%0 Journal Article
%T Setting Alarm Thresholds in Measurements with Systematic and Random Errors
%A Claude Norman
%A Elisa Bonner
%A Kamil Krzysztoszek
%A Tom Burr
%J Stats | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/stats2020020
%X Abstract For statistical evaluations that involve within-group and between-group variance components (denoted 考 W 2 and 考 B 2 , respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates 考 ^ W 2 and 考 ^ B 2 should be accounted for when setting alarm thresholds to check for a mean shift as both 考 W 2 and 考 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. View Full-Tex
%K ANOVA
%K approximate Bayesian computation
%K Bayesian approaches
%K frequentist approaches
%K parametric
%K semiparametric
%K non-parametric
%K tolerance interval
%U https://www.mdpi.com/2571-905X/2/2/20