Systematic component

The error of an analytical result is related to the (in)accuracy of an analytical method and consists of a systematic component and a random component [14]. Precision and bias studies form the basis for evaluation of the accuracy of an analytical method [18]. The accuracy of results only relates to the fitness for purpose of an analytical system assessed by method validation. Reliability of results however has to do with more than method validation alone. MU is more than just a singlefigure expression of accuracy. It covers all sources of errors which are relevant for all analyte concentration levels. MU is a key indicator of both fitness for purpose and reliability of results, binding together the ideas of fitness for purpose and quality control (QC) and thus covering the whole QA system [4,37]. 

Overall uncertainty can be estimated by identifying all factors which contribute to the uncertainty. Their contributions are estimated as standard deviations, either from repeated observations (for random components), or from other sources of information (for systematic components). The combined standard uncertainty is calculated by combining the variances of the uncertainty components, and is expressed as a standard deviation. The combined standard uncertainty is multiplied by a coverage factor of 2 to give a 95% level of confidence (approximately). 

The bias of a measurement result is defined as a consistent difference between the measured value and the true value. In mathematical terms it is the systematic component of measurement error. 

A many number of modelling and simulation systems have been developed to aid in process and product engineering. In this paper the knowledge based process plant simulation model was developed. On the model development side, the issues of knowledge representation in the form of systematic component composition, ontology, and interconnections were illustrated. As a case study a plant for starch sweet syrup production was used. The system approach permits the evaluation of feasibility and global plant integration, and a predicted behavior of the reaction systems. The obtained results of the this paper have shown the variety quality of syrups simulation for different products. 

The apparent lack of systematic component in the time series displayed here reflects only a relatively short-time behavior. For time exceeding another characteristic time, 72, typically ofthe order 1 h forthis problem, we observe what appears to be a systematic trend as seen in Fig. 7.2. 

In defining a mathematical model it is helpful to distinguish between the various components of the model. Models are built using experimentally derived data. This so-called data generating process is dependent on system inputs, system dynamics, and the device used to measure the output from a system (Fig. 1.1). But in addition to these systematic processes are the sources of error that confound our measurements. These errors may be measurement errors but also include process noise that is part of the system. One goal of mathematical modeling is to differentiate the information or systematic component in the system from the noise or random components in the system, i.e.,... 

Hence, models usually consist of a structural model or systematic component plus a statistical model that describes the error component of the model. Early in the modeling process the focus may lie with the systematic component and then move to a more holistic approach involving the error components. For example, the 1-compartment model after bolus administration is... 

The covariance matrices of the estimate errors a also have random and systematic components ... 

Multi-way PCA is statistically and algorithmically consistent with PCA (Wise et al. 1999 Westerhuis et al. 1999). Thus, it decomposes the initial matrix X in the summation of the product of scores vectors (t) and loading matrices (P), plus a residual matrix (. These residuals are minimized by least squares, and are considered to be associated to the non-deterministic part of the information. The systematic component of the information, expressed by the product (t x P), represents... 

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. 

A close look at Equation 48 leads to the following conclusion concerning the effect of uncorrected linear drift. The estimated ACF contains two systematic components, each proportional to a and b respectively, and two stochastic components, proportional to a and b. A final conclusion can be derived from the formulae a considerable error in the estimation of the ACF and derived quantities can be expected if baseline drift is not corrected. This leads us to the remaining question, the determination of the integration variance after baseline drift correction. 

With three or more groups of observations to compare, it is incorrect to compare each pair of groups with a two-sample r-test. Instead, a one-way analysis of variance (ANOVA) should be carried out. The ANOVA technique can be generalized to deal with observations from many other types of experimental design. In each case, the analysis separates out the variation due to specified components of variation (e.g. the differences between group means in a one-way ANOVA) and the variation due to the residual or error terms. The former components of variation are then compared with the latter component to see if the systematic components are too large to have arisen by chance. 

In quantitative forecasting, we assume that the time series data exhibit a systematic component, superimposed by a random component (noise). The systematic component may include the following ... 

Evaluate the overall inter-laboratory variation, and its random and systematic components. 

Within the Central Electricity Generating Board (CEGB), the "double contingency" principle is adopted in considering criticality in the CAGR fuel routes. Thus, at least two Independent low-probability events must occur before criticality can be reached. For clearances based on calculations a criterion is adopted that if one such event takes place, the cMculated Keff plus an appropriate allowance for uncertainties should be <0.95. This uncertainty allowance includes a systematic component and a random component, statistics plus data, etc., taken at the three standard deviation levels. Two computer codes are employed, the lattice code WIMS (Ref. 1) for survey work and the Monte Carlo cbcle MONK (Ref. 2) for... 

Systematic Component of Uncertainty. Laboratory detectors were calibrated using a geometry standard comprising a sample pot filled with dry soil, spiked with a certified mixed nuclide gamma standard. Systematic imcertainty (bias) of the means of the in situ measurements can be estimated by comparing these with the means of the ex situ measurements. 

Observed demand (0) = systematic component (5) -l- random component R)... 

The systematic component measures the expected value of demand and consists of what we will call level, the current deseasonalized demand trend, the rate of growth or decline in demand for the next period and seasonality, the predictable seasonal fluctuations in demand. 

The goal of any forecasting method is to predict the systanatic component of danand and estimate the random component. In its most general form, the systematic component of demand data contains a level, a trend, and a seasonal factor. The equation for calculating the systematic component may take a variety of forms ... 

Multiplicative Systematic component = level X trend X seasonal factor... 

The specific form of the systematic component applicable to a given forecast depends on the nature of demand. Companies may develop both static and adaptive forecasting methods for each form. We now describe these static and adaptive forecasting methods. 

A static method assumes that the estimates of level, trend, and seasonality within the systematic component do not vary as new demand is observed. In this case, we estimate each of these parameters based on historical data and then use the same values for aU future forecasts. In this section, we discuss a static forecasting method for use when demand has a trend as well as a seasonal component. We assume that the systematic component of demand is mixed that is. 

In adaptive forecasting, the estimates of level, trend, and seasonality are updated after each demand observation. The main advantage of adaptive forecasting is that estimates incorporate all new data that are observed. We now discuss a basic framework and several methods that can be used for this type of forecast. The framework is provided in the most general setting, when the systematic component of demand data has the mixed form and contains a level, a trend, and a seasonal factor. It can easily be modified for the other two cases, however. The framework can also be specialized for the case in which the systanatic component contains no seasonality or trend. We assume that we have a set of historical data for n periods and that demand is seasonal, with periodicity p. Given quarterly data, wherein the pattern repeats itself every year, we have a periodicity of p = 4. 

We now discuss various adaptive forecasting methods. The method that is most appropriate depends on the characteristic of demand and the composition of the systematic component of demand. In each case, we assume the period under consideration to be t. 

TREND-CORRECTED EXPONENTIAL SMOOTHING (HOLT S MODEL) The trend-corrected exponential smoothing (Holt s model) method is appropriate when demand is assumed to have a level and a trend in the systematic component, but no seasonality. In this case, we have... 

As mentioned earlier, every instance of demand has a random component. A good forecasting method should capture the systematic component of demand but not the random component. The random component manifests itself in the form of a forecast error. Forecast errors contain valuable information and must be analyzed carefully for two reasons ... 

Managers use error analysis to determine whether the current forecasting method is predicting the systematic component of demand accurately. For example, if a forecasting method consistently produces a positive error, the forecasting method is overestimating the systematic component and should be corrected. 

Demand in this case clearly has both a trend and seasonality in the systematic component. Thus, the team initially expects Winter s model to produce the best forecast. 

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