Error analysis, application

Chapter 7, Case Studies, uses examples that illustrate the application of the various error analysis and reduction techniques to real world process industry cases. 

The application of human error analysis (HEA) techniques is to predict possible errors that may occur in a task. The next stage of error analysis is to identify error recovery possibilities implicit within the task, and to specify possible... 

The other main application area for predictive error analysis is in chemical process quantitative risk assessment (CPQRA) as a means of identifying human errors with significant risk consequences. In most cases, the generation of error modes in CPQRA is a somewhat unsystematic process, since it only considers errors that involve the failure to perform some pre-specified function, usually in an emergency (e.g., responding to an alarm within a time interval). The fact that errors of commission can arise as a result of diagnostic failures, or that poor interface design or procedures can also induce errors is rarely considered as part of CPQRA. However, this may be due to the fact that HEA techniques are not widely known in the chemical industry. The application of error analysis in CPQRA will be discussed further in Chapter 5. 

Because the staff were consulted extensively during the application of task analysis and error analysis methods, the information presented on the graphic display in Figure 7.17 corresponds with their own information needs. 

A. J. Jerri, Integral and Discrete Transforms with Applications and Error Analysis (1992)... 

Application of the test substance to the test system is without doubt the most critical step of the residue field trial. Under-application may be corrected, if possible and if approved by the Study Director, by making a follow-up application if the error becomes known shortly after the application has been made. Over-application errors can usually only be corrected by starting the trial again. The Study Director must be contacted as soon as an error of this nature is detected. Immediate communication allows for the most feasible options to be considered in resolving the error. If application errors are not detected at the time of the application, the samples from such a trial can easily become the source of undesirable variability when the final analysis results are known. Because the application is critical, the PI must calculate and verify the data that will constitute the application information for the trial. If the test substance weight, the spray volume, the delivery rate, the size of the plot, and the travel speed for the application are carefully determined and then validated prior to the application, problems will seldom arise. With the advent of new tools such as computers and hand-held calculators, the errors traditionally associated with applications to small plot trials should be minimized in the future. The following paragraphs outline some of the important considerations for each of the phases of the application. 

Human error analysis This method is used to identify the parts and the procedures of a process that have a higher than normal probability of human error. Control panel layout is an excellent application for human error analysis because a control panel can be designed in such a fashion that human error is inevitable. 

Factor analysis extracts information from the sample data set (e.g., IR spectra) and does not rely on reference minerals. However, because abstract factors have no physical meaning, reference minerals may be needed in target transformations or other procedures to extract mineralogical information. One valuable piece of information obtainable without the use of extraneous data is the number of components required to represent the data within experimental error. Reported applications of factor analysis to mineralogy by FTIR are few (12). However, one commercial laboratory is offering routine FTIR mineral analyses to the petroleum industry, based on related methods (22). 

THOMPSON and MAGUIRE [1993] have compared sampling and analytical error for the example of trace metals in soils. They demonstrate that to obtain valuable information on the magnitude of sampling and analytical errors the application of robust nested analysis of variance is to be preferred to classical parametric analysis of variance. 

The activation of catalysts has been studied frequently, but mainly empirically and less systematically. Very often, in particular in academic research, the activation is performed under less defined conditions with respect to temperature control and gas-phase environment. Instead of parameter variation based on trial and error, the application of powerful standard techniques, like thermal analysis or temperature-programmed reaction, and the complementary use of in situ spectroscopic methods will contribute to a deeper understanding of activation processes. 

The most common error in application of this method lies in a lack of appreciation of the minimum statistical requirements involved. Thus, one needs to have about five well-chosen compounds for every variable term in a Hansch analysis in order to feel confident about the results. For example, an equation such as Equation 2 above should be derived from 10 or more compounds, and one such as Equation 3, from 15 or more examples. A smaller number of examples per term may lead to useful results, but one cannot often support these results by statistics. A frequent abuse is seen when a large number of variable terms are used in a complex equation (four or more terms) which was derived from only 10 or 12 examples. The statistician would prefer to have 15 to 20 more compounds than the degrees of freedom in the resulting equation not often is this luxury met. 

Normally, CRMs are used for the verification of accuracy, precision, and reliability of the results of analysis carried out in a laboratory (i.e., for checking the quality of its routine work). The CRM is analyzed at specific intervals and the results obtained are used to draw control charts (e.g., Shewhart chart) [63]. This allows visual assessment of the measurement system, the emergence of systematic errors, etc. Application of CRMs for the constmction of control charts is advantagous because of the homogeneity and stability of CRMs, and the ability to assess the accuracy of the results obtained in the laboratory by comparison with the certified value. 

As we checked in practical applications, the evolution of the collective variables can be modelled with a Langevin equation also for the Lagrangian metadynamics introduced in Sect. 2.1. Therefore, the error analysis performed in this section can be applied also for Lagrangian metadynamics. 

The treatment of statistics is focused on explicit applications of both linear and nonlinear least-squares methods, rather than on the alphabet soup (F, Q, R, T, etc.) of available tests. However, within that rather narrow framework, many practical aspects of error analysis and curve fitting are considered. They are chosen to illustrate the now almost two centuries old dictum of de Laplace that the theory of probability is merely common sense confirmed by calculation. 

Application of a simple error analysis to Eq. V.27 shows that the... 

Where A, B and R are matrices, reply is an error code and OK is a satisfactory completion code (zero, maybe), matrixjnultiply does the required manipulations and returns OK or an error code which is analysed by error out. However, in most of our applications, this is a little over-cautious and constant error analysis will prove unnecessary. 

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