Nonlinear Profiles with R

  • Emilio L. Cano
  • Javier M. Moguerza
  • Mariano Prieto Corcoba
Part of the Use R! book series (USE R)


In many situations, processes are often represented by a function that involves a response variable and a number of predictive variables. In this chapter, we show how to treat data whose relation between the predictive and response variables is nonlinear and, as a consequence, cannot be adequately represented by a linear model. This kind of data are known as nonlinear profiles. Our aim is to show how to build nonlinear control limits and a baseline prototype using a set of observed in-control profiles. Using R, we show how to afford situations in which nonlinear profiles arise and how to plot easy-to-use nonlinear control charts.


  1. 1.
    Boeing Commercial Airplane Group, M.D.P.Q.A.D.: Advanced Quality System Tools, AQS D1-9000-1. Toolbox (1998). url
  2. 2.
    Cano, E.L., Moguerza, J.M., Redchuk, A.: Six sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York (2012). url
  3. 3.
    Cano, J., Moguerza, J.M., Psarakis, S., Yannacopoulos, A.N.: Using statistical shape theory for the monitoring of nonlinear profiles. Appl. Stoch. Model. Bus. Ind. 31(2), 160–177 (2015). doi: 10.1002/asmb.2059. url
  4. 4.
    ISO TC69/SC4–Applications of statistical methods in process management: ISO 7870-2:2013 - Control charts – Part 2: Shewhart control charts. Published standard (2013). url
  5. 5.
    ISO TC69/SC4–Applications of statistical methods in process management: ISO 7870-5:2014 - Control charts – Part 5: Specialized control charts. Published standard (2014). url
  6. 6.
    ISO TC69/SC6–Measurement methods and results: ISO 11843-5:2008 - Capability of detection – Part 5: Methodology in the linear and non-linear calibration cases. Published standard (2012). url
  7. 7.
    ISO/TC 108, Mechanical vibration, shock and condition monitoring, Subcommittee SC 5, Condition monitoring and diagnostics of machines: Condition monitoring and diagnostics of machines – Data interpretation and diagnostics techniques – Part 1: General guidelines. Published standard (2012). url
  8. 8.
    ISO/TC 184, Automation systems and integration, Subcommittee SC 5, Interoperability, integration and architectures of automation systems and applications: Automation systems and integration – Integration of advanced process control and optimization capabilities for manufacturing systems – Part 1: Framework and functional model. Published standard (2015). url
  9. 9.
    Moguerza, J., Muñoz, A., Psarakis, S.: Monitoring nonlinear profiles using support vector machines. In: Rueda, L., Mery, D., Kittler, J. (eds.) Progress in Pattern Recognition, Image Analysis and Applications. Lecture Notes in Computer Science, vol. 4756, pp. 574–583. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-76725-1_60. url
  10. 10.
    Moguerza, J.M., Muñoz, A.: Support vector machines with applications. Stat. Sci. 21(3), 322–336 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Walker, E., Wright, W.: Comparing curves with additive models. J. Qual. Technol. 34(1), 118–129 (2002)Google Scholar
  12. 12.
    Woodall, W.H.: Current research in profile monitoring. Producão 17(3), 420–425 (2007). Invited paperGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Emilio L. Cano
    • 1
    • 2
  • Javier M. Moguerza
    • 1
  • Mariano Prieto Corcoba
    • 3
  1. 1.Department of Computer Science and StatisticsRey Juan Carlos UniversityMadridSpain
  2. 2.Statistics Area, DHEPThe University of Castilla-La ManchaCiudad RealSpain
  3. 3.ENUSA Industrias AvanzadasMadridSpain

Personalised recommendations