Control charts for monitoring process with time trend

using monitoring random source, profile monitoring and modified location chart

Authors

DOI:

https://doi.org/10.14488/BJOPM.2417.2025

Keywords:

Statistical Process Monitoring, Location Control Charts, Profile Monitoring, Quality 4.0

Abstract

Purpose: Statistical process monitoring has been a relevant practice incorporated into quality management systems. In a controlled process, the variabilities of statistical parameter estimates are expected to fluctuate within a pattern over time. Whenever this pattern is not identified, the root causes must be identified, and the necessary actions should be taken. However, there are situations where special causes are present but not practically significant. Recent studies on profile monitoring have tailored solutions for efficiently detecting trends and seasonality in high-capability processes. This paper proposes using profile curves and statistical modelling based on the location control chart approach.

Design/methodology/approach: Our research was carried out using decision-prescriptive models and the Design Science Research approach to identify solutions for real and complex problems. Additionally, the modeling and simulation method was utilized to assist in developing, analyzing, and testing the model, which was classified as an artifact.

Findings: The modeling results clearly demonstrate that utilizing location control charts and modified graphs is essential in defining equipment adjustments. This approach guarantees the minimum acceptable capacity and maximizes the use of productive resources.

Originality: This study provides novel opportunities for developing and implementing control charts in systems that do not conform to the principles of randomness but rather display intricate temporal patterns. This is particularly relevant in the context of Quality 4.0, where real-time data collection is pervasive.

Downloads

Download data is not yet available.

Author Biographies

Pedro Carlos Oprime, Federal University of São Carlos (UFSCar), São Carlos, SP, Brazil.

Pedro Carlos Oprime é Mestre em Engenharia de Produção pela Universidade Federal de São Carlos e Doutor em Direito, Economia e Ciências pela Université d'Aix-Marseille III. Fez estágio de Pós-Doutorado na Culverhouse College of Commerce, University of Alabama, EUA, e na University of Nantes, França. Atualmente, é professor associado da Universidade Federal de São Carlos. Escreve sobre garantia de controle de qualidade, melhoria contínua, inteligência competitiva, clusters, sistemas produtivos locais e pequenas e médias empresas.

Damaris Chieregato Vicentin, Federal University of São Carlos (UFSCar), São Carlos, SP, Brazil.

Damaris Chieregato Vicentin é atualmente Pesquisadora de Pós-Doutorado na Faculdade de Ciências Aplicadas da Universidade Estadual de Campinas (Unicamp). Possui doutorado em Engenharia de Produção pela Universidade Federal de São Carlos com doutorado em período parcial na Universidade de Waikato, mestrado em Engenharia de Produção pela Universidade Estadual Paulista, MBA em Gestão Financeira, Contabilidade e Auditoria pela Fundação Getúlio Vargas e bacharelado em Administração de Empresas pela Toledo Institution of Education. Possui experiência em Gestão da Qualidade, atuando principalmente nos seguintes temas: Ferramentas Estatísticas, Monitoramento Estatístico de Processos, Indústria 4.0, Lean Six Sigma e Melhoria Contínua.

Juliano Endrigo Sordan, Federal University of São Carlos (UFSCar), São Carlos, SP, Brazil.

Juliano Endrigo Sordan é graduado em Administração de Empresas pelo Centro Universitário de Araraquara (UNIARA) e Mestre em Engenharia de Produção pela Escola de Engenharia de São Carlos (EESC USP). Atualmente é doutorando em Engenharia de Produção pela Universidade Federal de São Carlos (UFSCar). Master Black Belt Lean Six Sigma. Professor de Gestão Empresarial (FATEC Sertãozinho) e de pós-graduação (FGV). Consultor líder em sistemas de gestão da qualidade ISO 9001 e pesquisador do Instituto Fábrica do Milênio. Diretor de Desenvolvimento de Negócios AD HOC. Com mais de treze anos de experiência, gerenciou projetos de melhoria da qualidade e produtividade em mais de 30 empresas. Possui experiência em Excelência Operacional, atuando principalmente nos seguintes temas: Excelência Operacional, Indústria 4.0, Teoria das Restrições - TOC e Lean Six Sigma.

References

Abbas, N. (2023), "On efficient change point detection using a step cumulative sum control chart", Quality Engineering, Vol. 35, No. 4, pp. 712-728.

Altun, E. (2020), “The Lomax regression model with residual analysis: an application to insurance data.” Journal of Applied Statistics, Vol. 48, No. 13–15, pp. 2515–2524.

Aslam, M., Anwar, S.M., Khan, M., Abiodun, N.L. and Rasheed, Z. (2022), “Efficient Auxiliary Information–Based Control Charting Schemes for the Process Dispersion with Application of Glass Manufacturing Industry.” Mathematical Problems in Engineering, 1265204, pp. 1-21.

Carstensen, A.K. & Bernhard, J. (2018), “Design science research – a powerful tool for improving methods in engineering education research.” European Journal of Engineering Education, Vol. 44, No. 1–2, pp. 85–102.

Chakraborti, S. (2000), “Run length, average run length and false alarm rate of Shewhart X-bar chart: exact derivations by conditioning.” Communications in Statistics-Simulation and Computation, Vol. 29, No. 1, pp. 61-81.

Chakraborti, S. (2006), “Parameter estimation and design considerations in prospective applications of the X chart.” Journal of Applied Statistics, Vol. 33, No. 4, pp. 439-459.

Cheng, C.S. and Jacroux, M. (1988), "The construction of trend-free run orders of two-level factorial designs", Journal of the American Statistical Association, Vol. 83, No. 404, pp. 1152-1158.

Colosimo, B.M. and Pacella, M. (2010), "A comparison study of control charts for statistical monitoring of functional data", International Journal of Production Research, Vol. 48, No. 6, pp. 1575-1601.

Draper, N.R. and Stoneman, D.M. (1968), "Factor changes and linear trends in eight-run two-level factorial designs." Technometrics, Vol. 10, No. 2, pp. 301-311.

Eyvazian, M., Noorossana, R., Saghaei, A. and Amiri, A. (2011), "Phase II monitoring of multivariate multiple linear regression profiles", Quality and Reliability Engineering International, Vol. 27, No. 3, pp. 281-296.

Freund, R. A. (1957), "Acceptance control charts", Industrial Quality Control, Vol. 14, No. 4, pp. 13-23.

Goedhart, R. and Woodall, W.H. (2022), "Monitoring proportions with two components of common cause variation", Journal of Quality Technology, Vol. 54, No. 3, pp. 324-337.

Haridy, S., Wu, Z. and Castagliola, P. (2011), "Univariate and multivariate approaches for evaluating the capability of dynamic-behavior processes (case study)", Statistical Methodology, Vol. 8, No. 2, pp. 185-203.

Hevner, A., vom Brocke, J. & Maedche, A. (2019), “Roles of digital innovation in design science research.” Business & Information Systems Engineering, Vol. 61, No. 1, pp. 3–8.

Hilow, H. (2013), "Comparison among run order algorithms for sequential factorial experiments", Computational Statistics & Data Analysis, Vol. 58, pp. 397-406.

Holmes, D.S. and Mergen, A.E. (2000), "Exponentially weighted moving average acceptance charts", Quality and Reliability Engineering International, Vol. 16, No. 2, pp.139-142.

Jardim, F.S., Chakraborti, S. & Epprecht, E.K. (2020), “Two perspectives for designing a phase II control chart with estimated parameters: The case of the Shewhart X Chart.” Journal of Quality Technology, Vol. 52, No. 2, pp. 198-217.

Jones-Farmer, L.A., Woodall, W.H., Steiner, S.H. and Champ, C.W. (2014), "An overview of phase I analysis for process improvement and monitoring", Journal of Quality Technology, Vol. 46, No. 3, pp. 265-280.

Kang, L. and Albin, S.L. (2000), "On-line monitoring when the process yields a linear profile", Journal of quality Technology, Vol. 32, No. 4, pp. 418-426.

Kuiper, A. and Goedhart, R. (2023), "Optimized control charts using indifference regions", Quality Engineering, Vol. 36, No. 2, pp. 371-389.

Liao, W., Chen, M. & Yang, X. (2017), “Joint optimization of preventive maintenance and production scheduling for parallel machines system.” Journal of Intelligent & Fuzzy Systems, Vol. 32, No. 1, pp. 525–536.

Maleki, M.R., Amiri, A., Taheriyoun, A.R. and Castagliola, P. (2017), "Phase I monitoring and change point estimation of autocorrelated poisson regression profiles", Communications in statistics-Theory and Methods, Vol. 47, No. 24, pp. 5885-5903.

Mhatre, S., Scheaffer, R.L. and Leavenworth, R.S. (1981), "Acceptance control charts based on normal approximations to the Poisson distribution", Journal of Quality Technology, Vol. 13, No. 4, pp. 221-227

Mohammadian, F. and Amiri, A. (2012), "Economic‐statistical design of acceptance control chart." Quality and Reliability Engineering International, Vol. 29, No. 1, pp. 53-61.

Montgomery, D.C. (2019), “Introduction to statistical quality control”, Ed 8th, John wiley & sons.

Mukherjee, A., Srimani, D., Chakraborty, S., Ben-David, Y. and Milstein, D. (2015), "Selective hydrogenation of nitriles to primary amines catalyzed by a cobalt pincer complex", Journal of the American Chemical Society, Vol. 137, No. 28, pp. 8888-8891.

Nemati Keshteli, R., Baradaran Kazemzadeh, R., Amiri, A. and Noorossana, R. (2014), "Developing functional process capability indices for simple linear pro le", Scientia Iranica, Vol. 21, No. 3, pp. 1096-1104.

Noorossana, R., Saghaei, A., and Amiri, A. (2011), “Statistical Analysis of Profile Monitoring”, edited, John Wiley and Sons.

Oprime, P.C. and Mendes, G.H.S. (2017), "The X-bar control chart with restriction of the capability indices", International Journal of Quality & Reliability Management, Vol. 34, No. 1, pp. 38-52.

Pureza, V., Morabito, R. and Luna, H.P. (2018), “Modeling and Solving the Traveling

Salesman Problem with Priority Prizes. Pesquisa Operacional”, Vol. 38, No. 3, pp. 499–522.

Shper, V. and Y. Adler. (2017), "The importance of time order with Shewhart control charts", Quality and Reliability Engineering International, Vol. 33, No. 6, pp. 1169-1177.

Sobue, C.E.F., Jardim, F.S., Camargo, V.C.B., Lizarelli, F.L. and Oprime, P.C. (2020), "Unconditional performance of the X̄ chart: comparison among five standard deviation estimators", Quality and Reliability Engineering International, Vol. 36, No. 5, pp. 1808-1819.

Srikaeo, K. and Hourigan, J.A. (2002), "The use of statistical process control (SPC) to enhance the validation of critical control points (CCPs) in shell egg washing", Food Control, Vol. 13, No. 4-5, pp. 263-273.

Steiner, S.H. and Wesolowsky, G.O. (1994), "Simultaneous acceptance control charts for products with multiple correlated characteristics", The International Journal of Production Research, Vol. 32, No.3, pp 531-543.

Woodall, W.H. (1985), "The statistical design of quality control charts", Journal of the Royal Statistical Society: Series D (The Statistician), Vol. 34, No. 2, pp.155-160.

Woodall, W.H. and Montgomery, D.C. (2014), "Some current directions in the theory and application of statistical process monitoring", Journal of Quality Technology, Vol. 46, No.1, pp. 78-94.

Woodall, W.H. and Faltin, F.W. (2019), “Rethinking control chart design and evaluation”, Quality Engineering, Vol. 31, No. 4, pp. 596–605.

Woodall, W.H., Spitzner, D.J., Montgomery, D.C. and Gupta, S. (2004), "Using control charts to monitor process and product quality profiles." Journal of Quality Technology, Vol. 36, No.3, pp. 309-320.

Yan, R., Wang, S., Zhen, L. & Jiang, S. (2024), “Classification and regression in prescriptive analytics: Development of hybrid models and an example of ship inspection by port state control.” Computers & Operations Research, Vol. 163, 106517.

Zhang, Y., Li, S., Deng, Y., Chen, H., Yan, X. & Li, J. (2022), “Joint decision-making model of preventive maintenance and delayed monitoring SPC based on imperialist competitive algorithm.” Journal of Intelligent & Fuzzy Systems, Vol. 42, No. 6, pp. 5321–5334.

Downloads

Published

2025-09-20

How to Cite

Oprime, P. C., Vicentin, D. C., & Sordan, J. E. (2025). Control charts for monitoring process with time trend: using monitoring random source, profile monitoring and modified location chart. Brazilian Journal of Operations & Production Management, 22(3), 2417 . https://doi.org/10.14488/BJOPM.2417.2025

Issue

Section

Research paper

Most read articles by the same author(s)