Statistical estimation of variation transmission model in a manufacturing process

  • José Antonio HerediaEmail author
  • Matias Gras


This article describes a method for obtaining a variation transmission model in a multi-stage manufacturing process in situations in which the characteristic that defines the quality of the product is an independent variable which variation is the consequence of the one generated and transmitted through the different process stages. The method uses regression analysis to obtain models that relate the quality characteristic to process variables, statistical process control techniques to estimate the variance of the variables and the analysis of variance to estimate the variance components from the observed data and to verify that data come from a stable process. This method can be applied to processes where the quality characteristics are different at each stage (a usual situation in chemical processes) and in cases where not all the process variables can be measured directly. The model also includes the measurement errors both of the quality characteristic and of the process variables. The new proposed approach has been applied to validate its suitability in a ceramic tiles manufacturing process.


Manufacturing process Quality control Statistical modelling Statistical process control Variation transmission Variance components 


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  1. 1.
    Box G, Hunter W, Hunter J, Hunter S (1993) Estadística para investigadores. Reverte, 571–599Google Scholar
  2. 2.
    Box G, Fung CA (1986) Studies in quality improvement: minimizing transmitted variation by parameter design. Technical report nº 8. Center for Quality and Productivity Improvement, MadisonGoogle Scholar
  3. 3.
    Ding Y, Jin J, Ceglarek D, Shi J (2005) Process-oriented tolerancing for multi-station assembly systems. IIE Trans 37:493–508CrossRefGoogle Scholar
  4. 4.
    Escardino A, Amorós JL, Enrique JE (1981) El diagrama de gresificación en la fabricación de pavimentos de gres. Cerám inf 84:211–220Google Scholar
  5. 5.
    Huang Q, Zhou S, Shi J (2002) Diagnosis of multi-operational machining processes through variation propagation analysis. Robotics and CIM Journal 18:233–239Google Scholar
  6. 6.
    Heredia J, Gras M (2009) Análisis y modelado de la transmisión de variabilidad dimensional en un proceso de producción de baldosas cerámicas. Bol Soc Esp Ceram V48:6Google Scholar
  7. 7.
    Heredia J, Gras M (2010) Empirical procedure for modeling the variation transmission in a manufacturing process. Quality Engineering, in pressGoogle Scholar
  8. 8.
    Jin J, Shi J (1999) State space modeling of sheet metal assembly for dimensional control. ASME Transactions, Journal of Manufacturing Science and Engineering 121:756–762CrossRefGoogle Scholar
  9. 9.
    Lowry CA, Montgomery DC (1995) A review of multivariate control charts. IIE Transactions 27:800–810CrossRefGoogle Scholar
  10. 10.
    Mallol G, Ferrer C, Llorens D, Monfort E (1994) Moreno Optimización de las condiciones de funcionamiento en hornos monoestrato. III. Medida de gradientes transversales de temperatura. ATécnica Cerámica 227:653–662Google Scholar
  11. 11.
    Montgomery DC (2001) Introduction to Statistical Quality Control, 4th edn. Wiley, New York, NYGoogle Scholar
  12. 12.
    Morrison SJ (1957) The study of variability in Engineering design. Appl Statistics (Royal Statistical Society) 6(2):133–138MathSciNetGoogle Scholar
  13. 13.
    Morrison SJ (1998) Variance synthesis revisited. Qual Eng 11(1):149–155CrossRefGoogle Scholar
  14. 14.
    Portoles J, Sanchez J, Negre F, Mallol G, Monzo M (1994) Estudio de la dinámica del ciclo de prensado y su influencia sobre la compactación de baldosas cerámicas mediante la sensorización de una prensa industrial. Qualicer 1994 III congreso mundial de la calidad del azulejo y del pavimento cerámico, 73-91Google Scholar
  15. 15.
    Shi J (2007) Stream of variation modeling and analysis for multistage manufacturing processes. CRC, New YorkzbMATHGoogle Scholar
  16. 16.
    Stoumbos ZG, Reynolds MR, Ryan TP, Woodall WH (2000) The state of statistical process control as we proceed into the 21st century. J Am Stat Assoc 95:992–998CrossRefGoogle Scholar
  17. 17.
    Taguchi G, Wu Y (1985) Introduction to Off-line Quality Control. Central Japan Quality Control Association, NagoyaGoogle Scholar
  18. 18.
    Woodall WH, Montgomery DC (1999) Research issues and ideas in statistical process control. J Qual Technol 31:376–386Google Scholar
  19. 19.
    Zhou S, Ding Y, Chen Y, Shi J (2003) Diagnosability study of multistage manufacturing processes based on linear mixed-effects models. Technometrics 45:312–325CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.ESID DepartmentUniversitat Jaume ICastellón de la PlanaSpain
  2. 2.KerabenCastellónSpain

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