Trial-and-error

There is a tendency among control and statistics theorists to refer to trial and error as one-variable-at-a-time (OVAT). The results are often treated as if only one variable were controlled at a time. The usual trial, however, involves variation in more than one controlled variable and almost always includes uncontrolled variations. The trial-and-error method is fortunately seldom a random process. The starting cycle is usually based on manufacturers specifications or experience with a similar process and/or material. Trial variations on the starting cycle are then made, sequentially or in parallel, until an acceptable cycle is found or until funds and/or time run out. The best cycle found, in terms of one or a combination of product qualities, is then selected. Because no process can be repeated exactly in all cases, good cure cycles include some flexibility, called a process window, based on equipment limitations and/or experience. 

Heat Heat-up Rate 1 to Intermediate Hold Temperature 

Hold at Intermediate Hold Temperature for at least Time 1 

Vent vacuum when pressure reaches 15 psig. 

Heat Heat-up Rate 2 to Final Hold Temperature. 

---

Before suggesting an approach for predicting the minimum number of shells for an entire network, a more convenient method for determining the number of shells in a single unit must first be found. Adopting the design criterion given by Eq. (7.13) as the basis, then any need for trial and error can be eliminated, since an explicit... 

As pointed out in Chap. 5, replacing simple columns by complex columns tends to reduce the vapor (and heat) load but requires more of the heat to be added or removed at extreme levels. This means that the introduction of complex columns in the design might prejudice heat integration opportunities. Thus the introduction of complex distillation arrangements needs to be considered simultaneously with the heat integration. This can be carried out manually with some trial and error or using an automated procedure such as that of Kakhu and Flower. ... 

The value of i given by this equation is known as the discounted cash-flow rate of return (DCFRR). It may be found graphically or by trial and error. 

Also, the result of any diffraction-based trial-and-error fitting is not necessarily unique it is always possible that there exists another untried structure that would give a better fit to experiment. Hence, a multi-teclmique approach that provides independent clues to the structure is very fniithil and common in surface science such clues include chemical composition, vibrational analysis and position restrictions implied by other structural methods. This can greatly restrict the number of trial structures which must be investigated. 

The presence of the multiple arrangements make molecular scattering very challenging theoretically. After much trial and error, several teclmiques have been developed. These teclmiques generally fall into two broad categories ... 

Extended defects range from well characterized dislocations to grain boundaries, interfaces, stacking faults, etch pits, D-defects, misfit dislocations (common in epitaxial growth), blisters induced by H or He implantation etc. Microscopic studies of such defects are very difficult, and crystal growers use years of experience and trial-and-error teclmiques to avoid or control them. Some extended defects can change in unpredictable ways upon heat treatments. Others become gettering centres for transition metals, a phenomenon which can be desirable or not, but is always difficult to control. Extended defects are sometimes cleverly used. For example, the smart-cut process relies on the controlled implantation of H followed by heat treatments to create blisters. This allows a thin layer of clean material to be lifted from a bulk wafer [261. 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

The described method can generate a first-order backward or a first-order forward difference scheme depending whether 0 = 0 or 0 = 1 is used. For 9 = 0.5, the method yields a second order accurate central difference scheme, however, other considerations such as the stability of numerical calculations should be taken into account. Stability analysis for this class of time stepping methods can only be carried out for simple cases where the coefficient matrix in Equation (2.106) is symmetric and positive-definite (i.e. self-adjoint problems Zienkiewicz and Taylor, 1994). Obviously, this will not be the case in most types of engineering flow problems. In practice, therefore, selection of appropriate values of 6 and time increment At is usually based on trial and error. Factors such as the nature of non-linearity of physical parameters and the type of elements used in the spatial discretization usually influence the selection of the values of 0 and At in a problem. 

Plot the probability density obtained from E in Problem 9 as a function of r, that is, simply square the function above with an appropriate scale factor as determined by trial and error. Comment on the relationship between your plot and the shell structure of the atom. 

One class of Al-based computational chemistry programs are de novo programs. These programs generally try to efficiently automate tedious tasks by using some rational criteria to guide a trial-and-error process. For example. 

Try quasi-Newton calculations starting from structures that look like what you expect the transition structure to be and that have no symmetry. This is a skill that improves as you become more familiar with the mechanisms involved, but requires some trial-and-error work even for the most experienced researchers. 

Once you are experienced at finding transition structures for a particular class of reactions, you will probably go directly to the technique that has been most reliable for those reactions. Until that time, the checklist above is our best advice for finding a transition structure with the least amount of work for the researcher and the computer. Regardless of experience, it is common to experience quite a bit of trial and error in finding transition structures. Even experienced researchers find that the way they have been regarding a reaction is often much more simplistic than the molecular motions actually involved. 

Next, by trial and error, we try to find a value for y such that sinh" y matches one of the 17/17 fractions in Table 2.2, say 17/17 = 0.80. This is easily done using either tables of sinh functions or the equation given in Table 2.1. The following results show that it is possible to place y within a range and then narrow that range without much difficulty. Remember, it is the inverse sinh values we are examining ... 

Additional trial and error manipulation of the data might yield agreement over a somewhat wider range of conditions with slightly modified parameters. 

The mechanism of oxidative dyeing involves a complex system of consecutive, competing, and autocatalytic reactions in which the final color depends on the efficiency with which the various couplers compete with one another for the available diimine. In addition, hydrolysis, oxidation, or polymerization of diimine may take place. Therefore, the color of a mixture caimot readily be predicted and involves trial and error. Though oxidation dyes produce fast colors, some off-shade fading does occur, particularly the development of a red tinge by the slow transformation of the blue indamine dye to a red phenazine dye. 

Historically, the discovery of one effective herbicide has led quickly to the preparation and screening of a family of imitative chemicals (3). Herbicide developers have traditionally used combinations of experience, art-based approaches, and intuitive appHcations of classical stmcture—activity relationships to imitate, increase, or make more selective the activity of the parent compound. This trial-and-error process depends on the costs and availabiUties of appropriate starting materials, ease of synthesis of usually inactive intermediates, and alterations of parent compound chemical properties by stepwise addition of substituents that have been effective in the development of other pesticides, eg, halogens or substituted amino groups. The reason a particular imitative compound works is seldom understood, and other pesticidal appHcations are not readily predictable. Novices in this traditional, quite random, process requite several years of training and experience in order to function productively. 

Static reliability models are used in preliminary analyses to determine necessary reliability levels for subsystems and components. A subsystem is a particular low level grouping of components. Some trial and error is usually necessary to obtain reasonable groupings for any particular system. Early identification of potential system weaknesses facilitates corrective action. 

In plotting on WeibuU paper, a downward concave plot implies a non2ero minimum life. Values for S < can be selected by trial and error. When they are subtracted from each /, a relatively straight line is produced. This essentially translates the three-parameter WeibuU distribution back to a two-parameter distribution. 

Experienced color matchers can achieve a good color match by trial and error without using any instmmentation. In some cases, however, this technique can be a lengthy process, and should the desired match be outside the color space defined by the available color standards, the technician might spend too much time just to determine that the match is not possible. To get the most cost-effective match using a low metamerism in the shortest possible time, the use of a computet color matching system is preferable. 

Some of the inherent advantages of the feedback control strategy are as follows regardless of the source or nature of the disturbance, the manipulated variable(s) adjusts to correct for the deviation from the setpoint when the deviation is detected the proper values of the manipulated variables are continually sought to balance the system by a trial-and-error approach no mathematical model of the process is required and the most often used feedback control algorithm (some form of proportional—integral—derivative control) is both robust and versatile. 

---