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Setting Alarm Thresholds in Measurements with Systematic and Random Errors

Author

Listed:
  • Tom Burr

    (SGIM/Nuclear Fuel Cycle Information Analysis, International Atomic Energy Agency, A1220 Vienna, Austria)

  • Elisa Bonner

    (Statistics Department, Colorado State University, Fort Collins, CO 80523, USA)

  • Kamil Krzysztoszek

    (SGIM/Nuclear Fuel Cycle Information Analysis, International Atomic Energy Agency, A1220 Vienna, Austria)

  • Claude Norman

    (SGIM/Nuclear Fuel Cycle Information Analysis, International Atomic Energy Agency, A1220 Vienna, Austria)

Abstract

For statistical evaluations that involve within-group and between-group variance components (denoted σ W 2 and σ B 2 , respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates σ ^ W 2 and σ ^ B 2 should be accounted for when setting alarm thresholds to check for a mean shift as both σ W 2 and σ B 2 must be estimated. One-way random effects analysis of variance (ANOVA) is the main tool for analysing such grouped data. Nearly all of the ANOVA applications assume that both the within-group and between-group components are normally distributed. However, depending on the application, the within-group and/or between-group probability distributions might not be well approximated by a normal distribution. This review paper uses the same example throughout to illustrate the possible approaches to setting alarm limits in grouped data, depending on what is assumed about the within-group and between-group probability distributions. The example involves measurement data, for which systematic errors are assumed to remain constant within a group, and to change between groups. The false alarm probability depends on the assumed measurement error model and its within-group and between-group error variances, which are estimated while using historical data, usually with ample within-group data, but with a small number of groups (three to 10 typically). This paper illustrates the parametric, semi-parametric, and non-parametric options to setting alarm thresholds in such grouped data.

Suggested Citation

  • Tom Burr & Elisa Bonner & Kamil Krzysztoszek & Claude Norman, 2019. "Setting Alarm Thresholds in Measurements with Systematic and Random Errors," Stats, MDPI, vol. 2(2), pages 1-13, May.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:2:p:20-271:d:229088
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    References listed on IDEAS

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