Models for Combining Random and Systematic Errors. Assumptions and Consequences for different Models

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Abstract
A series of models for handling and combining systematic and random variations/errors are investigated in order to characterize the different models according to their purpose, their application, and discuss their flaws with regard to their assumptions. The following models are considered 1. linear model, where the random and systematic elements are combined according to a linear concept (TE = absolute value(bias) + z x sigma), where TE is total error, bias is the systematic error component, sigma is the random error component (standard deviation or coefficient of variation) and z is the probability factor; 2. squared model with two sub-models of which one is the classical statistical variance model and the other is the GUM (Guide to Uncertainty in Measurements) model for estimating uncertainty of a measurement; 3. combined model developed for the estimation of analytical quality specifications according to the clinical consequences (clinical outcome) of errors. The consequences of these models are investigated by calculation of the functions of transformation of bias into imprecision according to the assumptions and model calculations. As expected, the functions turn out to be rather different with considerable consequences for these types of transformations. It is concluded that there are at least three models for combining systematic and random variation/errors, each created for its own specific purpose, with its own assumptions and resulting in considerably different results. These models should be used according to their purposes.

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