Reliability theory

I. Bazovsky, Reliability Theory andPractice, Prentice-HaU, Inc., Englewood CUffs, N.J., 1961. 

The well-known Flory treatment [50-52] of the en-thropic contribution to the Gibbs energy of mixing of polymers with solvents is still the simplest and most reliable theory developed. It is quite apparent, however, that the Flory-Huggins theory was established on the basis of the experimental behavior of only a few mixtures investigated over a very narrow range of temperature. Strict applications of the Flory-Huggins approach... 

Nevertheless it is important to be able to give a verbal description of the origin of barrier forces in terms of conventional quantum-mechanical language. Such a description might be of no use for quantitative predictions, but it could at least be plausible and not in conflict with known facts. It would strengthen the belief that a reliable theory only awaited the further refinement of the approximations used. 

Electrochemical impedance spectroscopy leads to information on surface states and representative circuits of electrode/electrolyte interfaces. Here, the measurement technique involves potential modulation and the detection of phase shifts with respect to the generated current. The driving force in a microwave measurement is the microwave power, which is proportional to E2 (E = electrical microwave field). Therefore, for a microwave impedance measurement, the microwave power P has to be modulated to observe a phase shift with respect to the flux, the transmitted or reflected microwave power APIP. Phase-sensitive microwave conductivity (impedance) measurements, again provided that a reliable theory is available for combining them with an electrochemical impedance measurement, should lead to information on the kinetics of surface states and defects and the polarizability of surface states, and may lead to more reliable information on real representative circuits of electrodes. We suspect that representative electrical circuits for electrode/electrolyte interfaces may become directly determinable by combining phase-sensitive electrical and microwave conductivity measurements. However, up to now, in this early stage of development of microwave electrochemistry, only comparatively simple measurements can be evaluated. 

As mentioned at the beginning of this chapter real phase-sensitive measurements of electrochemical systems have not yet been performed. Not only is the experimental technique difficult, but a reliable theory of... 

The theory of the separation of geometric isomers on stationary phases that have a number of sterogenic centers has not been developed to the point where a particular stationary phase together with an appropriate mobile phase can be deduced for the separation of a specific pair of isomers. A number of theories have been put forward to explain the resolution of geometric isomers (some of which have been quite "imaginative" and "colorful") yet a reliable theory to help in phase selection for a hitherto unresolved chiral pair is still lacking. Unfortunately, the analyst is left with only two alternatives. The first is to search the literature for a model separation similar to the problem in hand and start with that phase system or, alternatively, resort to the technique of the early days of LC, namely, find the best phase system by a trial-and-error routine. 

The range of dispersed-phase velocity studied by Keith and Hixson (K3) is from 10 to 30 cm/sec which, according to those authors, is of industrial interest. The results obtained by them in the absence of mass transfer can be predicted roughly by extrapolation of the Hayworth and Treybal correlation. In the presence of mass transfer, the results obtained (F2), the drop size distribution, flooding, etc. are different from those observed in the absence of mass transfer. There is no reliable theory at present which can predict the drop size distribution in sprays, though rough approximations are possible when mass transfer is completely avoided. 

DR. HUSH For myself, if I gave the impression of any feeling of self-satisfaction, it was certainly in the sense that I think we can say that there is a glimmer of light in the darkness. And in chemistry we must be grateful for the smallest spark. I have stressed also that our present theoretical approaches to rate calculations have been almost entirely confined to outer-sphere processes, and that the task of formulating reliable theories for inner-sphere transfers will be a formidable one. 

In this relatively young field of research, the experimental and theoretical results lend themselves better to associations and trends analysis than to quantitative correlations and theoretical predictions. Empirical structure-property relations should be regarded as temporary props that can be useful, but should be modified if serious exceptions are found. They should be regarded as a stage in the evolution from ignorance to empiricism, and then into knowledge and reliable theory, and should be supplanted when better ideas arrive. 

Depends on a large database and reliable theory Requires a few creative experts... 

The greatest obstacle to planning arises from the lack of reliable theories of society. What we have is a toolbox of mechanisms, not a set of laws. We cannot predict how rational people behave under conditions of uncertainty or multiple equilibria, nor whether their behavior will be governed by rationality or by social norms. Even more fundamentally, we cannot predict how preferences and norms might themselves come to change as a result of policy reforms. We cannot predict technical change. As... 

Nonrelativistic quantum mechanics, extended by the theory of electron spin and by the Pauli exclusion principle, provides a reliable theory for the computation of atomic spectral frequencies and intensities, of cross sections for scattering or capture of electrons by atomic systems, of chemical bonds and many properties of solids, including magnetic properties, although with much more complicated systems it has not always proved possible to develop with adequate accuracy the consequences of the theory. Quantum mechanics has also had a limited success in nuclear theory although m this field it is possible that a more fundamental system of mechanics is required. 

Thus the theory of relativity leads to very interesting and important results about energy and matter. These results appear to be in accordance with the facts so we may conclude that the theory of relativity is a reliable theory. 

Quantum chemistry plays vital central roles in clarifying and understanding the mechanisms of these photobiological events. Electronic structures and transitions of active centers in proteins obey the principles of quantum mechanics, and molecular properties dramatically change after the transitions. In addition, photochemical events in excited states are often transient and sometimes difficult to study in experimental approaches. If an accurate and reliable theory exists and can be applied to photobiological subjects, one can obtain not only rational explanations but also predictions on the photo-functions of the active centers and proteins. 

The theoretical predictions of Kr and K, are not suitable for cases in which either the solute or solvent are preferentially adsorbed on the walls, or when the wall affects the structure of the liquid in the pore. Unfortunately, at present there is no reliable theory for predicting the influence of these effects. 

The term Markov chain frequently appears in this chapter. This term is named after the Russian mathematician Andre Markov (1856-1922). The Markov theory is widely applied in many fields, including the analysis of stock-markets, traffic flows, queuing theories (e.g. modelling a telephone customer service hotline), reliability theories (e.g. modelling the time for a component to wear out) and many other systems involving random processes. 

Each of the transition elements tends to have several oxidation numbers. Thus iron forms one series of compounds with oxidation number -f-2 (ferrous compounds) and another series with oxidation number - -S (ferric compounds). For chromium the principal oxidation numbers are -f 3 and -f 6, and for manganese they are -f 2 and +7. It would be of great value to chemistry if a simple and reliable theory of the oxidation states of the transition elements were to be developed but this has not yet been done. 

In the absence of a reliable theory, computer simulations have become the most important means of tackling the question of ionic criticality. In the last ten years there have been numerous attempts to identify the universality class of what is perhaps the most basic model of ionic fluids, the restricted primitive model (RPM). The RPM consists of an equimolar mixture of positively and negatively charged hard spheres with diameter a, immersed in a dielectric continuum with dielectric constant D. The pair potential is,... 

The SAC-CI method can be applicable to various kinds of molecular spectroscopy excitation, ionization and electron-attached states in high accuracy. First, we overview the excitation [51 -53] and ionization spectra [51,54] of five-membered ring compounds, furan and thiophene. For these spectra, pioneering theoretical spectroscopy was performed by the SAC-Cl method [51] and has been followed by many theoretical works [52,53,55-58]. Comparisons of our old and new calculations show the importance of using the sufficiently flexible basis sets with valence and Rydberg functions as well as the reliable theory for the accurate descriptions of these spectra. We also explain the spectroscopy of p-benzoquinone (p-BQ), its anion radical [59], and aniline [60]. 

Information in the field of thermodynamic properties of concentrated non-aqueous electrolyte solutions is rather poor at present, in spite of increasing technological interest. No reliable theory is avaUable. Aqueous solutions have been better investigated. Pitzer et al. and Cruz and Renon extended the Debye-... 

Lacking a reliable theory, an empirical equation was used to reproduce the... 

Reliability theory has been formulated to deal with product failme, and this has been extended to death rates of living organisms (Gavrilov and Gavrilova, 2004). Some of the basic tenets of this theory me ... 

The difficulty in understanding the hydrophobic force law at such large distances is the absence of any reliable theory to describe the propagation of joint density and orientational correlation among water molecules. It is possible that orientational correlation is longer-ranged than spatial correlation. 

These goals are achievable if models based on systems theory, rather than reliability theory, underlie our safety engineering activities. 

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