Statistical data of disturbances

It was informed that 228 HEAs were damaged in 129 houses from 1987 to 1991. Among them, 49% for TV/video antennas, 18% for communication 

Number of damaged home electric appliances (HEAs) (a) 1987-1991 and (b) 1996-1997, 2004-2005, and 2006. 

Ratio of connecting circuits of damaged home electric appliances. 

Expenses (insurance) paid to damages. (From lEEJ WG, The fact of lightning disturbances in a highly advanced ICT society and the sut ect to be investigated, lEE. Tech. Report 902,2002.) 

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A third source of uncertainty is the occurrence of rare or unique events in the measurement, such as an incorrect reading by the observer, or a chance disturbance in the equipment. Such errors can often produce large deviations from the other readings, and are hence termed outliers . There are statistical tests for recognising such data points, but the occurrence of outliers can be a real problem in statistical data analysis. 

Set of various disturbances is obtained from different values of disturbance parameters. To simulate scenarios of disturbances, the probabilities of values occurrence are needed. These probabilities should be assessed by experts and/or obtained from statistical data. Probability matrix of disturbance parameters should be obtained (Table 6). 

Given a space G, let g (x) be the closest model in G to the real function, fix). As it is shown in Appendbc 1, if /e G and the L°° error measure [Eq. (4)] is used, the real function is also the best function in G, g = f, independently of the statistics of the noise and as long as the noise is symmetrically bounded. In contrast, for the measure [Eq. (3)], the real function is not the best model in G if the noise is not zero-mean. This is a very important observation considering the fact that in many applications (e.g., process control), the data are corrupted by non-zero-mean (load) disturbances, in which cases, the error measure will fail to retrieve the real function even with infinite data. On the other hand, as it is also explained in Appendix 1, if f G (which is the most probable case), closeness of the real and best functions, fix) and g (x), respectively, is guaranteed only in the metric that is used in the definition of lig). That is, if lig) is given by Eq. (3), g ix) can be close to fix) only in the L -sense and similarly for the L definition of lig). As is clear,... 

Before we can start to develop a model we also have to decide how to interpret the behavior observed in Fig. 2.1. The variations in insulin and glucose concentrations could be generated by a damped oscillatory system that was continuously excited by external perturbations (e.g. through interaction with the pulsatile release of other hormones). However, the variations could also represent a disturbed self-sustained oscillation, or they could be an example of deterministic chaos. Here, it is important to realize that, with a sampling period of 10 min over the considered periods of 20-24 h, the number of data points are insufficient for any statistical analysis to distinguish between the possible modes. We need to make a choice and, in the present case, our choice is to consider the insulin-glucose regulation to operate... 

Clonazepam is widely used for the treatment of sleep disturbances related to post-traumatic stress disorder, despite very limited published data supporting its use for this indication. In a randomized, single-blind, placebo-controlled, crossover trial of clonazepam 1 mg at bedtime for 1 week followed by 2 mg at bedtime for 1 week in six patients with combat-related post-traumatic stress disorder there were no statistically significant differences between clonazepam and placebo (4). Adverse effects of clonazepam were generally mild and essentially indiscernible from those attributed to placebo. Only one patient elected to continue taking clonazepam at the end of the trial. The small sample size was a significant limitation of the study. 

Contribution plots presented in Section 7.4 provide an indirect approach to fault diagnosis by first determining process variables that have inflated the detection statistics. These variables are then related to equipment and disturbances. A direct approach would associate the trends in process data to faults explicitly. HMMs discussed in the first three sections of this chapter is one way of implementing this approach. Use of statistical discriminant analysis and classification techniques discussed in this section and in Section 7.6 provides alternative methods for implementing direct fault diagnosis. 

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