Distribution curves/index

The variability or spread of the data does not always take the form of the true Normal distribution of course. There can be skewness in the shape of the distribution curve, this means the distribution is not symmetrical, leading to the distribution appearing lopsided . However, the approach is adequate for distributions which are fairly symmetrical about the tolerance limits. But what about when the distribution mean is not symmetrical about the tolerance limits A second index, Cp, is used to accommodate this shift or drift in the process. It has been estimated that over a very large number of lots produced, the mean could expect to drift about 1.5cr (standard deviations) from the target value or the centre of the tolerance limits and is caused by some problem in the process, for example tooling settings have been altered or a new supplier for the material being processed. 

The ratio Mw/ Mn must by definition be greater than unity for a polydisperse polymer and is known as the polydispersity or heterogeneity index. Its value often is used as a measure of the breadth of the molar mass distribution, though it is a poor substitute for knowledge of the complete distribution curve. Typically Mw/ Mn is in the range 1.5-2, though there are many polymers which have smaller or very much larger values of polydispersity index. A perfectly monodisperse polymer would have Mw/ Mn = 1.00. 

If all species in a polymer sample have same molecular weight (that is, the polymer is monodisperse) then Mn = M i — Mz- Such monodispersity is, however, unknown in synthetic polymers and it is always true that Mz > Mw > Mn- The ratio Mu,/M , or (A/ /M ) , is commonly taken to be a measure of the polydispersity of the sample. This ratio, called the polydispersity index (PDI), is not a sound statistical measure, however, and it is easy to make incorrect inferences from the magnitude of the M a/Mn ratio. The breadth and shape of the distribution curve are characterized most efiiciently with parameters derived from the moments of distribution. 

FIGURE 5—4 Frequency distribution curves and quantal concentration-effect and dose-effect curves. A. Frequency distribution curves. An experiment was performed on 100 subjects, and the effective plasma concentration that produced a quantal response was determined for each individual. The number of subjects who required each dose is plotted, giving a log-normal frequency distribution (colored bars). The gray bars demonstrate that the normal frequency distribution, when summated, yields the cumulative frequency distribution—a sigmoidal curve that is a quantal concentration-effect curve. B. Quantal dose-effect curves. Animals were injected with varying doses of sedative-hypnotic, and the responses were determined and plotted. The calculation of the therapeutic index, the ratio of the to the ED q, is an indication of how selective a drug is in producing its desired effects relative to its toxicity. (See text for additional explanation.)... 

In order to compare the results of critical chromatography with results of an independent method, SEC with coupled density (D) and refractive index (RI) detection was used, which has been shown to be very useful for the characterization of copolymers with respect to their chemical composition [39,40]. The MMD curve for one of the block copolymers and the mass distribution curves of the components are shown in Fig. 18. From these the overall chemical composition may be calculated. An excellent agreement between the results of critical chromatography and the SEC experiments was obtained. 

Figure 2.12 Typical chromatograms produced automatically by the data capture and data reduction software on a modern gel permeation chromatographic instrument (a) a calibration standard and (b) a typical sample with a dispersity index of 1.86 together with a full experimental report. Both the differential and integral distribution curves are plotted. Note that the molecular...

See correlated color temperature, color rendering index, and spectral power distribution curve. 

Figure 3. Distribution curves of discrimination indexes for high-position debris flows.

Figure 7.158 Residence time distribution curves for several power law index values...

To further interpret the results, the distribution curve may be divided into three segments, ie, low, medium, and high, and a polydispersity index, Mw/Afn, calculated for each segment (17). 

The term, a, in the above equations is the Sips index of heterogeneity, which is a measure of the broadness of the distribution curve. ... 

On the assumption of the Sips distribution curve, which leads to Eq. (2.7), A o can be evaluated experimentally, since it equals the reciprocal of the free hapten concentration (1/c) when r = 1, i.e., when one-half the combining sites are occupied (76). This is independent of a knowledge of the index of heterogeneity, a. Thus, for bivalent antibody, when r = 1 Eq. (2.7) becomes... 

The order of these three types of molecular weight is > M . The distributions of the polymer molecular weight are indicated by polydlspersity The polydlsperslty of the molecular weight of the polymer can be represented by a distribution curve or distribution index. Figure 1.3 is a typical distribution curve of the molecular weight. The relative sizes... 

Color Rendering Index, and Spectral Power Distribution Curve. 

Figure 9.18 Conelation between the melt flow index recoveiy and ratio of intrinsic viscosities of wt% of 95 and SO from the distribution curves. (From Ref. 22.)...

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

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