Prediction error

In so doing, we obtain the condition of maximum probability (or, more properly, minimum probable prediction error) for the entire distribution of events, that is, the most probable distribution. The minimization condition [condition (3-4)] requires that the sum of squares of the differences between p and all of the values xi be simultaneously as small as possible. We cannot change the xi, which are experimental measurements, so the problem becomes one of selecting the value of p that best satisfies condition (3-4). It is reasonable to suppose that p, subject to the minimization condition, will be the arithmetic mean, x = )/ > provided that... 

Equation (8-66) contains two types of design parameters that can also be used for tuning purposes. The move suppression factor 8 penalizes large control moves, while the weighting factors Wj allow the predicted errors to be weighed differently at each time step, if desired. 

Chapter 4 focuses on techniques which are applied to a new or existing system to optimize human performance or qualitatively predict errors. Chapter 5 shows how these teclmiques are applied to risk assessment, and also describes other techniques for the quantification of human error probabilities. Chapters 6 and 7 provide an overview of techniques for analyzing the underlying causes of incidents and accidents that have already occurred. 

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. 

FIGURE 4.16. Error Classification used in Predictive Error Analysis... 

In addition, the chapter will provide an overview of htunan reliability quantification techniques, and the relationship between these techniques and qualitative modeling. The chapter will also describe how human reliability is integrated into chemical process quantitative risk assessment (CPQRA). Both qualitative and quantitative techniques will be integrated within a framework called SPEAR (System for Predictive Error Analysis and Reduction). 

SYSTEM FOR PREDICTIVE ERROR ANALYSIS AND REDUCTION (SPEAR)... 

FIGURE 5.4. System for Predictive Error Analysis and Reduction. 

Predictive human error analysis (PHEA) is the process via which specific errors associated with tasks or task steps are predicted. The process also considers how these predicted errors might be recovered before they have negative consequences. The inputs to the process are the task structure and plans, as defined by the task analysis, and the results of the PIF analysis. The basic procedure of the PHEA is as follows ... 

Case study 3 illustrates the use of proactive techniques to analyze operator tasks, predict errors and develop methods to prevent an error occurring. Methods for the development of operating instructions and checklists are shown using the same chemical plant as in case study 2. 

PREDICTED ERROR DESCRIPTION PERFORMANCE-INFLUENCING FACTORS... 

It should also be acknowledged that in recent years computational quantum chemistry has achieved a number of predictions that have since been experimentelly confirmed (45-47). On the other hand, since numerous anomalies remain even within attempts to explain the properties of atoms in terms of quantum mechanics, the field of molecular quantum mechanics can hardly be regarded as resting on a firm foundation (48). Also, as many authors have pointed out, the vast majority of ab initio research judges its methods merely by comparison with experimental date and does not seek to establish internal criteria to predict error bounds theoretically (49-51). The message to chemical education must, therefore, be not to emphasize the power of quantum mechanics in chemistry and not to imply that it necessarily holds the final answers to difficult chemical questions (52). 

Even as the computational prediction error rate is reduced to acceptable levels, many cases will be encountered in which the predictions are indistinguishable to within error. In a scenario in which several different in silico designs are given equivalent but favorable activity predictions, the end user s medicinal experience may help decide which to promote to synthesis. The quality of that decision at this point will be strongly influenced by how easy it is to understand the different contributions to the computational predictions. Interpretability is thus critical for synergistically utilizing the experience of the end user. 

The identification of plant models has traditionally been done in the open-loop mode. The desire to minimize the production of the off-spec product during an open-loop identification test and to avoid the unstable open-loop dynamics of certain systems has increased the need to develop methodologies suitable for the system identification. Open-loop identification techniques are not directly applicable to closed-loop data due to correlation between process input (i.e., controller output) and unmeasured disturbances. Based on Prediction Error Method (PEM), several closed-loop identification methods have been presented Direct, Indirect, Joint Input-Output, and Two-Step Methods. 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

Fig. 36.10. Prediction error (RMSPE) as a function of model complexity (number of factors) obtained from leave-one-out cross-validation using PCR (o) and PLS ( ) regression.

TIME OBSERVED PREDICTED % ERROR RESIDUAL PLOT ... 

An optimization criterion for determining the output parameters and basis functions is to minimize the output prediction error and is common to all input-output modeling methods. The activation or basis functions used in data analysis methods may be broadly divided into the following two categories ... 

Ordinary least squares Linear projection Fixed shape, linear a, maximum squared correlation between projected inputs and output 0, minimum output prediction error... 

Nonlinear principal component Nonlinear projection, nonlocal Adaptive shape [a, ], minimum input prediction error... 

The g-statistic or square of predicted errors (SPE) is the sum of squares of the errors between the data and the estimates, a direct calculation of variability ... 

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