Error Representations

In this section, the results of the most comprehensive (usually the most recent) error analyses are presented and discussed for every error. An effort is made to present the results graphically, i.e., in the form of applicability diagrams that are easily usable by experimentalists. As the error is usually a function of many parameters, simple (two-dimensional) representation is possible only by using grouped (usually dimensionless) parameters occasionally, however, this results in some loss of generality. 

When the cathodic reaction is completely under mass-transport control, the current-density-polarization relation can be expressed as 

The intermediate case, when neither Eq. (1) nor Eq. (39) is applicable, results in curved Tafel plots. Consequently, the extrapolation technique for the determination of the corrosion current density can give erroneous results. Quantitative analysis of this error possibility has not been published, but qualitative discussions of the mixed-control Tafel plots have been given by Stern.  

For the idealized case, this error can be represented graphically as a function of two dimensionless parameters, b lb and /corrA/ using Eq. (15), as shown in Fig. 4. The error is directly proportional to / corrAA u relation that is intuitively expected since 

It is worth noting that the error is so small at small 6 /6 values that, for many practical corrosion measurement situations, it can be considered negligible. The maximum error is only 20% at Z /6 = 0.25, and 33% at 6 /6 = 0.5. While a complete generalization cannot be made, the Tafel slope of the anodic reaction in a corroding system is very often considerably smaller than the Tafel slope of the cathodic reaction. Typically, the Tafel slope of an anodic metal dissolution reaction is in the range of 0.03 to 0.06 while common cathodic reactions occurring during 

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Human-error representation is fully integrated with other safety analysis asp>ects... 

At low pressures, it is often permissible to neglect nonidealities of the vapor phase. If these nonidealities are not negligible, they can have the effect of introducing a nonrandom trend into the plotted residuals similar to that introduced by systematic error. Experience here has shown that application of vapor-phase corrections for nonidealities gives a better representation of the data by the model, oven when these corrections... 

Finally, we consider the complete molecular Hamiltonian which contains not only temis depending on the electron spin, but also temis depending on the nuclear spin / (see chapter 7 of [1]). This Hamiltonian conmiutes with the components of Pgiven in (equation Al.4,1). The diagonalization of the matrix representation of the complete molecular Hamiltonian proceeds as described in section Al.4,1.1. The theory of rotational synnnetry is an extensive subject and we have only scratched the surface here. A relatively new book, which is concemed with molecules, is by Zare [6] (see [7] for the solutions to all the problems in [6] and a list of the errors). This book describes, for example, the method for obtaining the fimctioiis ... 

RumeUiart D E, G W Hinton and R J Williams 1986. Learning Representations by Back-propagatin Errors. Nature 323 533-536. 

Error . Writing the potential, V(x), in the momentum representation is not quite as straightforward. The relationship between position and momentum is realized in their... 

A more useful representation of uncertainty is to consider the effect of indeterminate errors on the predicted slope and intercept. The standard deviation of the slope and intercept are given as... 

The truncation error in the first two expressions is proportional to Ax, and the methods are said to be first-order. The truncation error in the third expression is proportional to Ax, and the method is said to be second-order. Usually the last equation is used to insure the best accuracy. The finite difference representation of the second derivative is ... 

Variations in measurable properties existing in the bulk material being sampled are the underlying basis for samphng theory. For samples that correctly lead to valid analysis results (of chemical composition, ash, or moisture as examples), a fundamental theoiy of sampling is applied. The fundamental theoiy as developed by Gy (see references) employs descriptive terms reflecting material properties to calculate a minimum quantity to achieve specified sampling error. Estimates of minimum quantity assumes completely mixed material. Each quantity of equal mass withdrawn provides equivalent representation of the bulk. 

Usually, simplified representations of the data are used to obtain preliminary structures. Thus, lower and upper bounds on the interproton distances are estimated from the NOE intensity [10], using appropriate reference distances for calibration. The bounds should include the estimates of the cumulative error due to all sources such as peak integration errors, spin diffusion, and internal dynamics. 

For a sequenee of reaetion steps two more eoneepts will be used in kinetics, besides the previous rules for single reaetions. One is the steady-state approximation and the seeond is the rate limiting step eoneept. These two are in strict sense incompatible, yet assumption of both causes little error. Both were explained on Figure 6.1.1 Boudart (1968) credits Kenzi Tamaru with the graphical representation of reaction sequences. Here this will be used quantitatively on a logarithmic scale. 

Rumelhart, D.E., Hinton, G.E. and Williams, R.J. (1986) Learning internal representations by error propagation. In Parallel Distributed Processing, Rumelhart, D.E. and McClelland, J.L. (eds.), M.I.T. Press, Cambridge, Mass. 

This allows for the equivalence between crossed cylinders and the particle on a plane problem. Likewise, the mechanics of two spheres can be described by an equivalently radiused particle-on-a-plane problem. The combination of moduli and the use of an effective radius greatly simplifies the computational representation and allows all the cases to be represented by the same formula. On the other hand, it opens the possibility of factors of two errors if the formula are used without realizing that such combinations have been made. Readers are cautioned to be aware of these issues in the formulae that follow. 

The human-machine interface (usually abbreviated to interface) is a major focus of interest for the HF/E approach to the reduction of human error. A representation of the interface in a CPI context is provided in Figure 2.2. The interface is the boimdary across which information from the process is transduced by sensors and then displayed in a form that can be utilized by the... 

Figure 4.4 gives an example of an OAET for events that might follow release of gas from a furnace. In this example a gas leak is the initiating event and an explosion is the final hazard. Each task in the sequence is represented by a node in the tree structure. The possible outcomes of the task are depicted as "success" or "failure" paths leading out of the node. This method of task representation does not consider how alternative actions (errors of commission) could give rise to other critical situations. To overcome such problems, separate OAETs must be constructed to model each particular error of commission. 

The intention of this chapter has been to provide an overview of analytical methods for predicting and reducing human error in CPI tasks. The data collection methods and ergonomics checklists are useful in generating operational data about the characteristics of the task, the skills and experience required, and the interaction between the worker and the task. Task analysis methods organize these data into a coherent description or representation of the objectives and work methods required to carry out the task. This task description is subsequently utilized in human error analysis methods to examine the possible errors that can occur during a task. 

This stage involves representing the structure of the tasks in which errors with severe consequences could occur, in a manner that allows the probabilities of these consequences to be generated. The usual forms of representation are event trees and fault trees. 

If the results of the qualitative analysis are to be used as a starting-point for quantification, they need to be represented in an appropriate form. The form of representation can be a fault tree, as shown in Figure 5.2, or an event tree (see Bellamy et al., 1986). The event tree has traditionally been used to model simple tasks at the level of individual task steps, for example in the THERP (Technique for Human Error Rate Prediction) method for human reliability... 

The decomposition approach is used, it is necessary to represent the way in which the various task elements and other possible failures are combined to give the failure probability of the task as a whole. Generally, the most common form of representation is the event tree (see Section 5.7). This is the basis for THERP, which will be described in the next section. Fault trees are only used when discrete human error probabilities are combined with hardware failure probabiliHes in applications such as CPQRA (see Figure 5.2). 

PROBLEM DEFINITION, QUALITATIVE ERROR PREDICTION AND REPRESENTATION. The recommended problem definition and qualitative error prediction approach for use with SLIM has been described in Section 5.3.1 and 5.3.2. The fact that PIFs are explicitly assessed as part of this approach to qualitative error prediction means that a large proportion of the data requirements for SLIM are already available prior to quantification. SLIM usually quantifies tasks at whatever level calibration data are available, that is, it does not need to perform quantification by combining together task element probabilities from a data base. SLIM can therefore be used for the global quantification of tasks. Task elements quantified by SLIM may also be combined together using event trees similar to those used in THERP. 

The case study has documented the investigation and root cause analysis process applied to the hydrocarbon explosion that initiated the Piper Alpha incident. The case study serves to illustrate the use of the STEP technique, which provides a clear graphical representation of the agents and events involved in the incident process. The case study also demonstrates the identification of the critical events in the sequence which significantly influenced the outcome of the incident. Finally the root causes of these critical events were determined. This allows the analyst to evaluate why they occurred and indicated areas to be addressed in developing effechve error reduchon strategies. 

An event tree provides a diagrammatic representation of event sequences tliat begin with a so-called initiating event and terminate in one or more undesirable consequences. In contrast to a fault tree, which works backward from an undesirable consequence to possible causes, an event tree works forward from the initiating event to possible undesirable consequences. The initiating event may be equipment failure, human error, power failure, or some other event that has the potential for adversely affecting an ongoing process. 

The increased speed of structure determination necessary for the structural genomics projects makes an independent validation of the structures (by comparison to expected properties) particularly important. Structure validation helps to correct obvious errors (e.g. in the covalent structure) and leads to a more standardised representation of structural data, e.g. by agreeing on a common atom name nomenclature. The knowledge of the structure quality is a prerequisite for further use of the structure, e.g. in molecular modelling or drug design. 

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