Environmental Engineering Reference
In-Depth Information
2.4.1 Statistical Properties of Measurements and Measurement
Errors
The measurement error statistical properties, as well as the methods used to process
them, depend upon the category they belong to. Measurements can be classified into
the following categories:
•
On-line or off-line measurement. For instance, flowmeters or density gauges are
on-line while chemical or physical analysis of a sample in a laboratory is off-
line. Automatic sampling followed by centralized X-ray fluorescence analysis is
considered an on-line analysis.
•
Measurement either on part of the material, for instance, chemical analysis of
an ore sample, or on the whole material, as performed by a flowmeter installed
around a pipe.
•
Continuous or discrete measurement. A flowmeter or a particle size analyzer
delivers a continuous signal, while the analysis of a sample of material taken at
constant time intervals is delivered at a given frequency.
•
Averaged measurement value or instantaneous measurement. The reading of a
flowmeter can be averaged in a given time window, or a sample made of com-
posite increments can be analyzed for its physical or chemical properties. On the
contrary a sampled flowmeter signal gives an instantaneous value.
•
For discrete measurements, averaged or instantaneous samples can be taken at
constant time periods (systematic sampling), or randomly (random sampling), or
randomly within constant time intervals (stratified sampling).
Moreover, one can distinguish three main types of measurement errors that must
be processed differently by the process observers:
• Systematic errors, or biases, are the consequences of sensor calibration drifts,
interaction effects - such as the interaction of foreign chemical elements on the
analyzed species - or biases in sampling procedures.
• Random centered errors. They results from many independent sources of noise
due to the heterogeneous nature of the material to be analyzed and to the inherent
fluctuations of the analytical devices. They have a zero mean value and are usu-
ally considered as obeying normal distributions, unless the error variance is large
compared with the nominal value of the process variable, in which case the nor-
mal distribution might mean that a process variable could have negative values,
an unacceptable property for inherently positive variables such as concentrations
or flowrates.
• Accidental gross errors, due, for instance, to contamination of samples, tagging
mistakes, transmission faults.
For correct use of measurements, systematic errors must be detected, corrected,
and their sources eliminated, for instance by maintenance and calibration of sen-
sors, or by redesigning sampling procedures. Accidental gross errors must also be
detected, using fault detection and isolation (FDI) techniques, and the corresponding
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