Pure chance model

The pure chance model of accident distribution states that basically every one in a certain population has an equal chance of sustaining an accident, although by pure chance some of them meet with more accidents than others. As a consequence, without being susceptible to accidents but by pure chance, there... 

Concerning the results of the Greenwood Yule (1920) study, in nearly all of the cases the pure chance model did not fit the data, whereas the best fit was obtained in conjunction with the negative binomial model calculated on the basis of the assumed unequal liability. This result is representative of a large number of follow-up studies (e.g. Adelstein 1952, Mintz Blum 1949, Burkardt 1962, 1970), in which the negative binomial distribution fit the data better than all other models did. 

Before leaving this chapter we will consider one final model, the purely probabilistic model > i, = 0 + rXj (see Section 4.2 and Equation 4.3). Whether obtained at different levels of the factor or at the same level (replicates), there is a possibility that the two observed responses, yu = 3 and yl2 = 5, belong to a population for which the mean (ja) is zero. The fact that the two numbers we have obtained give a sample mean (j ) of 4 might have occurred simply by chance. Thus, when judging the adequacy of various models, we should not overlook the possibility that the purely probabilistic model is adequate. 

Having recognized the theoretical inadequacy of the dielectric theory for polar solvents, I started to reconsider the entire problem of solvation models. Because the good performance of dielectric continuum solvation models for water cannot be a result of pure chance, in some way there must be an internal relationship between these models and the physical reality. Therefore I decided to reconsider the problem from the north pole of the globe, i.e., from the state of molecules swimming in a virtual perfect conductor. I was probably the first to enjoy this really novel perspective, and this led me to a perfectly novel, efficient, and accurate solvation model based upon, but going far beyond, the dielectric continuum solvation models such as COSMO. This COSMO for realistic solvation (COSMO-RS) model will be described in the remainder of this book. 

As shown in the previous section a common feature of all systems in the liquid state is their molar entropy of evaporation at similar particle densities at pressures with an order of magnitude of one bar. Taking this into account a reference temperature, Tr, will be selected for systems at a standard pressure, p° = 105 Pa = 1 bar, having the same molar entropy as for the pressure unit, p = 1 Pa at T = 2.98058 K. As can easily be verified, the same value of molar entropy and consequently the same degree of disorder results at p if a one hundred-fold value of the above T-value is used in Eq. (6-14). This value denoted as Tw = 298.058 K = Tr is used as the temperature reference value for the following model for diffusion coefficients. The coincidence of Tw with the standard temperature T = 298.15 K is pure chance. 

The t distribution can be used to assess the probabiUty that an observed difference di is actually outside the expected range of random variation for the model parameter. To do so, we must decide on a significance level a. Often a significance level 0 = 5 % is used. This means that we accept that there is a 5 % risk that the observed difference by pure chance is outside the expected range. For the given... 

This is an example of the fractional fault case that was examined in [Bishop 2002a]. The result could also be interpreted as saying that there is at least a 74% chance of zero faults in the logic. This result should be reasonably conservative as some customer tests were not available for inclusion in the coverage measurement. A purely linear model would have predicted N= 1. 

Incidents rarely occur by pure chance. In the analysis of how incidents occur, we rely on the OARU model of Section 5.3. An incident is usually preceded by deviations at the workplace that increase its frequency and/or the consequences of it. SHE measures that eliminate existing deviations (e.g. repair of faulty safety equipment) will have an immediate effect on the risk of accidents. They will, however, not have lasting effects if the deviation may occur again. 

If the purely experimental uncertainty were known, it would then be possible to judge the adequacy of the model y, = Po + r, if s were very much greater than (see Figure 5.6), then it would be unlikely the large residuals for that model occurred by chance, and we would conclude that the model does not adequately describe the true behavior of the system. However, if 5 were approximately the same as 5 (see Figure 5.7), then we would conclude that the model was adequate. (The actual decision compares s to a variance slightly different from s], but the reasoning is similar.)... 

Calculated descriptors have generally fallen into two broad categories those that seek to model an experimentally determined or physical descriptor (such as ClogP or CpKJ and those that are purely mathematical [such as the Kier and Hall connectivity indices (4)]. Not surprisingly, the latter category has been heavily populated over the years, so much so that QSAR/QSPR practitioners have had to rely on model validation procedures (such as leave-k-out cross-validation) to avoid models built upon chance correlation. Of course, such procedures are far less critical when very few descriptors are used (such as with the Hansch, Leo, and Abraham descriptors) it can even be argued that they are unnecessary. 

Although relationships between small-molecule structures and protein families can be established on a purely empirical basis, and 3D protein-structure information is not a necessary precondition, it would be foolish not to consider such information whenever it is available. With the rapidly growing number of protein structures collated in the PDB [5], the chance of finding either the experimentally determined 3D structure of the target protein or at least one of a closely related protein that allows a sufficiently reliable homology model to be built [6] are constantly increasing. 

The only factor of some chemical importance that features prominently in the theories of cosmology is the synthesis of small nuclides such as deuterium and helium. Unfortunately, the initial conditions that are considered to be crucial in these models are purely conjectural. There is little hope of a meaningful test against chemical reality and, in the present climate, no chance for the growth of a mathematically based alternative cosmology. However, the simple qualitative model of a non-orientable universe provides interesting insight into the nature of matter, non-local interaction and quantum theory. 

From a so-called wideline spectrum, one may naively think that it is difficult to obtain the relaxation curve of a particular polymer in a blend. This is not true, because in many blends a short T2 is caused by the mobility of the one of the component polymers or that of side-chains. Thus, there is a chance to discriminate between polymers by their different T2 (mobility). For example, Segre et al. [146] observed two T2 decays for PS/PB. The fast-decaying component was attributed to rigid PS. The slow-decaying component shows the presence of two Ti relaxations. These were attributed to the interphase and pure rubbery PB (Model B). Parizel et al. [147] observed that the FID of polyurethane (PU) in a cross-linked PMMA consists of three... 

Many school-made misconceptions occur because there are problems with the specific terminology and the scientific language, specially involved substances, particles and chemical symbols are not clearly differentiated. If the neutralization is purely described through the usual equation, HC1 + NaOH —> NaCl + H20, then the students have no chance to develop an acceptable mental model that uses ions as smallest particles. 

Parallel events in the field of in situ IR spectroscopy (for a review of sulfate IR studies, see Ref. 26) resulted in a coupled shift to molecular level bi-sulfate anion was recognized in sulfate adlayer even in solutions with predominating sulfate. It was com-pletey new situation, when chemical equilibrium is affected by adsoibate-surface interactioa In usual terms of solution equilibria, the effect corresponds to increase of pKa from its bulk value (ca. 2) to 3.3-4.7 (pKa is potential-dependent). To agree this situation with bulk thermodynamics, one should simply use electrochemical potential instead of chemical. The phenomena of adsorption-induced protonation is relative to UPD, when adsoibate-surface interaction shifts redox equihbria. In more molecular terms, the species determined as bi-sidfate ions are probably interfacial ion pairs, i.e., the phenomenon can be considered as coadsorptioa This situation is screened in purely thermodynamic analysis, as excess surface protonation is hidden in Gibbs adsorptions of sulfate and H. However it becomes important for any further model consideration, as it can affect lateral interactions and the order in the adlayer. The excess adsorption-induced protonation of various anions is a very attractive field. In particular it is the only chance to explain why multicharged oxoanions can form complete mono-layers on platinum. 

After identiflcation of the thresholds, Reppenhagen and Werther (1999a) derived the value of the exponent n in Eq. (19) from all measurements taken under conditions of pure abrasion (straight lines drawn in Fig. 19) to n = —0.5. They explained the negative value of n by some kind of cushioning effect, i.e., the chance for a given particle to impact on the wall decreases with increasing solids concentration in the flow. With n = —0.5, the model equation can now finally be written as... 

The procedure to calculate fiber orientation is the same as explained above, but their implementation into explicit solvers and non-linear material models is more complex than it is for quasi-static load-cases and purely elastic material models. The fiber orientation is characterized by a so called orientation distribution function (ODE) that describes the chance of a fiber being oriented into a certain direction. For isotropic, elastic matrix materials an integral of the individual stiffness in every possible direction weighted with the ODE provides the complete information about the anisotropic stiffness of the compound. However, this integral can not be solved in case of plastic deformation as needed for crash-simulation. Therefore it is necessary to approximate and reconstruct the full information of the ODE by a sum of finite, discrete directions with their stiffness, so called grains [10]. Currently these grains are implemented into a material description and different methods of formulation are tested. 

---