Taking into account other Practical Points

The various mathematical methods for determining optimum conditions, as presented in this chapter, represent on a theoretical basis the conditions that best meet the requirements. However, factors that cannot easily be quantitized or practical considerations may change the final recommendation to other than the theoretically correct optimum condition. Thus, a determination of an optimum condition, as described in this chapter, serves as a base point for a cost or design analysis, and it can often be quantitized in specific mathematical form. From this point, the engineer must apply judgment to take into account other important practical factors, such as return on investment or the fact that commercial equipment is often available in discrete intervals of size. 

Suppose that masses are distributed within a plane layer whose thickness is much smaller than the distance from these masses to the observation point. Fig. 1.13a. In other words, the distance between the observation point and any point of the elementary volume is practically the same. Taking into account this fact, we can replace this layer by a plane surface with the same mass, located somewhere at the middle of the layer. Fig. 1.13b. Inasmuch as every elementary volume contains the mass dm — 5(q)hdS,its distribution on the surface can be described by dm — a(q)dS, where... 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

Parameter R is no physical observable, merely a fitting parameter like any other, even though it represents a special point on a curve of V(i ) that is likewise no physical observable. Jones and coworkers reported no value of R their value (611.6337 + 0.0045) m u [92] of (actually Bq.i) implies J e/10 °m = 1.6601699 + 0.0000061, which differs inappreciably from a corresponding value in table 1. Because we take into account practically all factors that influence the value of i e, the latter value is highly accurate, within its stated uncertainty, not merely precise and prone to systematic error. That tabulated value of i e is larger... 

The other point to take into account is the conditioning of the lightweight papers prior to printing and folding. This just means that the paper should be kept, as far as practical, in optimum storage conditions. 

Moreover, as a consequence of working with conditional probabilities that force them to change their point of view back and forth fi om data to model, Bayesians are less prone to fall in love with their model, whichhelps to step back, discuss hypotheses and entertain the cycle of statistical analysis (Box, 1980). The possibility to take into account expert knowledge, the more natural way of interpreting probabilities, credibility intervals, statistical tests are other interesting features in practical applications. In spite ofthat, it cannot be denied that Bayesian setting is not very common in the industrial practice, at least less common than the frequentist approach. 

If we look at general components within a workplace, weakness may exist at matty points in procedures and practices. For example, if a procedure for purchasing chemicals does not take into account safety requirements or its toxicity, an accident or loss m result. Mary chemicals can be substituted by less toxic ones and personal protective equipment may need to be ordered along with the chemicals. Other safety considerations which should be included when purchasing chemicals are ... 

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