Single measurements

This method of displaying the data makes it most comfortable for the tester to evaluate large numbers of single measurements ( shots ) at a glance. 

A similar decision-making problem consists of very many measurements of var iable a on a large sample from population A, followed by a single measurement of the same property a of an individual. The single measurement will not be... 

The normal distribution of measurements (or the normal law of error) is the fundamental starting point for analysis of data. When a large number of measurements are made, the individual measurements are not all identical and equal to the accepted value /x, which is the mean of an infinite population or universe of data, but are scattered about /x, owing to random error. If the magnitude of any single measurement is the abscissa and the relative frequencies (i.e., the probability) of occurrence of different-sized measurements are the ordinate, the smooth curve drawn through the points (Fig. 2.10) is the normal or Gaussian distribution curve (also the error curve or probability curve). The term error curve arises when one considers the distribution of errors (x — /x) about the true value. 

Example 5 The true value of a quantity is 30.00, and cr for the method of measurement is 0.30. What is the probability that a single measurement will have a deviation from the mean greater than 0.45 that is, what percentage of results will fall outside the range 30.00 0.45 ... 

Analytical chemists make a distinction between error and uncertainty Error is the difference between a single measurement or result and its true value. In other words, error is a measure of bias. As discussed earlier, error can be divided into determinate and indeterminate sources. Although we can correct for determinate error, the indeterminate portion of the error remains. Statistical significance testing, which is discussed later in this chapter, provides a way to determine whether a bias resulting from determinate error might be present. 

The one-point fixed-time integral method has the advantage of simplicity since only a single measurement is needed to determine the analyte s initial concentration. As with any method relying on a single determination, however, a... 

Control charts were originally developed in the 1920s as a quality assurance tool for the control of manufactured products.Two types of control charts are commonly used in quality assurance a property control chart in which results for single measurements, or the means for several replicate measurements, are plotted sequentially and a precision control chart in which ranges or standard deviations are plotted sequentially. In either case, the control chart consists of a line representing the mean value for the measured property or the precision, and two or more boundary lines whose positions are determined by the precision of the measurement process. The position of the data points about the boundary lines determines whether the system is in statistical control. 

The nature of the opening between cells determines how readily different gases and Hquids can pass from one cell to another. Because of variation in flow of different Hquids or gases through the cell-wall openings, a single measurement of fraction open cells does not fully characterize this stmctural variable, especially in a dynamic situation. 

The objective ia any analytical procedure is to determine the composition of the sample (speciation) and the amounts of different species present (quantification). Spectroscopic techniques can both identify and quantify ia a single measurement. A wide range of compounds can be detected with high specificity, even ia multicomponent mixtures. Many spectroscopic methods are noninvasive, involving no sample collection, pretreatment, or contamination (see Nondestructive evaluation). Because only optical access to the sample is needed, instmments can be remotely situated for environmental and process monitoring (see Analytical METHODS Process control). Spectroscopy provides rapid real-time results, and is easily adaptable to continuous long-term monitoring. Spectra also carry information on sample conditions such as temperature and pressure. 

In principle, the two-angle interval method can produce all CBC parameters within a single measurement channel, uniquely providing ceU-by-ceU hemoglobin concentration. The mean of the concentrations provides an alternative (and direct) measurement of MCHC. The method also provides an alternative HGB measurement, because HGB may be set equal to (RBC x MCV x MCHC)/1000. This method, like the basic light-scattering method, uses the same flow cell to measure platelets and ted cells with the result that the method is capable of providing the CBC parameters RBC, HGB, HCT, MCV, MCHC, MCH, and PLT. The method can also count a sample s white blood cells if the sample s red blood cells have been lysed. 

The mass transport influence is easy to diagnose experimentally. One measures the rate at various values of the Thiele modulus the modulus is easily changed by variation of R, the particle size. Cmshing and sieving the particles provide catalyst samples for the experiments. If the rate is independent of the particle size, the effectiveness factor is unity for all of them. If the rate is inversely proportional to particle size, the effectiveness factor is less than unity and

experimental points allow triangulation on the curve of Figure 10 and estimation of Tj and ( ). It is also possible to estimate the effective diffusion coefficient and thereby to estimate Tj and ( ) from a single measurement of the rate (48). 

There are many techniques available for measuring the particle-size distribution of powders. The wide size range covered, from nanometers to millimeters, cannot be analyzed using a single measurement principle. Added to this are the usual constraints of capital costs versus running costs, speed of operation, degree of skill required, and, most important, the end-use requirement. 

Equation (1) can be viewed in an over-simplistic manner and it might be assumed that it would be relatively easy to calculate the retention volume of a solute from the distribution coefficient, which, in turn, could be calculated from a knowledge of the standard enthalpy and standard entropy of distribution. Unfortunately, these properties of a distribution system are bulk properties. They represent, in a single measurement, the net effect of a large number of different types of molecular interactions which, individually, are almost impossible to separately identify and assess quantitatively. 

The bias error is a quantity that gives the total systematic error of a measuring instrument under defined conditions. As mentioned earlier, the bias should be minimized by calibration. The repeatability error consists of the confidence limits of a single measurement under certain conditions. The mac-curacy or error of indication is the total error of the instrument, including the... 

The situation is perhaps not quite so bad as is implied here, since single measurements of a, are usually made at the sodium D line, 589.6 nm. Nevertheless, it is clearly better to state the wavelength than to assume that this will be understood. 

Capital investments can also be selected on the basis of other measures of performance such as return on investment, internal rate of return, and benefit-cost ratio (or savings-to-investment ratio). Flowever, care must be taken in the application of these methods, as an incremental analysis is required to ensure consistent comparison of mutually exclusive alternatives. Also, rather than requiring a separate value to be calculated for each alternative, as in the case of the life-cycle cost method, these other methods incorporate the difference between two mutually exclusive alternatives within a single measure. For example, the net benefits measure directly pressures the degree to which one alternative is more economically desirable than another. 

The Fisher information Ip in a single measurement of a physical system is given by... 

This procedure of using a single measurement of electrode potential to determine the concentration of an ionic species in solution is referred to as direct potentiometry. The electrode whose potential is dependent upon the concentration of the ion to be determined is termed the indicator electrode, and when, as in the case above, the ion to be determined is directly involved in the electrode reaction, we are said to be dealing with an electrode of the first kind . 

Mendeleev s genius lay in recognizing that just as It was the element in the abstract sense that survived intact in the course of compound formation, so atomic weight was the only quantity that survived in measurable amounts. He therefore took the step of associating these two features an element was to be characterized by its atomic weight. In a sense an abstract element had acquired a single measurable attribute that would remain unchanged... 

Normally, the impedance plots are fitted to an often-complex equivalent circuit. Mathematically, this means searching for a global solution in R". However, problems arise if a complicated equivalent circuit is found which does not allow physical interpretation. Therefore, it is preferable to run a wide variety of experiments with different samples rather than trying to fit in detail the results of a single measurement in order to analyze the resulting impedance plots. 

It is well to remember that the equations of this section deal with cases that differ fundamentally from that of Equation 10-3. This equation deals with the different errors in the result of a single measurement (that is, N or x), and the others are combinations of standard counting errors of different quantities that go to make up a complex datum that usually cannot be obtained in a single measurement. 

The problem we face is that we have to estimate a wavefront, which has an infinite number of degrees of freedom, from a finite number of measurements. At first this may seem impossible, but in reality an infinite range of possible solutions describes most practical situations, not just wavefront sensing. The key to solving the problem is that we need to make an assumption about the relative likelihood of the solutions. As an example of how this is done, consider a wavefront sensor which makes a single measurement that is sensitive to only two basis functions. 

Finally, we return to our example of a two mode turbulence, tilt and coma, with a single measurement of the centroid displacement, d. We assume, for simplicity, that there is no noise on the measurements, hence = 0. If we as-... 

Example 58 Fig. 4.33 explains the theoretical basis and Fig. 4.34 depicts increasingly sophisticated ways of reducing the risk of having a single measurement beyond the specification limit. Between two and 10 measurements are performed and the mean is calculated in order to decide whether a product that is subject to the specifieation limits ( 95. .. 105% of nominal) can or cannot be released. A normal distribution ND(/x = variable, = 1.00) is assumed the case x ,ean = 105 is explained the same arguments apply for Xmean = 95, of course. Tables 4.30-4.32 give the key figures. 

Table 4.31. The Maximal OOS-Risk [%] This Implies for any Single Measurement as Created by the Assumptions in Table 4.30...

Figures 4 and 5 give a broad indication of the relevant biomechanical properties of a number of flow sensitive biomaterials. In the case of the data shown in Fig. 5, the surface mechanical properties are lumped into a single measure of the surface integrity. Admittedly, in view of what has been said in the introduction about the viscoelastic nature of the wall material, the information given in Figs. 4 and 5 are oversimplistic. The data in Fig. 5 are based on reported critical minimum stresses (often expressed in terms of the mean bulk fluid stresses) at which physical damage is first observed. Figure 6 gives an indication of the...

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