Calibration systematic/random error

The confidence limits of a measurement are the limits between which the measurement error is with a probability P. The probability P is the confidence level and a = 1 - P is the risk level related to the confidence limits. The confidence level is chosen according to the application. A normal value in ventilation would be P = 95%, which means that there is a risk of a = 5 /o for the measurement error to be larger than the confidence limits. In applications such as nuclear power plants, where security is of prime importance, the risk level selected should be much lower. The confidence limits contain the random errors plus the re.sidual of the systematic error after calibration, but not the actual systematic errors, which are assumed to have been eliminated. 

The ultimate goal of multivariate calibration is the indirect determination of a property of interest (y) by measuring predictor variables (X) only. Therefore, an adequate description of the calibration data is not sufficient the model should be generalizable to future observations. The optimum extent to which this is possible has to be assessed carefully when the calibration model chosen is too simple (underfitting) systematic errors are introduced, when it is too complex (oveifitting) large random errors may result (c/. Section 10.3.4). 

We chose the number of PCs in the PCR calibration model rather casually. It is, however, one of the most consequential decisions to be made during modelling. One should take great care not to overfit, i.e. using too many PCs. When all PCs are used one can fit exactly all measured X-contents in the calibration set. Perfect as it may look, it is disastrous for future prediction. All random errors in the calibration set and all interfering phenomena have been described exactly for the calibration set and have become part of the predictive model. However, all one needs is a description of the systematic variation in the calibration data, not the... 

The pipette has a stated volume of 25 ml. However, due to the manufacturing process the actual volume of liquid from a particular pipette filled to the calibration mark (ignoring any random errors) is found to be 25.02 ml. This is within the permitted tolerance for a 25 ml Class A pipette ( 0.03 ml according to BS 1583 1986 [6]). This is a systematic error, as the volume of liquid delivered from the pipette will always be 0.02 ml greater than the stated volume each time the... 

Measurements can contain any of several types of errors (1) small random errors, (2) systematic biases and drift, or (3) gross errors. Small random errors are zero-mean and are often assumed to be normally distributed (Gaussian). Systematic biases occur when measurement devices provide consistently erroneous values, either high or low. In this case, the expected value of e is not zero. Bias may arise from sources such as incorrect calibration of the measurement device, sensor degradation, damage to the electronics, and so on. The third type of measurement... 

Because measurements always contain some type of error, it is necessary to correct their values to know objectively the operating state of the process. Two types of errors can be identified in plant data random and systematic errors. Random errors are small errors due to the normal fluctuation of the process or to the random variation inherent in instrument operation. Systematic errors are larger errors due to incorrect calibration or malfunction of the instruments, process leaks, etc. The systematic errors, also called gross errors, occur occasionally, that is, their number is small when compared to the total number of instruments in a chemical plant. 

Define Quality Control, Quality Assurance, sample, analyte, validation study, accuracy, precision, bias, calibration, calibration curve, systematic error, determinate error, random error, indeterminate error, and outlier. 

There are three types of data error random error in the reference laboratory values, random error in the optical data, and systematic error in the relationship between the two. The proper approach to data error depends on whether the affected variables are reference values or spectroscopic data. Calibrations are usually performed empirically and are problem specific. In this situation, the question of data error becomes an important issue. However, it is difficult to decide if the spectroscopic error is greater than the reference laboratory method error, or vice versa. The noise of current NIR instrumentation is usually lower than almost anything else in the calibration. The total error of spectroscopic data includes... 

This variation in ionisation can spontaneously occur when the matrix naturally contains one or more alkaline elements. To avoid these random errors, a buffer of potassium or sodium salt is systematically added to the solutions. An alternative is to construct a calibration curve using a matrix that is very close to that of the analyte. 

A 25-mL Class A volumetric pipet is certified by the manufacturer to deliver 25.00 0.03 mL. The volume delivered by a given pipet is reproducible, but can be anywhere in the range 24.97 to 25.03 mL. The difference between 25.00 mL and the actual volume delivered by a particular pipet is a systematic error. It is always the same, within a small random error. You could calibrate a pipet by weighing the water it delivers, as in Section 2-9. 

Calibration eliminates systematic error, because we would know that the pipet always delivers, say, 25.991 0.006 mL. The remaining uncertainty ( 0.006 mL) is random error. 

This discussion deals with random errors and their propagation in reported HO concentrations. Equal attention should be given, of course, to systematic errors of calibration or instrument drift. 

Calibration of FAGE1 from a static reactor (a Teflon film bag that collapses as sample is withdrawn) has been reported (78). In static decay, HO reacts with a tracer T that has a loss that can be measured by an independent technique T necessarily has no sinks other than HO reaction (see Table I) and no sources within the reactor. From equation 17, the instantaneous HO concentration is calculated from the instantaneous slope of a plot of ln[T] versus time. The presence of other reagents may be necessary to ensure sufficient HO however, the mechanisms by which HO is generated and lost are of no concern, because the loss of the tracer by reaction with whatever HO is present is what is observed. Turbulent transport must keep the reactor s contents well mixed so that the analytically measured HO concentration is representative of the volume-averaged HO concentration reflected by the tracer consumption. If the HO concentration is constant, the random error in [HO] calculated from the tracer decay slope can be obtained from the slope uncertainty of a least squares fit. Systematic error would arise from uncertainties in the rate constant for the T + HO reaction, but several tracers may be employed concurrently. In general, HO may be nonconstant in the reactor, so its concentration variation must be separated from noise associated with the [T] measurement, which must therefore be determined separately. 

Thus, if the instrument output records a reading of G = 5.50kg/min then the estimate of the true value of the rate of flow will be the corresponding value of GT 2confidence limits. The total error obtained in the calibration may be split into two parts, viz. the bias (or systematic error), i.e. 5.50 - 5.68 = - and the error due to imprecision (random error or... 

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). 

All experimental measurements are affected by errors. In general, experimental errors are made out of systematic errors and random errors. Systematic errors show a dependence on the operating conditions and may be caused, e.g., by calibration errors of sensors. Since these errors are absent in a well-performed experimental campaign and can be corrected by an improved experimental practice, they are not considered any more in this context. 

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. 

The accuracy of a measurement refers to how close it is to the true value. An inaccurate result occurs as a result of some flaw (systematic error) in the measurement the presence of an interfering substance, incorrect calibration of an instrument, operator error, and so on. The goal of chemical analysis is to eliminate systematic error, but random errors can only be minimized. In practice, an experiment is almost always done in order to find an unknown value (the true value is not known—someone is trying to obtain that value by doing the experiment). In this case the precision of several replicate determinations is used to assess the accuracy of the result. The results of the replicate experiments are expressed as an average (which we assume is close to the true value) with an error limit that gives some indication of how close the average value may be to the true value. The error limit represents the uncertainty of the experimental result. 

Hyphenated multidimensional analytical instrumentation requires careful calibration and maintenance to obtain high quality, meaningful data (J9). Because of the propagation of systematic and random errors as different analytical instrumentation are interfaced, frequent calibration using well-characterized polymer standards is required even for absolute M -sensitive detectors. Eurthermore, the relatively low signal-to-noise ratio at the ends of the MWD can lead to significant uncertainties in these regions of the distribution unfortunately, these areas of the distribution can profoundly affect polymer properties. 

Error thus arises from two sources. Lack of precision (random errors) can be estimated by a statistical analysis of a series of measurements. Lack of accuracy (systematic errors) is much more problematic. If a systematic error is known to be present, we should do our best to correct for it before reporting the result. (For example, if our apparatus has not been calibrated correctly, it should be recalibrated.) The problem is that systematic errors of which we have no knowledge may be present. In this case the experiment should be repeated with different apparatus to eliminate the systematic error caused by a particular piece of equipment better still, a different and independent way to measure the property might be devised. Only after enough independent experimental data are available can we be convinced of the accuracy of a result— that is, how closely it approximates the true result. 

Linearity is tested by examination of a plot produced by linear regression of responses in a calibration set. Unless there are serious errors in preparation of calibration standards, calibration errors are usually a minor component of the total uncertainty. Random errors resulting from calculation are part of run bias which is considered as a whole systematic errors usually from laboratory bias are also considered as a whole. There are some characteristics of a calibration that are useful to know at the outset of method validation... 

In order to provide a means for the precise recalculation of nitrogen chemical shifts reported since 1972, it is necessary to have accurate values of the differences in the screening constants between neat CH3N02 and the large number of reference compounds which have so far been used. Table VII shows the results of precise, 4N measurements (61) which have been carried out in concentric spherical sample and reference containers in order to eliminate bulk susceptibility effects on the shifts. Since the technique adopted (61, 63) involves the accumulation of a large number of individually calibrated spectra with the subsequent use of a full-lineshape analysis by the differential saturation method, (63) the resulting random errors comprise those from minor temperature variations, phase drifts, frequency instability, sweep nonlinearity, etc. so that systematic errors should be insignificant as compared with random errors. 

The underlying assumption in statistical analysis is that the experimental error is not merely repeated in each measurement, otherwise there would be no gain in multiple observations. For example, when the pure chemical we use as a standard is contaminated (say, with water of crystallization), so that its purity is less than 100%, no amount of chemical calibration with that standard will show the existence of such a bias, even though all conclusions drawn from the measurements will contain consequent, determinate or systematic errors. Systematic errors act uni-directionally, so that their effects do not average out no matter how many repeat measurements are made. Statistics does not deal with systematic errors, but only with their counterparts, indeterminate or random errors. This important limitation of what statistics does, and what it does not, is often overlooked, but should be kept in mind. Unfortunately, the sum-total of all systematic errors is often larger than that of the random ones, in which case statistical error estimates can be very misleading if misinterpreted in terms of the presumed reliability of the answer. The insurance companies know it well, and use exclusion clauses for, say, preexisting illnesses, for war, or for unspecified acts of God , all of which act uni-directionally to increase the covered risk. 

Quantitative analytical measurements are always subject to some degree of error. No matter how much care is taken, or how stringent the precautions followed to minimize the effects of gross errors from sample contamination or systematic errors from poor instrument calibration, random errors will always... 

Precision (how close values are to each other) and accuracy (how close values are to the actual value) are two aspects of certainty. Systematic errors result in values that are either all higher or all lower than the actual value. Random errors result in some values that are higher and some values that are lower than the actual value. Precise measurements have low random error accurate measurements have low systematic error and often low random error. The size of random errors depends on the skill of the measurer and the precision of the instrument. A systematic error, however, is often caused by faulty equipment and can be compensated for by calibration. 

It can be assumed that with the development and study of new methods, the ability to determine M (S), the method bias component of uncertainty, cannot be done given that it can be evaluated only relative to a true measure of analyte concentration. This can be achieved by analysis of a certified reference material, which is usually uncommon, or by comparison to a well-characterized/accepted method, which is unlikely to exist for veterinary drug residues of recent interest. Given that method bias is typically corrected using matrix-matched calibration standards, internal standard or recovery spikes, it is considered that the use of these approaches provides correction for the systematic component of method bias. The random error would be considered part of the interlaboratory derived components of uncertainty. 

Eq. (4) also can be used as a basis for discussion of both systematic and random errors involved in flowrate measurements using these provers. Systematic errors may be considered as characteristics of instruments ordinarily used for measurement PiAV(./At. Calibration and reading errors of the instruments, not their dynamic response errors, are summarized below ... 

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