Coefficients of variation

The application of this equation enables a surface area to be calculated from a summation of increments, i.e. 

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For the final rule, another parameter, K, the coefficient of variation, is introduced. 

Another measure of dispersion is the coefficient of variation, which is merely the standard deviation expressed as a fraction of the arithmetic mean, viz., s/x. It is useful mainly to show whether the relative or the absolute spread of values is constant as the values are changed. 

The modem ionization chamber, called a dose caUbrator in this appHcation, is capable of linear measurements of radioactivity having a precision in the range of several percent coefficient of variation over a range of 370 kBq (10 -lCi) to at least 370 GBq (10 Ci). This extraordinary range is the chief advantage of this instmment. It may only be used when the sample is known to have only a single isotope. It has no capacity to distinguish radiation from different isotopes. 

The coefficient of variation (cp) of a distribution is a measure of the spread of the distribution about some characteristic size. It is often used in conjunction with dominant size to characterize crystal populations through the equation... 

The dominant crystal size is given by = 3Gr. This quantity is also the ratio mJwhich is often given the symbol 2-(J) Prom the definition of the coefficient of variation given by equation 41, cv = 50% for an MSMPR crystallizer. Such a cp may be too large for certain commercial products, which means either the crystallizer must be altered or the product must be screened to separate the desired fraction. 

Coefficient of Variation One of the problems confronting any user or designer of crystallization equipment is the expected particle-size distribution of the solids leaving the system and how this distribution may be adequately described. Most crystalline-product distributions plotted on arithmetic-probability paper will exhibit a straight line for a considerable portion of the plotted distribution. In this type of plot the particle diameter should be plotted as the ordinate and the cumulative percent on the log-probability scale as the abscissa. 

It is common practice to use a parameter characterizing crystal-size distribution called the coefficient of variation. This is defined as follows ... 

In order to be consistent with normal usage, the particle-size distribution when this parameter is used should Be a straight line between approximately 10 percent cumulative weight and 90 percent cumulative weight. By giving the coefficient of variation ana the mean particle diameter, a description of the particle-size distribution is obtained which is normally satisfactory for most industrial purposes. If the product is removed from a mixed-suspension ciystallizer, this coeffi-... 

Note that the calculated distribution shows some deviation from the measured values because of the small departure of the actual sample from the theoretical coefficient of variation (i.e., 47.5 versus 52 percent). 

At X-ray fluorescence analysis (XRF) of samples of the limited weight is perspective to prepare for specimens as polymeric films on a basis of methylcellulose [1]. By the example of definition of heavy metals in film specimens have studied dependence of intensity of X-ray radiation from their chemical compound, surface density (P ) and the size (D) particles of the powder introduced to polymer. Have theoretically established, that the basic source of an error of results XRF is dependence of intensity (F) analytical lines of determined elements from a specimen. Thus the best account of variations P provides a method of the internal standard at change P from 2 up to 6 mg/sm the coefficient of variation describing an error of definition Mo, Zn, Cu, Co, Fe and Mn in a method of the direct external standard, reaches 40 %, and at use of a method of the internal standard (an element of comparison Ga) value does not exceed 2,2 %. Experiment within the limits of a casual error (V changes from 2,9 up to 7,4 %) has confirmed theoretical conclusions. 

There have been also found the quantitative characteristics of the methods. They are as follows for HPLC method the linearity is 0.1 ng to 2 ng the detecting limit is 0.1 ng the limit of the quantitative estimation makes up 0.0004 mg/kg a coefficient of variation is 2.74% for the chromatodensitometry method the linearity is 2 ng to 10 ng the detecting limit is 0.6 ng the coefficient of variation is 2.37%. The data obtained have been treated using a regressive analysis. 

Table 4.5 Typical coefficient of variation, C, for various materials and mechanical properties Su = ultimate tensile strength)...

There is very little information on the variational nature of loads commonly encountered in mechanical engineering. Several references provide guidance in terms of the coefficient of variation, C , for some common loading types as shown in Table 4.9 (Bury, 1975 Ellingwood and Galambos, 1984 Faires, 1965 Lincoln... 

Example - determining the stress distribution using the coefficient of variation... 

Before a probabilistic model can be developed, the variables involved must be determined. It is assumed that the variables all follow the Normal distribution and that they are statistically independent, i.e. not correlated in anyway. The scatter of the pre-load, F, using an air tool with a clutch is approximately 30% of the mean, which gives the coefficient of variation, = 0.1, assuming 3cr covers this range, therefore ... 

A suitable material would be hot rolled mild steel 070M20, which has a minimum yield strength, S jVin = 215 MPa (BS 970, 1991). By considering that the minimum yield strength is —3 standard deviations from the mean and that the typical coefficient of variation = 0.08 for the yield strength of steel, the Normal distribution parameters for 070M20 can be approximated by ... 

A useful measure of the Normal distribution is derived from its parameters, and is called the coefficient of variation, C,j ... 

Coefficient of variation FMEA Detectability Rating Frequency... 

Various novel applications in biotechnology, biomedical engineering, information industry, and microelectronics involve the use of polymeric microspheres with controlled size and surface properties [1-31. Traditionally, the polymer microspheres larger than 100 /urn with a certain size distribution have been produced by the suspension polymerization process, where the monomer droplets are broken into micron-size in the existence of a stabilizer and are subsequently polymerized within a continuous medium by using an oil-soluble initiator. Suspension polymerization is usually preferred for the production of polymeric particles in the size range of 50-1000 /Ltm. But, there is a wide size distribution in the product due to the inherent size distribution of the mechanical homogenization and due to the coalescence problem. The size distribution is measured with the standard deviation or the coefficient of variation (CV) and the suspension polymerization provides polymeric microspheres with CVs varying from 15-30%. 

The coefficient of variation is a measure of relative dispersion of a set of values and is given for the population by... 

There are instances where deviations, as measured by the standard error, are scaled to the magnitude of the mean to yield the coefficient of variation. This is calculated by... 

Cobalt, sepn. of from nickel, (cm) 532 Codeine and morphine, D. of 740 Coefficient of variation 135 Colloidal state 418 See also Lyophilic, Lyophobic Colorimeters light filters for, 661 photoelectric, 645, 666 Colorimetric analysis 645 criteria for, 672 general remarks on, 645, 672 procedure, 675 solvent selection, 674 titration, 652... 

Thermal expansion — as elasticity — depends directly upon the strength of the intermolecular forces in the material. Strongly bonded materials usually expand little when heated, whereas the expansion of weak materials may be a hundred times as large. This general trend is confirmed by Table 5.1. The coefficient of thermal expansion a was found to be lower in the crosslinked polymers and higher in the less crosslinked or thermoplastic materials as observed by Nielsen [1], In addition, Table 5.1 presents the Young s moduli E of the polymers at ambient temperatures as well as the products a2E. The values of oc2E are all close to 13.1 Pa K 2 with a coefficient of variation of 1.6%. 

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