Measurement errors Instrumentation

We now introduce several terms that are commonly associated with the accuracy of process instruments. The measurement error (or error) is the difference between the true value and the measured error. Instrument vendors often express accuracy as a percentage of full scale (% FS) where the term full scale refers to the span of the instrument. Suppose that the % FS error of a temperature transmitter is reported as 1% and the zero and span are adjusted so that the instrument operates over the range of 10-70 °C. Since the span is 70-10 = 60 °C, the measurement error is 1% of 60 °C, or 0.6 °C. Consequently, the relative error (obtained by dividing the error by the value of the measurement) at 10 °C is 0.6/10 = 6%. Thus, when instrument accuracy is expressed as % FS, the relative error can be quite large for small values of the measured variable. 

The uncertainties of the system parameters are induced by measurement errors, instrumentation accuracy, and random variation during the operation and control. The determination of the total engineering uncertainty is sensitive to these system parameter uncertainties, and these uncertainties are considered by using their random values directly and statistically. 

For interpretation of measuring results, calibration characteristics obtained on the samples in advance is used in the above instruments. However, if number of impediment factors increases, the interpretation of the signals detected becomes more complicated in many times. This fact causes the position that the object thickness T and crack length I are not taken into consideration in the above-mentioned instruments. It is considered that measuring error in this case is not significant. 

The maximum determinate measurement error for equipment or instrument as reported by the manufacturer. 

Determinate measurement errors can be minimized by calibration. A pipet can be calibrated, for example, by determining the mass of water that it delivers and using the density of water to calculate the actual volume delivered by the pipet. Although glassware and instrumentation can be calibrated, it is never safe to assume that the calibration will remain unchanged during an analysis. Many instruments, in particular, drift out of calibration over time. This complication can be minimized by frequent recalibration. 

Accuracy The accuracy of a controlled-current coulometric method of analysis is determined by the current efficiency, the accuracy with which current and time can be measured, and the accuracy of the end point. With modern instrumentation the maximum measurement error for current is about +0.01%, and that for time is approximately +0.1%. The maximum end point error for a coulometric titration is at least as good as that for conventional titrations and is often better when using small quantities of reagents. Taken together, these measurement errors suggest that accuracies of 0.1-0.3% are feasible. The limiting factor in many analyses, therefore, is current efficiency. Fortunately current efficiencies of greater than 99.5% are obtained routinely and often exceed 99.9%. 

Random Measurement Error Third, the measurements contain significant random errors. These errors may be due to samphng technique, instrument calibrations, and/or analysis methods. The error-probability-distribution functions are masked by fluctuations in the plant and cost of the measurements. Consequently, it is difficult to know whether, during reconciliation, 5 percent, 10 percent, or even 20 percent adjustments are acceptable to close the constraints. 

Systematic Measurement Error Fourth, measurements are subject to unknown systematic errors. These result from worn instruments (e.g., eroded orifice plates, improper sampling, and other causes). While many of these might be identifiable, others require confidence in all other measurements and, occasionally, the model in order to identify and evaluate. Therefore, many systematic errors go unnoticed. 

The second section of the spreadsheet contains the overall flows, the calculated component flows, and the material balance closure of each. The weighted nonclosure can be calculated using the random error calculated above, and a constraint test can be done with each component constraint if desired. Whether the measurement test is done or not, the nonclosure of the material balance for each component gives an indication of the validity of the overall flows and the compositions. If particiilar components are found to have significant constraint error, discussions with laboratory personnel about sampling and analysis and with instrument personnel about flow-measurement errors can take place before any extensive computations begin. 

As well as measurement errors due to the pressure measurement instrument itself, other errors related to pressure measurements must be considered. In ventilation applications a frequently measured quantity is the duct static pressure. This is determined by drilling in the duct a hole or holes in which a metal tube is secured. The rubber tube of the manometer is attached to the metal tube, and the pressure difference between the hole and the environment or some other pressure is measured. 

For a thermometer to react rapidly to changes in the surrounding temperature, the magnitude of the time constant should be small. This involves a high surface area to liquid mass ratio, a high heat transfer coefficient and a low specific heat capacity for the bulb liquid. With a large time constant, the instrument will respond slowly and may result in a dynamic measurement error. 

Determinate errors may be constant or proportional. The former have a fixed value and the latter increase with the magnitude of the measurement. Thus their overall effects on the results will differ. These effects are summarized in Figure 2.1. The errors usually originate from one of three major sources operator error instrument error method error. They may be detected by blank determinations, the analysis of standard samples, and independent analyses by alternative and dissimilar methods. Proportional variation in error will be revealed by the analysis of samples of varying sizes. Proper training should ensure that operator errors are eliminated. However, it may not always be possible to eliminate instrument and method errors entirely and in these circumstances the error must be assessed and a correction applied. 

In the previous development it was assumed that only random, normally distributed measurement errors, with zero mean and known covariance, are present in the data. In practice, process data may also contain other types of errors, which are caused by nonrandom events. For instance, instruments may not be adequately compensated, measuring devices may malfunction, or process leaks may be present. These biases are usually referred as gross errors. The presence of gross errors invalidates the statistical basis of data reconciliation procedures. It is also impossible, for example, to prepare an adequate process model on the basis of erroneous measurements or to assess production accounting correctly. In order to avoid these shortcomings we need to check for the presence of gross systematic errors in the measurement data. 

A run is therefore regarded as being carried out under repeatability conditions, i.e. the random measurement errors are of a magnitude that would be encountered in a short period of time. In practice the analysis of a run may occupy sufficient time for small systematic changes to occur. For example, reagents may degrade, instruments may drift, minor adjustments to instrumental settings may be called for, or the laboratory temperature may rise. However, these systematic effects are, for the purposes of IQC, subsumed into the... 

I have also chosen the interest domain to illustrate a simple but important methodological principle—the importance of measurement error and specificity. Measurement error and specificity saturate all psychological instruments and failure to take them into account results in theoretically misleading conclusions1. 

A second problem in whole molecule mass spectrometry is that fluctuations in ion current may introduce substantial errors. Recall that ions of different m/z are not measured simultaneously in whole molecule mass spectrometry. If the ion current is not stable (and it commonly fluctuates in El sources), then after first peak (say m/z = 112 in our example) is measured, and instrumental parameters are changed in order to focus the next peak (m/z = 114) on the collector, the ion current of this second peak may no longer correspond to that existing at the time the first peak was measured. One can try to switch the detector from peak to peak more rapidly but that shortens the collection time for each peak, fewer ions will be counted, and errors in counting statistics will increase. Normally this problem is dealt with by statistical... 

As electrode systems involving ISEs usually have a high resistance, up to several Gf2, the meter should have the highest possible input impedance. To obtain a measuring error of 0.1%, the input impedance of the meter should be 10 times the cell resistance. To keep the overall measuring error at a level of a few per cent, the meter should have a resolution of the order of 0.1 mV. Modem instruments readily comply with these requirements. For a useful view of these aspects see [21]. 

A major concern surrounding isotope data obtained during analysis is the measurement error associated with mass fractionation within the instrument owing to variations in operating conditions (e.g. Marechal etat. 1999). In order to constrain the errors associated with copper isotope analyses on our instrument, we compared all of the copper ratios to the NIST 976 copper standard (eq. 1) using standard-sample-standard bracketing. The 2a error for the variation of the standard for eight analytical sessions was observed to be +... 

This study demonstrates that the nonlinear optimization approach to parameter estimation is a flexible and effective method. Although computationally intensive, this method lends itself to a wide variety of process model formulations and can provide an assessment of the uncertainty of the parameter estimates. Other factors, such as measurement error distributions and instrumentation reliability can also be integrated into the estimation procedure if they are known. The methods presented in the crystallization literature do not have this flexibility in model formulation and typically do not address the parameter reliability issue. 

The classic texts on the design of experiments in scientific and engineering studies emphasize (1) measurement and instrumentation, (2) sources of error, (3) factor design etc. [30, 31] This section addresses step-by-step many of these issues for in situ studies, and does so by integrating relevant chemical and chemical engineering concerns and concepts. This section attempts to provide a very useful short-list of design considerations for the experimentalist so that Eq. (2) can be solved. 

Designed Experiments Produce More Precise Models. In the context of linear regression, this is demonstrated by examining the statistical uncertainties of the regression coefficients. Equation 2.1 is the regression model where the response for the th sample (r ) of an instrument is shown as a linear function of the sample concentration (c.) with measurement error... 

There are two main sources of error propagation in static measurements, errors due to successive dilutions and errors due to initial instrument offset. Other errors which are also applicable to SEC analysis are discussed in (J ). These errors can be propagated using the criteria presented here. If w is the intial mass of polymer and Vj is the amount of solvent added to obtain the desired concentration Ci, the dilution process can be represented by the following set of equations ... 

The main objectives in calibrating the SEC detection system in absolute refractive index and absorption units are the estimation of v and E at the normal flow conditions and the standardization of the measurement errors. The first step in the calibration process is the estimation of the instrument s constants to transform the computer units into absorbances and refractive index units. The Waters AAO UV spectrophotometer displays absorbance units. Therefore, step changes in the instrument s balance and sampling of the signal provide the necessary data for the calibration. The equations obtained are ... 

The more the precision of the instrument, and the more the points for the time unit in the acquired profile, the better the result of the fitting of experimental data. For this reason instruments with a low measure error and connectable to a computer for the automatic and continous aquisition of data are very much prefered. The UV-Vis spectrophotometer is by far the most used instrument in chemical kinetics. It has a good sensitivity and a good control of the temperature. It is connected or easily connectable to a computer and is available nearly everywhere. The absorbance has a very low dependence on the temperature so that, in the used temperature range, its variation can be neglected during the VTK experiments. 

In chemistry, as in many other sciences, statistical methods are unavoidable. Whether it is a calibration curve or the result of a single analysis, interpretation can only be ascertained if the margin of error is known. This section deals with fundamental principles of statistics and describes the treatment of errors involved in commonly used tests in chemistry. When a measurement is repeated, a statistical analysis is compulsory. However, sampling laws and hypothesis tests must be mastered to avoid meaningless conclusions and to ensure the design of meaningful quality assurance tests. Systematic errors (instrumental, user-based, etc.) and gross errors that lead to out-of-limit results will not be considered here. 

---