Simple Event Example

Suppose a safety manager collected data from accident reports involving back injuries. Over a three-year period, 300 reports were filed, of which 18 involved back injuries. Using the simple event formula, the probability of randomly selecting a report for which a back injury was recorded from the 300 reports filed is determined by  

P(A) = 18 / 300 =. 06 or a 6% chance of selecting a report involving a back injury from the 300 filed. 

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To explain an event is to give an account of why it happened. Usually, and always ultimately, this takes the form of citing an earlier event as the cause of the event we want to explain, together with some account of the causal mechanism connecting the two events. Here is a simple, paradigmatic example. We want to know why someone changed his mind about a job he... 

In real-life situations, the problems and applications likely to be encountered are not simple textbook examples. You must be able to observe an event, hypothesize a cause, and then test this hypothesis. You must be able to carry forward what has been learned in class to new, different situations. 

The answer depends on the student s responses/examples. Chemistry is not just a set of facts that have to be memorized. To be successful in chemistry, you have to be able to apply what you have learned to new situations, new phenomena, new experiments. Rather than just learning a list of fects or studying someone else s solution to a problem, your instmctor hopes you win learn hew to solve problems yourself, so that you will be able to apply what you have learned in future circumstances. In real-life situations, the problems and applications likely to be encountered are not simple textbook examples. You must be able to observe an event, hypothesize a cause, and then test this hypothesis. You must be able to carry what has been learned in class forward to new, different situations. 

In analyzes of risk of adverse events event tree or fault tree may be used for the case of the railway system. In (Albrechtsen Hokstad 2003) this kind of analysis has been extended to include the risk influencing factors. The issue has been shown on the example of a single-track line, for which the peak event is the collision of two trains coming from the opposite directions. An analysis of the factors affecting the risk shows the relationships and sequences of cause and effect going beyond a simple event tree analysis. In the studies case it... 

Perhaps the most fascinating detail is the surface reconstruction that occurs with CO adsorption (see Refs. 311 and 312 for more general discussions of chemisorption-induced reconstructions of metal surfaces). As shown in Fig. XVI-8, for example, the Pt(lOO) bare surface reconstructs itself to a hexagonal pattern, but on CO adsorption this reconstruction is lifted [306] CO adsorption on Pd( 110) reconstructs the surface to a missing-row pattern [309]. These reconstructions are reversible and as a result, oscillatory behavior can be observed. Returning to the Pt(lOO) case, as CO is adsorbed patches of the simple 1 x 1 structure (the structure of an undistorted (100) face) form. Oxygen adsorbs on any bare 1 x 1 spots, reacts with adjacent CO to remove it as CO2, and at a certain point, the surface reverts to toe hexagonal stmcture. The presumed sequence of events is shown in Fig. XVIII-28. 

A simple example of fault tree analysis applied to an internal combustion engine (Figure 3.4.4-2) is the Figure 3.4.4-3 fault tree diagram of how the undesired event "Low Cylinder Compression" may occur. The Boolean equation of this fault tree is in the caption of Figure 3.4.4-3. Let the occurrence of these events be represented by a 7, non-occurrence by 0, and consider that there may he a long history of occurrences with this engine. Several sets of occunrence.s (trials) are... 

From a human reliability perspective, a number of interesting points arise from this example. A simple calculation shows that the frequency of a major release (3.2 x lO"" per year) is dominated by human errors. The major contribution to this frequency is the frequency of a spill during truck unloading (3 X10" per year). An examination of the fault tree for this event shows that this frequency is dominated by event B15 Insufficient volume in tank to imload truck, and B16 Failure of, or ignoring LIA-1. Of these events, B15 could be due to a prior human error, and B16 would be a combination of instrument failure and human error. (Note however, that we are not necessarily assigning the causes of the errors solely to the operator. The role of management influences on error will be discussed later.) Apart from the dominant sequence discussed above, human-caused failures are likely to occur throughout the fault tree. It is usually the case that human error dominates a risk assessment, if it is properly considered in the analysis. This is illustrated in Bellamy et al. (1986) with an example from the analysis of an offshore lifeboat system. 

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... 

Although blood pressure control follows Ohm s law and seems to be simple, it underlies a complex circuit of interrelated systems. Hence, numerous physiologic systems that have pleiotropic effects and interact in complex fashion have been found to modulate blood pressure. Because of their number and complexity it is beyond the scope of the current account to cover all mechanisms and feedback circuits involved in blood pressure control. Rather, an overview of the clinically most relevant ones is presented. These systems include the heart, the blood vessels, the extracellular volume, the kidneys, the nervous system, a variety of humoral factors, and molecular events at the cellular level. They are intertwined to maintain adequate tissue perfusion and nutrition. Normal blood pressure control can be related to cardiac output and the total peripheral resistance. The stroke volume and the heart rate determine cardiac output. Each cycle of cardiac contraction propels a bolus of about 70 ml blood into the systemic arterial system. As one example of the interaction of these multiple systems, the stroke volume is dependent in part on intravascular volume regulated by the kidneys as well as on myocardial contractility. The latter is, in turn, a complex function involving sympathetic and parasympathetic control of heart rate intrinsic activity of the cardiac conduction system complex membrane transport and cellular events requiring influx of calcium, which lead to myocardial fibre shortening and relaxation and affects the humoral substances (e.g., catecholamines) in stimulation heart rate and myocardial fibre tension. 

The Merrill and Hamrin criterion was derived for a first-order reaction. It should apply reasonably well to other simple reactions, but reactions exist that are quite sensitive to diffusion. Examples include the decomposition of free-radical initiators where a few initial events can cause a large number of propagation reactions, and coupling or cross-linking reactions where a few events can have a large effect on product properties. 

Often you want to redefine an already existing variable within a SAS DATA step. As simple as this may sound, it can lead to unexpected results if not done carefully. The following example displays some unexpected behavior that may occur when you redefine a variable within a DATA step. In this example you want to flag the subject who had the Fatal MI adverse event as having died (death =1). 

The fault trees for even a simple process unit will be complex, with many branches. Fault trees are used to make a quantitive assessment of the likelihood of failure of a system, using data on the reliability of the individual components of the system. For example, if the following figures represent an estimate of the probability of the events... 

The probability of a given event is often represented as a function of a random variable, say, x. The random variable can take on various discrete values Xj with probabilities given by W x-,). The variable jt is then an independent variable that describes a random or stochastic process. The function W(Xf) in simple examples is discontinuous, although as the number of samples increase, it approaches a denumerable infinity. 

Semantic uncertainty is the type of uncertainty for which we shall need fuzzy logic. Expressed by phrases such as "acidic" or "much weaker," this is imprecision in the description of an event, state, or object rather than its measurement. Fuzzy logic offers a way to make credible deductions from uncertain statements. We shall illustrate this with a simple example. 

The effect of the bulk solution temperature lies primarily in its influence on the bubble content before collapse. With increasing temperature, in general, sonochemical reaction rates are slower. This reflects the dramatic influence which solvent vapor pressure has on the cavitation event the greater the solvent vapor pressure found within a bubble prior to collapse, the less effective the collapse. In fact, one can quantitate this relationship rather well (89). From simple hydrodynamic models of the cavitation process, Neppiras, for example, derives (26) the peak temperature generated during collapse of a gas-filled cavity as... 

Fig. 4.11. Proposed RNA life. The membrane was made by the production of oils. The monomers were made from basic available forms of elements, H20, C02, NH3 and HP042. The source of energy was, for example, an energised Fe/S particle trapped on the membrane. The system reproduces when the duplex polymer, say [ATJ ATJ]2, is released as two single strands only for each to be trapped in a new synthesising vesicle. The improbability of such a scheme emerging is very high, yet some such event happened. Note that it is not necessary to have a simple [ATJ]n unit and a variety of units of any ordering A and U is reproducible with fidelity on second copying.

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