Statistics preparation

Scheme 5.18. Statistical preparation of dendrimers possessing 1, 2, or 3 nitrile surface groups.

Statistical mechanics and kinetic theory, as we have seen, are typically concerned with the average behaviour of an ensemble of similarly prepared systems. One usually hopes, and occasionally can demonstrate, that the variations of these properties from one system to another in the ensemble, or that the variation with time of the properties of any... 

Quack M 1982 Reaction dynamics and statistical mechanics of the preparation of highly excited states by intense infrared radiation Adv. Chem. Rhys. 50 395-473... 

Analysis of Standards The analysis of a standard containing a known concentration of analyte also can be used to monitor a system s state of statistical control. Ideally, a standard reference material (SRM) should be used, provided that the matrix of the SRM is similar to that of the samples being analyzed. A variety of appropriate SRMs are available from the National Institute of Standards and Technology (NIST). If a suitable SRM is not available, then an independently prepared synthetic sample can be used if it is prepared from reagents of known purity. At a minimum, a standardization of the method is verified by periodically analyzing one of the calibration standards. In all cases, the analyte s experimentally determined concentration in the standard must fall within predetermined limits if the system is to be considered under statistical control. 

The sample labeled atactic in Fig. 7.10 was prepared by a free-radical mechanism and, hence, is expected to follow zero-order Markov statistics. As a test of this, we examine Fig. 7.9 to see whether the values of p, P, and Pj, which are given by the fractions in Table 7.9, agree with a single set of p values. When this is done, it is apparent that these proportions are consistent with this type... 

From appropriate ratios of these sequence lengths, what conclusions can be drawn concerning terminal versus penultimate control of addition The following are experimental tacticity fractions of polymers prepared from different monomers and with various catalysts. On the basis of Fig. 7.9, decide whether these preparations are adequately described (remember to make some allowance for experimental error) by a single parameter p or whether some other type of statistical description is required ... 

Manufacturing processes have been improved by use of on-line computer control and statistical process control leading to more uniform final products. Production methods now include inverse (water-in-oil) suspension polymerization, inverse emulsion polymerization, and continuous aqueous solution polymerization on moving belts. Conventional azo, peroxy, redox, and gamma-ray initiators are used in batch and continuous processes. Recent patents describe processes for preparing transparent and stable microlatexes by inverse microemulsion polymerization. New methods have also been described for reducing residual acrylamide monomer in finished products. 

The LIMS software is essentially a database for tracking, reporting, and archiving lab data as well as scheduling and guiding lab activities. Graphical and statistical treatment of data for improved process control (qv) as well as preparation of certificates of analysis (COA) for the customer are some of the other features of a comprehensive LIMS package (30). 

Randomization means that the sequence of preparing experimental units, assigning treatments, miming tests, taking measurements, and so forth, is randomly deterrnined, based, for example, on numbers selected from a random number table. The total effect of the uncontrolled variables is thus lumped together into experimental error as unaccounted variabiUty. The more influential the effect of such uncontrolled variables, the larger the resulting experimental error, and the more imprecise the evaluations of the effects of the primary variables. Sometimes, when the uncontrolled variables can be measured, their effect can be removed from experimental error statistically. 

Roughly 65% of the substituents are trifluoroethoxy, and 35% are telomer alcohols prepared from tetrafluoroethylene and methanol. About 0.5 mol % of an aHyhc substituent is used as a cross-link site. The substituent pattern is beUeved to be stricdy statistical. 

Suppose we have two methods of preparing some product and we wish to see which treatment is best. When there are only two treatments, then the sampling analysis discussed in the section Two-Population Test of Hypothesis for Means can be used to deduce if the means of the two treatments differ significantly. When there are more treatments, the analysis is more detailed. Suppose the experimental results are arranged as shown in the table several measurements for each treatment. The goal is to see if the treatments differ significantly from each other that is, whether their means are different when the samples have the same variance. The hypothesis is that the treatments are all the same, and the null hypothesis is that they are different. The statistical validity of the hypothesis is determined by an analysis of variance. 

Because X-ray counting rates are relatively low, it typically requires 100 seconds or more to accumulate adequate counting statistics for a quantitative analysis. As a result, the usual strategy in applying electron probe microanalysis is to make quantitative measurements at a limited collection of points. Specific analysis locations are selected with the aid of a rapid imaging technique, such as an SEM image prepared with backscattered electrons, which are sensitive to compositional variations, or with the associated optical microscope. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

The standard does not require you to use statistical techniques but identify the need for them. Within your procedures you will therefore need a means of determining when statistical techniques will be needed to determine product characteristics and process capability. One way of doing this is to use checklists when preparing customer specifications, design specifications, and verification specifications and procedures. These checklists need to prompt the user to state whether the product characteristics or process capability will be determined using statistical techniques and if so which techniques are to be used. 

Summaries of the data resourees considered useful were prepared. Useful data was defined as information that was publicly availdWe, scientifically collected, had statistical merit, and could be used for CPQRAs. A list of rejected resources was retained to identify references for supplemental reading and to avoid review duplication when the anticipated second edition of this book is developed. In total, 72 resources were accepted, and over 200 references were rejected. 

Secondly, making measurements on atomic and molecular systems generally interferes with the system. If we were to repeatedly make measurements on a single system, we would change the system at each measurement and so would not be dealing necessarily with the same system. The correct interpretation is a statistical one. We would have to prepare a very large number of systems all in the same electronic state, and then do the measurements on all of them. 

A spectacular application of the acyloin ester condensation was the preparation of catenaries like 11. These were prepared by a statistical synthesis which means that an acyloin reaction of the diester 10 has been carried out in the presence of an excess of a large ring compound such as 9, with the hope that some diester molecules would be threaded through a ring, and would then undergo ring closure to give the catena compound ... 

In the preparation of the first edition of this volume, contact was made with IMS, Inc. of Ambler,Pa.,a well-knownsourceof international statistics. Withtheir help,a list was prepared of the 100 top products based on U.S. sales volume in 1976 that list is given in Table 1. 

Olefin metatheses are equilibrium reactions among the two-reactant and two-product olefin molecules. If chemists design the reaction so that one product is ethylene, for example, they can shift the equilibrium by removing it from the reaction medium. Because of the statistical nature of the metathesis reaction, the equilibrium is essentially a function of the ratio of the reactants and the temperature. For an equimolar mixture of ethylene and 2-butene at 350°C, the maximum conversion to propylene is 63%. Higher conversions require recycling unreacted butenes after fractionation. This reaction was first used to produce 2-butene and ethylene from propylene (Chapter 8). The reverse reaction is used to prepare polymer-grade propylene form 2-butene and ethylene ... 

A convenient size for a circular coupon is 3 8 cm dia., a thickness of 0 - 32 cm and a central hole of 1 1 cm. Although inherent in the philosophy of corrosion testing, the use of coupons with surfaces that simulate those in service has been found to be unsatisfactory owing to irreproducibility, and the standard procedure normally adopted is to abrade down to 120-grit. ASTM Method G4 1984 gives details of preparation of specimens, evaluation of replicate exposures and the application of statistical methods. 

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