Variation homogeneity

In this study, we only focus on within-group variation (homogeneity within package) however, in process control, not only within-group but also between-group variation has to be considered to maintain the process stability. In addition, the performance measure, e.g., average run length (ARL) of our control charts will be studied. 

The results found for the coating controlled parts allow to consider during the testing the exploitation of the information provided by the measured variation impedance for the processed products by the coating thickness determination and low frequency homogeneity and to evaluate the high frequency coating nature. 

It was found that that in the case of soft beta and X-ray radiation the IPs behave as an ideal gas counter with the 100% absorption efficiency if they are exposed in the middle of exposure range ( 10 to 10 photons/ pixel area) and that the relative uncertainty in measured intensity is determined primarily by the quantum fluctuations of the incident radiation (1). The thermal neutron absorption efficiency of the present available Gd doped IP-Neutron Detectors (IP-NDs) was found to be 53% and 69%, depending on the thicknes of the doped phosphor layer ( 85pm and 135 pm respectively). No substantial deviation in the IP response with the spatial variation over the surface of the IP was found, when irradiated by the homogeneous field of X-rays or neutrons and deviations were dominated by the incident radiation statistics (1). 

The encircling probe was characterised with its mirror in water. As we did not own very tiny hydrophone, we used a reflector with hemispherical tip with a radius of curvature of 2 mm (see figure 3c). As a result, it was possible to monitor the beam at the tube entrance and to measure the position of the beam at the desired angle relatively to the angular 0° position. A few acoustic apertures were verified. They were selected on an homogeneous criteria a good one with less than 2 dB of relative sensitivity variations, medium one would be 4 dB and a bad one with more than 6 dB. 

Mitsui Toatsu Chemical, Inc. disclosed a similar process usiag Raney copper (74) shortiy after the discovery at Dow, and BASF came out with a variation of the copper catalyst ia 1974 (75). Siace 1971 several hundred patents have shown modifications and improvements to this technology, both homogeneous and heterogeneous, and reviews of these processes have been pubHshed (76). Nalco Chemical Company has patented a process based essentially on Raney copper catalyst (77) ia both slurry and fixed-bed reactors and produces acrylamide monomer mainly for internal uses. Other producers ia Europe, besides Dow and American Cyanamid, iaclude AUied CoUoids and Stockhausen, who are beheved to use processes similar to the Raney copper technology of Mitsui Toatsu, and all have captive uses. Acrylamide is also produced ia large quantities ia Japan. Mitsui Toatsu and Mitsubishi are the largest producers, and both are beheved to use Raney copper catalysts ia a fixed bed reactor and to sell iato the merchant market. 

Another method of manufacturing SiC by the decomposition of a gas mixture containing silane, propane, and hydrogen, and hydrogen chloride has been described (80). With such a mixture, it was possible to work at a relatively lower (1200°C) temperature and it was claimed that compact, homogeneous P SiC crystals were obtained. In a variation of this gas-phase synthesis theme, SiC has been produced from the reaction of SiCl and methane (81). SiC precipitates from 1000 to 3000°C. 

Method of Variation of Parameters This method is apphcable to any linear equation. The technique is developed for a second-order equation but immediately extends to higher order. Let the equation be y" + a x)y + h x)y = R x) and let the solution of the homogeneous equation, found by some method, he y = c f x) + Cofoix). It is now assumed that a particular integral of the differential equation is of the form P x) = uf + vfo where u, v are functions of x to be determined by two equations. One equation results from the requirement that uf + vfo satisfy the differential equation, and the other is a degree of freedom open to the analyst. The best choice proves to be... 

Method of Variation of Parameters This technique is applicable to general linear difference equations. It is illustrated for the second-order system -2 + yx i + yx = ( )- Assume that the homogeneous solution has been found by some technique and write yY = -I- Assume that a particular solution yl = andD ... 

Variable Coejftcients The method of variation of parameters apphes equally well to the linear difference equation with variable coefficients. Techniques are therefore needed to solve the homogeneous system with variable coefficients. 

Evaluation Statistical tests can be used to evaluate relative homogeneity based on observed variations in spot sample composition. For a simple binaiy mixture such as that shown in Fig. 19-8, it can be shown (see Ref. 9) that the expected variance among samples containing n particles each is given by... 

The major artifacts contributing to uncertainties in PDCE results stem from effects caused by bombardment of nonideal specimens, particularly thick specimens. The ideal thick specimen would be a homogeneous, smooth electrical conductor that does not change during bombardment. Except for rather simple, well-defined layered structures (e.g., surface oxide layers), specimens having compositional variations with depth yield spectra whose analyses can have large inaccuracies. 

Most room models contain only one zone air node, thus assuming perfect mixing of the zone air and a homogenous temperature distribution in the space. Spatial temperature variations, such as vertical temperature gradients, are not considered. For specific applications such as displacement ventilation or atria, models with several zone air nodes in the vertical direction have been developed. ... 

The solution to this fourth-order partial differential equation and associated homogeneous boundary conditions is just as simple as the analogous deflection problem in Section 5.3.1. The boundary conditions are satisfied by the variation in lateral displacement (for plates, 5w actually is the physical buckle displacement because w = 0 in the membrane prebuckling state however, 5u and 8v are variations from a nontrivial equilibrium state. Hence, we retain the more rigorous variational notation consistently) ... 

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%. 

Figure 14 The variation of average size of the polystyrene particles by the average solubility parameter of the homogeneous alcohol-water dispersion medium. (From Ref. 89. Reproduced with the permission of John Wiley Sons, Inc.)...

Gases. Few problems arise over homogeneity of gas mixtures where the storage vessel is not subjected to temperature or pressure variations. Difficulties may arise if precautions are not taken to clear valves, taps and connecting lines of any other gas prior to passage of the sample. Similarly care must be taken that no gaseous components will react with the sampling and analytical devices. 

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