Setting Alarm Thresholds in Measurements with Systematic and Random Errors

Tom Burr, Elisa Bonner, Kamil Krzysztoszek and Claude Norman
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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

Stats, 2019, vol. 2, issue 2, 1-13

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.

Keywords: ANOVA; approximate Bayesian computation; Bayesian approaches; frequentist approaches; parametric; semiparametric; non-parametric; tolerance interval (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2019
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