Accuracy Assessment of Chemical Analytical Instruments Based on Their Calibration Results
Abstract Generated abstract
The paper examines how the accuracy of chemical analytical instruments should be assessed from calibration results, emphasizing that such instruments involve both measurement of an analytical property and inference of substance concentration. It argues that applying uniform metrological requirements borrowed from other instrument fields leads to excessive testing and delayed implementation, and proposes a differentiated approach based on operational purpose. The author distinguishes absolute analyzers from calibrated instruments, then subdivides calibrated instruments into exemplary, control measuring, and regulating analyzers, linking each class to appropriate requirements for calibration dependence, systematic and random error treatment, and necessary metrological characteristics. This framework suggests that, especially for narrowly targeted or regulating instruments, calibration accuracy requirements can often be reduced without compromising practical use.
Full Text
ASSESSING THE ACCURACY OF CHEMICAL ANALYTICAL INSTRUMENTS BASED ON THEIR CALIBRATION RESULTS
V. Ya. Dubrovinskii
Questions of assessing the accuracy of chemical analytical instruments are gradually acquiring particular importance in connection with the expansion of their range and the intensive introduction of new types of instruments into the production practice of monitoring and regulating technological processes.
From the metrological point of view, a chemical analytical instrument is a quite special phenomenon, since, as applied to it, the concept of measurement accuracy may have two aspects: the accuracy of measuring an analytical property inherent in a substance (electrical conductivity, thermal conductivity, optical density, etc.), and the accuracy of measuring the amount of the substance being determined; moreover, the transition from the first assessment to the second often requires comparison of the result of measurement by the instrument with the amount of the substance determined by chemical analysis.
The possibility of two kinds of assessment of measurement accuracy by one and the same instrument has led to the necessity of a complete study both of the operation of the instrument itself (reproducibility and correctness of readings) and of the assessment of the metrological characteristics of the methods adopted for its calibration.
Such studies naturally conclude with clarification of the question of the interrelation between the errors of the instrument and of the method of its calibration and of their joint influence on the results of measuring the amount of substance by the instrument, for which purpose mathematical studies of the type of the problem of error propagation are carried out.
Serially produced chemical analytical instruments are supplied with instructional documentation of the Committee of Standards, which reflects the recommended solution of the questions listed above. In developing new instruments, according to established practice, in order to obtain permission for their use, the instruments undergo laboratory and production tests to an extent that pursues the aim of obtaining the most complete and, in terms of accuracy, ideal information possible on the metrological characteristics of the instruments, although the values of these characteristics achieved are not used in the further operation of the instrument.
As a result, the enormous efforts expended on creating a basis for research and on conducting tests prove useless, while the time required to bring the developed instruments to the consumer is unjustifiably prolonged. Often an instrument becomes obsolete before it is put into production use.
The reason for the situation that has arisen, in our opinion, is the absence of a differentiated metrological policy with respect to chemical analytical instruments of different purposes; as a result, in the methodology for calibrating and verifying chemical analytical instruments, research techniques are carried over from, for example, electrical, thermal-engineering, and other instruments, where the requirements in assessing metrological characteristics are dictated by the need to obtain highly accurate information about the measured quantity and are justified by the possibility of strictly reproducing the latter.
The question of the level of requirements for the metrological characteristics being determined can be resolved if it is approached from the standpoint of operational requirements. In this case it is possible to reduce to a minimum the number of variants of standard requirements for determining the metrological characteristics of chemical analytical instruments, limiting oneself in each type of instrument to obtaining only the absolutely necessary information.
All chemical analytical instruments, regardless of the principle of their operation, may be divided into two large groups:
- Absolute analyzers.
- Calibrated instruments.
The instruments we assign to the group of absolute analyzers are relatively few in number. Their operation is based on the application of precise physical or physicochemical laws for the purposes of analysis. Examples of such instruments are coulometric meters, as well as chromatographs operating in the mode of determining the concentration of a substance by the value of the ratio of the normalized peak area of the substance being determined to the sum of the normalized areas of all the components of the analyzed mixture. As is easy to see, these instruments do not require calibration involving results of measurement of the substance under study by an independent method: the reproducibility of measurement results by the instrument under identical conditions is an objective and sufficient metrological characteristic of the accuracy of the instrument’s operation, analogous to what is observed when working with physical instruments.
The instruments we assign to the group of calibrated instruments may be constructed on the basis of a correlation between the properties of the object being analyzed and the directly measured quantity; that is, in principle, an instrument calibrated on a scale of conventional marks contains information about indirectly measured quantities that are only distantly related to the directly measured quantity. Examples of such instruments are, above all, potentiometric instruments (pH meters and redox meters), spectrophotometric instruments used for measuring the amount of a substance, and so on.
Within the group of calibrated instruments we distinguish three subgroups according to the nature of the tasks solved with their aid.
Table 1, given below, shows how taking the nature of the tasks solved by an instrument in operation as a classification feature makes it possible to formulate logically consistent requirements for the metrological characteristics of instruments.
It follows from Table 1 that in many cases, when developing instruments of narrowly targeted purpose, the number of metrological characteristics needed for classification of the instrument can be reduced without reducing the possibilities of its application.
A reduction in the number of metrological characteristics substantially lowers the requirements for the accuracy of the calibration method. In the limiting case (regulating analyzers), the accuracy of the calibration method may
Table 1
Relationship between the metrological characteristics of graduated chemical-analytical instruments and the nature of the problems solved with their aid
| Requirement | Exemplary analytical instruments | Control-measuring analytical instruments and indicators | Regulating analyzers |
|---|---|---|---|
| 1 | 2 | 3 | 4 |
| Problem being solved | Accurate conversion of the measured quantity into an output signal; used for checking and calibrating instruments with another nature and measure | Obtaining information on the measured value suitable for establishing an objective relation between the given measured quantity and other characteristics of the process | Generating an output signal of the measured quantity within limits predetermined by the regulation range, which ensures maintenance of the technological process under the specified operating conditions |
| Characteristics, the provision of which constitutes the solution of the problem | $\overline{A};\ \Delta A;\ \sigma_A$ | $\overline{A};\ \sigma_A;\ (\Delta A)^*$ | $\sigma_A;\ (\overline{A})^*$ |
| Requirements on the form of the calibration dependence | Maximum approximation to the true relation between the measured value and the output signal | Possibility of obtaining exact information on the measured value within the limits of the measurement range | Any dependence that allows representation of conditional marks of the scale and values of the measured quantity |
| Influence of the components of the error of the calibration method: a) systematic, b) random, $\Delta$, $\sigma$ | Is taken into account or eliminated Is estimated $\Delta < \sigma$ |
Is taken into account Is estimated $\Delta \approx \sigma$ |
Is not taken into account Is estimated $\Delta \gtrsim \sigma$ |
Continuation of Table 1
| 1 | 2 | 3 | 4 |
|---|---|---|---|
| Requirements for the accuracy of estimating the errors of the calibration method and the measurement error | \(\Delta\) and \(\sigma\) are determined with maximum accuracy | \(\sigma\) is within the limits of the operating requirements; \(\Delta\) is estimated only when the instrument operates in the range of values of the measured quantity comparable with \(\sigma\). In all other cases, the influence of \(\Delta\) is taken into account by increasing the limits of the value of \(\sigma\). | \(\sigma\) is within the limits of the operating requirements |
| Relationship between the characteristics of the result of measurement by the instrument and the characteristics of the operation of the instrument and the calibration method. | \(\displaystyle A_{\text{meas}} = f(A_{\text{instr}})= f(\overline{A}_{\text{grad}})\) \(\displaystyle (\Delta A)_{\text{meas}}=\varphi\bigl((\Delta A)_{\text{instr}},(\Delta A)_{\text{grad}}\bigr)\) \(\displaystyle (\sigma_A^2)_{\text{meas}}=(\sigma_A^2)_{\text{instr}}+(\sigma_A^2)_{\text{grad}}\) |
\(\displaystyle A_{\text{meas}}=(\overline{A})_{\text{instr}}\pm(\Delta_A)_{\text{instr}}\) \(\displaystyle (\sigma_A)^2_{\text{meas}}=(\sigma_A)^2_{\text{instr}}\,[[unclear: operator]]\,(\sigma_A)^2_{\text{grad}}\) \(\displaystyle (\sigma)_{\text{meas}}\simeq(\sigma_A)_{\text{instr}}\) |
need not be taken into account at all; it is important only that the control limits for the measured quantity be assigned on the basis of measurements by the same method.
Notes:
- The symbols used in the table have the following meanings:
\(A\) — the true value of the measured quantity;
\(\overline{A}\) — the mean value of the measured quantity, established as a result of measurement or calibration;
\(\sigma^2\) — the variance of the measurement results;
\(\Delta\) — the systematic error of the measurements.
-
Quantities marked with an asterisk are reference values; their estimation during instrument testing provides a reserve for expanding the possibilities of using the instrument.
-
While this communication was being prepared for publication, paper [1] was published, in which limits are indicated for the ratios between \(\Delta\) and \(\sigma\) under which it is mandatory (from a metrological point of view) to describe measurement results in terms of:
a) only the systematic error, when
\[ \frac{\Delta}{\sigma} > 6, \]
b) only the random error, when
\[ \frac{\Delta}{\sigma} < 2, \]
c) both components of the error, when
\[ 2 < \frac{\Delta}{\sigma} < 6. \]
It is possible that such a division of measurement results according to the quality of their execution may be used as the basis for assigning quantitative criteria for dividing calibrated instruments into subgroups.
REFERENCES
- E. F. Dolinskii, P. P. Kremlevskii, and K. P. Shirokov, Izmeritel’naya tekhnika, No. 12, 6–7, 1967.