Model errors

Qualitative assessment Determine performance requirements Evaluate performance situation Specify performance objectives Identify potential human errors Model human performance... 

The analysis of accidents and disasters in real systems makes it clear that it is not sufficient to consider error and its effects purely from the perspective of individual human failures. Major accidents are almost always the result of multiple errors or combinations of single errors with preexisting vulnerable conditions (Wagenaar et al., 1990). Another perspective from which to define errors is in terms of when in the system life cycle they occur. In the following discussion of the definitions of human error, the initial focus will be from the engineering and the accident analysis perspective. More detailed consideration of the definitions of error will be deferred to later sections in this chapter where the various error models will be described in detail (see Sections 5 and 6). 

FIGURE 2.5. Dynamics of Generic Error Modeling System (GEMS) (adapted from Reason, 1990). 

Analysis of Incident Root Causes Using the Sequential Error Model... 

In the previous chapter, a comprehensive description was provided, from four complementary perspectives, of the process of how human errors arise during the tasks typically carried out in the chemical process industry (CPI). In other words, the primary concern was with the process of error causation. In this chapter the emphasis will be on the why of error causation. In terms of the system-induced error model presented in Chapter 1, errors can be seen as arising from the conjunction of an error inducing environment, the intrinsic error tendencies of the human and some initiating event which triggers the error sequence from this imstable situation (see Figure 1.5, Chapter 1). This error sequence may then go on to lead to an accident if no barrier or recovery process intervenes. Chapter 2 describes in detail the characteristics of the basic human error tendencies. Chapter 3 describes factors which combine with these tendencies to create the error-likely situation. These factors are called performance-influencing factors or PIFs. 

There will be strong emphasis on the collection of data on possible causal factors that could have contributed to an accident. The specific data that are collected may be based on an error model such as that shown in Figure 6.2. However, this model will usually be modified depending upon the extent to which it fits the data collected over a period of time. The systems approach is therefore dynamic rather than static. 

It should be emphasized that it is usually necessary to develop the data collection specification on an incremental basis and to utilize feedback from the system to modify the initial model relating causal factors to error types. This dynamic approach provides the best answer to the problem that no predefined error model will be applicable to every situation. 

Watters, R. L., Jr., Carroll, R. J., and Spiegelman, C. H., Error Modeling and Confidence Interval Estimation for Inductively Coupled Plasma Calibration Curves, Anal. Chem. 59, 1987, 1639-1643. 

The application of optimisation techniques for parameter estimation requires a useful statistical criterion (e.g., least-squares). A very important criterion in non-linear parameter estimation is the likelihood or probability density function. This can be combined with an error model which allows the errors to be a function of the measured value. A simple but flexible and useful error model is used in SIMUSOLV (Steiner et al., 1986 Burt, 1989). 

Finally, the contribution to error, that is specific to this laboratory, especially when compared to other laboratories, is not known. On the other hand, there are some very interesting and noteworthy observations to be made from the error study. First, repeated attempts to include polymer type and temperature into the error model failed. This observation implies that temperature control of the device is independent of temperature and that any fluctuation is the same throughout the interval that was used in this study. Secondly, repeated attempts to include sample type into the analysis also failed, implying that the estimated variances were independent not only of temperature but of material. This result suggests very strongly that the variances are due to the magnitude of the measurement, the device that was used, and our own set of laboratory circumstances. 

Deterministic trend models are based on the assumption that the trend of a time series can be approximated closely by simple mathematical functions of time over the entire span of the series. The most common representation of a deterministic trend is by means of polynomials or of transcendental functions. The time series from which the trend is to be identified is assumed to be generated by a nonstationary process where the nonstationarity results from a deterministic trend. A classical model is the regression or error model (Anderson, 1971) where the observed series is treated as the sum of a systematic part or trend and a random part or irregular. This model can be written as... 

Statistical Prediction Errors (Model and Sample Diagnostic) Figure 5-28 shows the stss tical prediction errors for all four components for the samples in the validat n set. For MCB and ODCB the maximum value is —0.004 and for EB and C5IM the maximum value is —0.01. These errors are small compared to thecsncentration ranges. 

Statistical Prediction Errors (Model and Sample Diag Jostic) Uncertainties in the concentrations can be estimated because the predicted concentrations are regression coefficients from a linear regression (see Equations 5.7-5.10). These are referred to as statistical prediction errors to distinguish them from simple concentration residuals (c — c). Tlie statistical prediction errors are calculated for one prediction sample as... 

Statistical Prediction Errors (Model and Sample Diagnostic) From the S matrix it is possible to predict all four components (caustic, salt, water concentration, and temperature). However, in this application the interest is only in caustic and, therefore, only the results for this component are presented. The statistical prediction errors for the caustic concentration for the validation data vary from 0.006 to 0.028 wt.% (see Figure 5-54). The goal is to predict the caustic concentration to 0.1 wt.% (lo), and the statistical prediction errors indicate that the precision of the method is adequate. Also, there do not appear to be any sample(s) that have an unusual error when compared to the rest of the samples. 

Figure 2. CIO volume mixing ratio profiles across the vortex edge as measured by the ASUR instrument (solid line) on March 6, 1996, compared to results of the SI.IMCAT 3-D model (dashed line, rectangles) for identical positions at 12 UT. Also indicated are average times, positions, solar zenith angles, and 475 K-PV s for the individual measurements. The thick error bars represent the relevant statistical errors due to measurement noise, the thin dotted error bars include also the error due to the limited altitude resolution (the so-called null-space error). Modelled and measured data are in relatively good agreement inside, at the edge, and outside the Arctic polar vortex.

The residual variability describes the extent of deviation between the observed and the model predicted value, including IIV and IOV. Deviations might be caused by errors in the documentation of the dosing and blood sampling times, analytical errors, misspecification in the models and other factors. The most common error models describing the residual variability are presented in the following. 

This error model applies if the deviations from the individual predictions are increasing proportionally with increasing observations (i.e. the relative deviations... 

The combination of all submodels together results in a population model which can be described by the following equation, where exemplarily an additive error model is used ... 

A particular type of within-array analysis is the so called self-self hybridization [9], in which two dyes are used to label the same RNA species, so that the fluorescence values acquired by the scanner for each gene is supposed to be the same for the two channels. This approach allows the identification of the variability which depends only on systematic biases or on stochastic processes. Some authors suggest the performance of some self-self hybridization for each experiment, to establish an error model used to correct data derived from experimental measurements. 

Then, given a model for data from a specific drug in a sample from a population, mixed-effect modeling produces estimates for the complete statistical distribution of the pharmacokinetic-dynamic parameters in the population. Especially, the variance in the pharmacokinetic-dynamic parameter distributions is a measure of the extent of inherent interindividual variability for the particular drug in that population (adults, neonates, etc.). The distribution of residual errors in the observations, with respect to the mean pharmacokinetic or pharmacodynamic model, reflects measurement or assay error, model misspecification, and, more rarely, temporal dependence of the parameters. 

The error model used in the minimization is based on the hypothesis that the residuals have zero mean and are normally distributed. The first is easily checked, the latter is only possible when sufficient data points are available and a distribution histogram can be constructed. An adequate model also follows the experimental data well, so if the residuals are plotted as a function of the dependent or independent variable(s) a random distribution around zero should be observed. Nonrandom trends in the residuals mean that systematic deviations exist and indicate that the model is not completely able to follow the course of the experimental data, as a good model should do. This residual trending can also be evaluated numerically be correlation calculations, but visual inspection is much more powerful. An example is given in Fig. 12 for the initial rate data of the metathesis of propene into ethene and 2-butenc [60], One expression was based on a dual-site Langmuir-Hinshelwood model, whereas the other... 

Figure 6.1 Safety culture, human error model, and response to incidents based on Lucas (1992) and Westrum (1988).

Supporting the safety staff is necessary to fully appreciate the cognitive backgrounds of the human error model, and to ensure an objective and uniform approach in describing, classifying and interpreting the reported events, ... 

Reason, J.T. (1987). Generic Error-Modelling Systems (GEMS) a cognitive framework for locating human error forms. In J. Rasmussen, K. Duncan and J. Leplat (eds). New Technology and Human Error. Wiley. New York. 

An important feature of the replication-mutation kinetics of Eq. (2) is its straightforward accessibility to justifiable model assumptions. As an example we discuss the uniform error model [18,19] This refers to a molecule which is reproduced sequentially, i.e. digit by digit from one end of the (linear) polymer to the other. The basic assumption is that the accuracy of replication is independent of the particular site and the nature of the monomer at this position. Then, the frequency of mutation depends exclusively on the number of monomers that have to be exchanged in order to mutate from 4 to Ij, which are counted by the Hamming distance of the two strings, d(Ij,Ik) ... 

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