Nonparametric Individual Control Charts for Silica in Water

  • Luís M. GriloEmail author
  • Mário A. Santos
  • Helena L. Grilo
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


The soluble silica content in the demineralized water is a continuous variable measured and controlled in the Chemical Laboratory of a Portuguese thermoelectric central, in order to keep the equipment operating under the best conditions, allowing, in particular, to extend its useful life. In this case study, this variable could be considered approximately normal distributed and because we just have one measure, for each group of the sample, an individual control chart to monitor the silica content is obtained based on average moving range. Once the available sample size is small and it is hard to fit a model, robust control limits using a nonparametric method based on empirical quantiles (which according to some simulations studies perform also well under the normality of the observations) are also estimated with the bootstrap procedure. The comparison of the control limits obtained with different approaches and with(out) outliers is very important for technicians since the value of silica should be as small as possible. The process capability study, also developed, shows that the process does not stay within the engineering specification limits, although it seems stable.



This work was partially supported by the Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/ /2013 (Centro de Matemática e Aplicações).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Luís M. Grilo
    • 1
    • 2
    Email author
  • Mário A. Santos
    • 3
  • Helena L. Grilo
    • 4
  1. 1.Unidade Departamental de Matemática e FísicaInstituto Politécnico de TomarTomarPortugal
  2. 2.FCT, UNL, Centro de Matemática e Aplicações (CMA)CaparicaPortugal
  3. 3.Unidade Departamental de EngenhariaInstituto Politécnico de TomarTomarPortugal
  4. 4.Centro de Sondagens e Estudos EstatísticosInstituto Politécnico de TomarTomarPortugal

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