Random error basic principles

Accuracy (absence of systematic errors) and uncertainty (coefficient of variation or confidence interval) as caused by random errors and random variations in the procedure are the basic parameters to be considered when discussing analytical results. As stressed in the introduction, accuracy is of primary importance however, if the uncertainty in a result is too high, it cannot be used for any conclusion concerning, e.g. the quality of the environment or of food. An unacceptably high uncertainty renders the result useless. When evaluating the performance of an analytical technique, all basic principles of calibration, of elimination of sources of contamination and losses, and of correction for interferences should be followed (Prichard, 1995). 

You are right a normal distribution, for the individual observations, or Student s -distribution, for the averages. When the process is under control, its variability is only due to random errors, and for this reason its responses should follow a normal distribution or a distribution closely related to it. This is the basic principle of quality control — again, another consequence of the central limit theorem. 

Monitoring by Electromechanical Instrumentation. According to basic engineering principles, no process can be conducted safely and effectively unless instantaneous information is available about its conditions. AH sterilizers are equipped with gauges, sensors (qv), and timers for the measurement of the various critical process parameters. More and more sterilizers are equipped with computerized control to eliminate the possibiUty of human error. However, electromechanical instmmentation is subject to random breakdowns or drifts from caUbrated settings and requires regular preventive maintenance procedures. 

In such statistically designed experiments one wants to exclude the random effects of a limited number of features by varying them systematically, i.e. by variation of the so-called factors. At the same time the order in which the experiments are performed should be randomized to avoid systematic errors in experimentation. In another basic type of experiment, sequential experiments, the set-up of an experiment depends on the results obtained from previous experiments. For help in deciding which design is preferable, see Section 3.6. In principle, statistical design is one recommendation of how to perform the experiments. The design should always be based on an exact question or on a working hypothesis. These in turn are often based on models. 

In principle, for laboratory experiments the ensemble average is the most desirable because it allows us to reduce random experimental errors by repeating the basic experiment. However, we often have problems performing repeatable experiments in a operating process equipments and the physical interpretation of the experimental data is complicated. 

In principle, two basic approaches to estimating uncertainty are available. The bottom-up approach identifies each separate stage of an analysis, including sampling steps wherever possible, assigns appropriate random and systematic errors to each, and then combines these components using the rules summarized in Section 2.11 to give an overall u value. However, for a number of reasons this process may not be as simple as it seems. The first problem is that even simple analytical processes may involve many individual experimental steps and possible... 

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