Reliability mathematics

Bertram L. Anisiadter, Reliability Mathematics, McGraw-Hill, New York, 1971. 

It is interesting to note that a number of researchers have attempted, more or less successfully, to construct reliable mathematical models which combine structural elements and experimental data to predict the toxicities of new substances not yet experimentally tested for humans and other species.110152 Furthermore pharmacology, toxicity, metabolism and enzyme-inhibiting effects of fluorine-containing aromatic systems (e.g., anilines, ben-zothiadiazines, butyrophenones, corticoids, phenothiazines, steroids, uracils) have been discussed in depth in the literature.153-156... 

In order to obtain a reliable mathematical apparatus there has to be a reasonably simple, yet accurate, model of the structure of a syntactic foam. Attempts to extend the known models of monolithic plastics to syntactic structures filled with solid spherical particles have not proved successfull 8,76). Models which rely on close microsphere packing 157,158> have not been very accurate either. For example, Krzhechkovsky et al.,59) showed that syntactic foams can be treated as homogeneous uniform materials with small Ks (up to 20%) only if there is no stress field in the polymer matrix around the microspheres (see Sect. 3.5). 

Experiments with the system H2-02 were performed also by Horak et al. (21-23) who observed pronounced ignition-extinction phenomena. They were able to construct a reliable mathematical model based on the heat and mass balances describing the gas-to-solid heat and mass transfer. Their general conclusion is that the multiplicity phenomena may be explained in terms of thermokinetic theory. However, on the other hand, because of the high thermal capacity of the pellet, the oscillations cannot be described by this mechanism (72). Obviously we should examine a more detailed kinetic mechanism to be able to analyze successfully this phenomenon (25). 

The aim and the hope of the authors is to provide, through this book, a unitary perspective of the main problems and challenges related to modeling, control, and diagnosis of chemical batch reactors. A special emphasis is put on the interaction between the development of effective and reliable mathematical models of the plant and on the subsequent design of the control and diagnosis systems. Hence, the recommendation for the reader is to read this monograph as a whole. 

The control of a fed-batch alcoholic fermentation process can be obtained by controlling the substrate concentration in the medium by manipulation of the feed flow. The fermentation process presents complicated kinetic mechanisms. In addition, there is the absence of accurate and reliable mathematical models as well as the difficulty of obtaining direct measurements of the process variables owing to a lack of appropriate on-line analyzers and sensors. Control systems are formed by a set of instruments and control mechanisms connected through electrical signals in the... 

In our urban areas, we recognize two main types of pollution one coming from single sources—e.g., power plants and foundries, the other coming from multiple sources—e.g., the automobile. For the single, isolated sources, the ambient air standards are translated without too much difficulty into source emission standards. We have reasonably reliable mathematical formulae and empirical data to predict ground concentra-... 

The use of expert systems [13-14] allows the solution of problems which lack reliable mathematical models and are characterized by a great amount of empirical knowledge acquired in heterogeneous ways and by a high level of abstraction. The study of corrosion phenomena has such characteristics and is a very promising field for the realization of expert systems. 

Neutralization or Demilitarization Hazardous items may be neutralized by detonation in place, or they may be removed to a demilitarization facility located on, or at some distance from, the site undergoing remediation. Detonation in place, which is often the only safe method for neutralization of explosive items, carries with it concerns for blast, noise, and vapor containment. Blast containment coverings tend to be heavy, bulky, and difficult to position. Sand tamping for noise control is labor intensive and time consuming, and it creates problems with dust. Reliable mathematical models for predicting the noise impact on neighboring communities do not appear to be available, although their development should not be particularly difficult. 

The book is written in the spirit of bringing to chemical engineers in both academia and industry a comprehensive text for the development of reliable mathematical models for industrial fixed bed catalytic reactors from the first step of surface phenomena to the final stage of putting the verified model into a user friendly software package with... 

Several interactions, competition for resources and feeding of one population upon another in particular, have been studied in some detail and reasonably reliable mathematical models of some simple types of these interactions are available. Other interactions have not received so much attention, however, and in some cases nothing but qualitative statements about an interaction can be made. The review is concluded with a listing of areas where research is needed to provide and Improve knowledge of interspecific microbial interactions. 

Once a reliable mathematical model of electronic motion in atoms has been established, it would be possible to return the favour and use this model to upgrade the celestial mechanics of the solar system. We shall return to this topic in due course. 

However, in spite of the known advantages and applications of liquid membrane separation processes in hollow-fiber contactors, there are scarce examples of industrial application. The industrial application of a new technology requires a reliable mathematical model and parameters that serve for design, cost estimation, and optimization purposes allowing to accurate process scale-up. " The mathematical modeling of liquid membrane separation processes in HFC is divided into two steps (1) the description of the diffusive mass transport rate and (2) the development of the solute mass balances to the flowing phases. 

Amstadter, B.L. 1971. Reliability mathematics. McGRAW-HILL, chapter 9. 

Schematic representation of the process for obtaining a reliable mathematical model. 

A second consideration in scaling down a reactive extrusion process concerns the axial temperature profile. Because of the different volume to surface ratio between large-scale and small-scale equipment the cooling capacity of the latter will be far better than in production size machines. To obtain similar axial temperature profiles, the temperature settings of the barrel wall in the small-size extruder should be different from those in the large-size machine. The most convenient situation is, of course, if a reliable mathematical model of the reactive extrusion process is available. An alternative is the use of an approximating heat balance over the extruder ... 

Extensive utilization of reliable mathematical and computer modeling to minimize the cost of development of novel efficient and environmentally friendly technologies capable of achieving Maximum Production-Minimum Pollution (MPMP). 

Previous knowledge on random variables, the probability density function, and the cumulative probability distribution function will be utilized to smdy reliability mathematical equations where random variable time (t) is the major issue ... 

To design and evaluate scale-up feasibility, the development of a reliable mathematical model to describe the process is important. In a packed bed extraction, the extraction fluid first penetrates and diffuses into the solid matrix. Then the solute solubilizes and moves from the solid matrix to the pores where diffusion inside the pores takes place. At the end, the fluid with the dissolved extract axially diffuses back along the extraction bed and leaves the extractor. 

On an industrial scale, it is very important to produce exactly the same extract yield as in the small-scale system. Due to high capital investment in supercritical fluid extraction, the development of a reliable mathematical model that describes the process is necessary to design and evaluate scale-up feasibility. To guarantee the success... 

---