on cost-efficiency analysis. In: 2023 6th Int Conf Comput Netw Electron Autom (ICCNEA). IEEE; 2023. p. 325–329. https://doi.org/10.1109/ICCNEA60107.2023.00076
Rahman MM, Uddin MS, Haque MA. Addressing autocorrelation in SPC charts for dynamic manufacturing environments. Qual Eng. 2021;33(2):215-29. doi:10.1080/08982112.2020.1767891.
Rahman T, Adeyemi A, Yusuf M. Probabilistic modeling of maintenance strategies using Monte Carlo simulation. Reliab Eng Syst Saf. 2024;241:108034. doi:10.1016/j.ress.2024.108034.
Ramadhan GJM, Niam S. Big data analytics: Techniques, tools, and applications in various industries. JURNAL AR RO'IS MANDALIKA (ARMADA). 2023;3(2):56–65. https://doi.org/10.59613/armada.v3i2.2835
Rane NL, Mallick SK, Kaya Ö, Rane J. Emerging trends and future directions in machine learning and deep learning architectures. In: Applied machine learning and deep learning: Architectures and techniques. Deep Science Publishing; 2024. p. 192–211. https://doi.org/10.70593/978-81-981271-4-3_10
Roy RK. A primer on the Taguchi method. 2nd ed. Dearborn (MI): Society of Manufacturing Engineers; 2010.
Sadollah A, Nasir M, Geem ZW. Sustainability and optimization: From conceptual fundamentals to applications. Sustainability. 2020;12(5):2027. https://doi.org/10.3390/su12052027
Salmeron JL, Correia MB, Palos-Sanchez PR. Complexity in forecasting and predictive models. Complexity. 2019. https://doi.org/10.1155/2019/8160659
Segovia-Hernández JG, Hernández S, Cossío-Vargas E, Sánchez-Ramírez E. Challenges and opportunities in process intensification to achieve the UN's 2030 agenda: Goals 6, 7, 9, 12, and 13. Chem Eng Process Process Intensif. 2023;192:109507. https://doi.org/10.1016/j.cep.2023.109507
Sequeira SE, Graells M, Puigjaner L. Integration of available CAPE tools for real-time optimization systems. Comput Aided Chem Eng. 2001;9:1077–1082. https://doi.org/10.1016/S1570-7946(01)80173-5
Singh R, Adepoju O. Monte Carlo-based supply chain risk modeling under demand uncertainty. Int J Prod Res. 2020;58(14):4321-35. doi:10.1080/00207543.2020.1712493.
Singh R, Jain V. Statistical control limits and their role in process monitoring: A comparative study. Measurement. 2022;190:110636. doi:10.1016/j.measurement.2021.110636.
Smirnova OO, Karlina EP. Theoretical foundations of building management systems for modern enterprises. Vestn Astrakhan State Tech Univ Ser Econ. 2024;(3).
Stremersch S, Gonzalez J, Valenti A, et al. The value of context-specific studies for marketing. J Acad Mark Sci. 2023;51(1):50–65. https://doi.org/10.1007/s11747-022-00872-9
Sutanto W, Prajitna SH, Harito C. Enhancing efficiency in industrial metal roof replacement: Utilizing goal programming for cost optimization. JTI J Tek Ind. 2024;10(1). http://dx.doi.org/10.24014/jti.v10i1.29476
Swetha S, Gayatri S. Statistical process control tools & applications. In: Futuristic trends in pharmacy & nursing. Vol. 3. IIP Series; 2024. p. 224–234. https://doi.org/10.58532/V3BGPN19P2CH7
Torabi M. Interdisciplinary approaches in business studies: Applications and challenges. Int J Bus Manag. 2023;18(5):1–33. https://doi.org/10.5539/ijbm.v18n5p33
Uribe C, Isaza C. Expert knowledge-guided feature selection for data-based industrial process monitoring. Rev Fac Ing Univ Antioquia. 2012;65:112–125.
Uzair M, Khurshid SH, Iftikhar MU, Ahmed H, Hameed H, Ali H. Optimizing industrial processes in beverages and aerospace sector: A case study analysis. MATEC Web Conf. 2024;398:01015. https://doi.org/10.1051/matecconf/202439801015
Vadlaman S, Kankanampati PK, Goel O, Jain A, Khan S. Integrating AI and machine learning for optimized supply chain and procurement systems. Univ Res Rep. 2022;9(4):540–560. https://urr.shodhsagar.com/index.php/j/article/view/1391
Vakrilov NV, Kafadarova NM. A review of industry quality improvement strategies through DoE statistical techniques. In: Proceedings of the 2023 XXXII International Scientific Conference Electronics (ET). IEEE; 2023. p. 1–5. https://doi.org/10.1109/ET59121.2023.10278638
Wang H, Chen K, Lin B, Kou J, Li L, Wu S, et al. Process development and optimization of linagliptin aided by the design of experiments (DoE). Org Process Res Dev. 2022;26(12):3254–3264. https://doi.org/10.1021/acs.oprd.2c00230
Woodall WH, Montgomery DC. Some current directions in the theory and application of statistical process monitoring. J Qual Technol. 2014;46(1):78-94. doi:10.1080/00224065.2014.11917961.
Yee JT, Oh SC. Technology integration to business: Focusing on RFID, interoperability, and sustainability for manufacturing, logistics, and supply chain management. Springer Science & Business Media; 2012. https://doi.org/10.1007/978-1-4471-4391-8
Zhang Y, Li K, Wang S. A hybrid forecasting and optimization approach for production scheduling under uncertainty. Comput Ind Eng. 2020;139:105570. doi:10.1016/j.cie.2019.105570.
Zhang Y, Li K. Time-series forecasting for energy demand using ARIMA and Prophet models. Appl Energy. 2021;285:116382. doi:10.1016/j.apenergy.2020.116382.
Zhao J, Li L, Luo LX, Liu F, Wang YG. Analyzing and applying big data technologies based on industrial internet data. J Phys Conf Ser. 2023;2665(1):012003. https://doi.org/10.1088/1742-6596/2665/1/012003
Zhou Y, Zhang T, Huang L. Machine learning-enhanced SPC for anomaly detection in smart factories. Comput Ind Eng. 2024;185:108493. doi:10.1016/j.cie.2023.108493.
