Systematic measurement error

In contrast, a systematic error remains constant or varies in a predictable way over a series of measurements. This type of error differs from random error in that it cannot be reduced by making multiple measurements. Systematic error can be corrected for if it is detected, but the correction would not be exact since there would inevitably be some uncertainty about the exact value of the systematic error. As an example, in analytical chemistry we very often run a blank determination to assess the contribution of the reagents to the measured response, in the known absence of the analyte. The value of this blank measurement is subtracted from the values of the sample and standard measurements before the final result is calculated. If we did not subtract the blank reading (assuming it to be non-zero) from our measurements, then this would introduce a systematic error into our final result. 

The outcome of the different exercises should be discussed among all participants in technical meetings, in particular to identify random and/or systematic errors in the procedures. Whereas random errors can be detected and minimised by intralaboratory measures, systematic errors can only be identified and eliminated by comparing results with other laboratories/techniques. When all steps have been successfully evaluated, i.e. all possible sources of systematic errors have been removed and the random errors have been minimised, the methods can be considered as valid. This does not imply that the technique(s) can directly be used routinely and further work is likely to be needed to test the robustness and ruggedness of the method before being used by technicians for daily routine measurements . 

Unfortunately, the 1 /factor ultimately overwhelms the patience of the experimenter. Suppose a single measurement (for example, determination of the endpoint of a titration) takes ten minutes. The average of four measurements is expected to be twice as accurate, and would only take thirty extra minutes. The next factor of two improvement (to four times the original accuracy) requires a total of 16 measurements, or another 120 minutes of work the next factor of two requires an additional 480 minutes of work. In addition, this improvement only works for random errors, which are as likely to be positive as negative and are expected to be different on each measurement. Systematic errors (such as using an incorrectly calibrated burette to measure a volume) are not improved by averaging. Even if you do the same measurement many times, the error will always have the same sign, so no cancellation occurs. 

Accuracy and precision are the most important characteristics of an analytical method they give the best indication of random and systematic error associated with the analytical measurement. Systematic error refers to the deviation of an analytical result from the true value, and therefore affects the accuracy of a method. One the other hand, random errors influence the precision of a method (Kallner et al., 1999). Ideally, accuracy and precision should be assessed at multiple concentrations within the linear range of the assay (low, medium and high concentration). 

Random errors are observed by scatter in the data and can be dealt with effectively by taking the average of many measurements. Systematic errors, conversely, are the bane of the experimental scientist. They are not readily apparent and must be avoided by carefully calibrating a method against a known sample or result. Systematic errors influence the accuracy of a measurement, whereas random errors are linked to the precision of measurements. 

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

There are two types of measurement errors, systematic and random. The former are due to an inherent bias in the measurement procedure, resulting in a consistent deviation of the experimental measurement from its true value. An experimenter s skill and experience provide the only means of consistently detecting and avoiding systematic errors. By contrast, random or statistical errors are assumed to result from a large number of small disturbances. Such errors tend to have simple distributions subject to statistical characterization. 

In the maximum-likelihood method used here, the "true" value of each measured variable is also found in the course of parameter estimation. The differences between these "true" values and the corresponding experimentally measured values are the residuals (also called deviations). When there are many data points, the residuals can be analyzed by standard statistical methods (Draper and Smith, 1966). If, however, there are only a few data points, examination of the residuals for trends, when plotted versus other system variables, may provide valuable information. Often these plots can indicate at a glance excessive experimental error, systematic error, or "lack of fit." Data points which are obviously bad can also be readily detected. If the model is suitable and if there are no systematic errors, such a plot shows the residuals randomly distributed with zero means. This behavior is shown in Figure 3 for the ethyl-acetate-n-propanol data of Murti and Van Winkle (1958), fitted with the van Laar equation. 

If there is sufficient flexibility in the choice of model and if the number of parameters is large, it is possible to fit data to within the experimental uncertainties of the measurements. If such a fit is not obtained, there is either a shortcoming of the model, greater random measurement errors than expected, or some systematic error in the measurements. 

An apparent systematic error may be due to an erroneous value of one or both of the pure-component vapor pressures as discussed by several authors (Van Ness et al., 1973 Fabries and Renon, 1975 Abbott and Van Ness, 1977). In some cases, highly inaccurate estimates of binary parameters may occur. Fabries and Renon recommend that when no pure-component vapor-pressure data are given, or if the given values appear to be of doubtful validity, then the unknown vapor pressure should be included as one of the adjustable parameters. If, after making these corrections, the residuals again display a nonrandom pattern, then it is likely that there is systematic error present in the measurements. ... 

Any systematic error that causes a measurement or result to always be too high or too small can be traced to an identifiable source. 

If this error was found to be consistent throughout several series of measurements, there would be good reason to correct" all subsequent determinations by a factor of 100.9/100 = 1.009, viz., the method involves systematic errors. 

Because experimental measurements are subject to systematic error, sets of values of In y and In yg determined by experiment may not satisfy, that is, may not be consistent with, the Gibbs/Duhem equation. Thus, Eq. (4-289) applied to sets of experimental values becomes a test of the thermodynamic consistency of the data, rather than a valid general relationship. 

The measurements are also subjec t to systematic errors ranging from sensor position, sampling methods, and instrument degradation... 

These measurements with their inherent errors are the bases for numerous fault detection, control, and operating and design decisions. The random and systematic errors corrupt the decisions, amplifying their uncertainty and, in some cases, resulting in substantially wrong decisions. 

The primary assumption in reconciliation is that the measurements are subject only to random errors. This is rarely the case. Misplaced sensors, poor sampling methodology, miscalibrations, and the like add systematic error to the measurements. If the systematic errors in the... 

Rectification accounts for systematic measurement error. During rectification, measurements that are systematically in error are identified and discarded. Rectification can be done either cyclically or simultaneously with reconciliation, and either intuitively or algorithmically. Simple methods such as data validation and complicated methods using various statistical tests can be used to identify the presence of large systematic (gross) errors in the measurements. Coupled with successive elimination and addition, the measurements with the errors can be identified and discarded. No method is completely reliable. Plant-performance analysts must recognize that rectification is approximate, at best. Frequently, systematic errors go unnoticed, and some bias is likely in the adjusted measurements. 

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. 

Systematic Operating Errors Fifth, systematic operating errors may be unknown at the time of measurements. Wriile not intended as part of daily operations, leaky or open valves frequently result in bypasses, leaks, and alternative feeds that will add hidden bias. Consequently, constraints assumed to hold and used to reconcile the data, identify systematic errors, estimate parameters, and build models are in error. The constraint bias propagates to the resultant models. 

An example adapted from Verneuil, et al. (Verneuil, V.S., P. Yan, and F. Madron, Banish Bad Plant Data, Chemical Engineeiing Progress, October 1992, 45-51) shows the impact of flow measurement error on misinterpretation of the unit operation. The success in interpreting and ultimately improving unit performance depends upon the uncertainty in the measurements. In Fig. 30-14, the materi balance constraint would indicate that S3 = —7, which is unrealistic. However, accounting for the uncertainties in both Si and S9 shows that the value for S3 is —7 28. Without considering uncertainties in the measurements, analysts might conclude that the flows or model contain bias (systematic) error. 

Model Development PreHminary modeling of the unit should be done during the familiarization stage. Interactions between database uncertainties and parameter estimates and between measurement errors and parameter estimates coiJd lead to erroneous parameter estimates. Attempting to develop parameter estimates when the model is systematically in error will lead to systematic error in the parameter estimates. Systematic errors in models arise from not properly accounting for the fundamentals and for the equipment boundaries. Consequently, the resultant model does not properly represent the unit and is unusable for design, control, and optimization. Cropley (1987) describes the erroneous parameter estimates obtained from a reactor study when the fundamental mechanism was not properly described within the model. 

Validation versus Rectification The goal of both rectification and validation is the detecI ion and identification of measurements that contain systematic error. Rectification is typically done simultaneously with reconciliation using the reconciliation resiilts to identify measurements that potentially contain systematic error. Vahdation typically rehes only on other measurements and operating information. Consequently, vahdation is preferred when measurements and their supporting information are hmited. Further, prior screening of measurements limits the possibihty that the systematic errors will go undetected in the rectification step and subsequently be incorporated into any conclusions drawn during the interpretation step. 

Single-Module Analysis Consider the single-module unit shown in Fig. 30-10. If the measurements were complete, they would consist of compositions, flows, temperatures, and pressures. These would contain significant random and systematic errors. Consequently, as collected, they do not close the constraints of the unit being studied. The measurements are only estimates of the actual plant operation. If the actual operation were known, the analyst could prepare a scatter diagram comparing the measurements to the actual values, which is a useful analysis tool Figure 30-19 is an example. 

If the measurements were completely accurate and precise (i.e., they contained neither random nor systematic error), all of the symbols representing the individual measurements woiild fall on the zero deviation line. Since the data do contain error, the measurements should fall within 2 on this type of diagram. This example scatter diagram shows that some of the measurements do not compare well to the ac tual values. 

This test code specifies procedures for evaiuation of uncertainties in individuai test measurements, arising from both random errors and systematic errors, and for the propagation of random and systematic uncertainties... 

SEXAFS can be measured from adsorbate concentrations as low as "0.05 mono-layers in favorable circumstances, although the detection limits for routine use are several times higher. By using appropriate standards, bond lengths can be determined as precisely as 0.01 A in some cases. Systematic errors often make the accu-... 

The means and habit of making highly precise measurements, with careful attention to the identification of sources of random and systematic error, were well established by the period I am discussing. According to a recent historical essay by... 

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