Probability and Frequency

Frequency with the dimensions of per unit time, ranges from zero to infinity and means the number of occurrences per time interval. Probability is dimensionless, ranges from zero to one, and has several definitions. The confusion between frequency and probability arises from the need to determine the probability that a given system will fail in a year. Such a calculation of probability explicitly considers the time interval and, hence, is frequency. However, considerable care must be used to ensure that calculations are dimensionally correct as well as obeying the appropriate algebra. Three interpretations of the meaning of probability are  

Numbe r of ways a result can occur The total number of wavs all results can occur 

Equation 2.3-1 expresses the Laplacian meaning of probability. It is applicable when the number of result,s are countable and 

The disadvantage of Laplacian probability is its use is limited to calculating the probability of processes for which all outcomes are known and equally probable. This eliminates the use of Laplacian probability for determining the probability of process system failure. 

This is experimental probability determined from operahng experience by counting the number of lim n 

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The accident sequence frequencies are quantified by linking the system fault tree models together as indicated by the event trees for the accident sequence and quantified with plant-specific data to estimate initiator frequencies and component/human failure rates. The SETS code solves the fault trees for their minimal cutsets the TEMAC code quantitatively evaluates ihe cm sols and provides best estimates of component/event probabilities and frequencies. 

The overall frequency of the top event is calculated by combining together the constituent probabilities and frequencies of the various events in the fault tree using the appropriate logical relationships described by the AND and OR gates (the detailed calculation is given in CCPS, 1989b). 

The initiating events are the causes of the incident, and the top events are the final outcomes. The two methods are related in that the top events for fault trees are the initiating events for the event trees. Both are used together to produce a complete picture of an incident, from its initiating causes all the way to its final outcome. Probabilities and frequencies are attached to these diagrams. 

In discussing uncertainty, it is important to distinguish efforts to quantify uncertainty from the related and oft confused endeavor of theorizing about the nature and extent of frequencies in a population or series. Although uncertainties may often be reasonably calculated or based on frequencies (i.e., statistical uncertainty), frequencies may be of interest on their own (e.g., population variability), while some uncertainties are not frequency based (e.g., model uncertainty). As depicted in Figure 3 the difference between probability and frequency is often a matter of context. The same distribution might be used to describe the frequency of an event when the question is about a population, or serve as the basis... 

However, in many applications, the reduction in vent header and protective relief equipment, together with the lower probability and frequency of discharge, can justify this technique. The author has experienced one case with a high-pressure, close-boiling system where the reduction in vent header and protective equipment cost was by itself sufficient to pay for the required increase in column design pressure. 

Likelihood is the measure of the expected probability and frequency of an event occurring (i.e., a 1 percent chance, a frequency of 0.01 events/year). The factors that comprise the eshmate of likelihood include ... 

In order to use fault trees for the quantitative determination of the probability of occurrence of the top event, probabilities and frequencies are attributed to the individual states and malfunctioning components. But also in this case certain rules must be obeyed ... 

The distribntor effect can be quite significant such that the gas-liquid mass transfer correlation can vary by up to a factor of 2 (Lau et al., 2004). The extent to which the gas distributor affects gas holdup and bubble dynamics depends on the BC geometry and snperficial gas velocity. The taller the column is, the smaller the influence of the initial bubble diameter will be on the global gas holdup. A higher superficial gas velocity increases the probability and frequency of bubble collisions and decreases the effect of the initial bubble diameter and gas distributor design. 

Probability and frequency of random hardware failure Numerical ranges are specified for each SIL. The designed system probabihty is calculated using component failure mode and failure rate data. 

Probability and frequency of loss events are only half of the risk picture. The severity of the loss event must also be considered. Severity refers to the magnitude of the loss in a given period of time. When used as part of the risk assessment tool in system safety. 

If the number of gradations for probability, frequency of exposure, or severity is excessive, distinctions between them are difficult to make. Five gradations were chosen for probability and frequency of exposure for severity, there are four. 

Table 25 displays The Risk Scoring System. It shows the various combinations with respect to incident probability, the frequency of exposure, and the severity of consequences how probability and frequency ratings are totaled to become mid-scores and the final score, arrived at by multiplying the severity score by the mid-score. 

The probability and frequency of each occurrence, and the severity of the outcome-including an estimation of the maximum potential loss-will also need to be incorporated into any meaningful evaluation. 

Epistemic uncertainty is uncertainty that comes from lack of knowledge. This lack of knowledge comes from many sources, for example, inadequate understanding of the processes, incomplete knowledge of the phenomena, imprecise evaluation of the related charactetistics, etc. Epistemic uncertainties affect the values of the probabilities and frequencies of the events included in the accident scenarios, such as mechanical failure and repair rate, probability of failure on demand for a control system, or human error. There are three different cases in this regard ... 

Calculate probability and frequency of branch failure in power grid... 

The data is usually composed of ground motion records, which are used to develop probabilistic parametric models for fragility curves or to improve and update existent models on earthquake probabilities and frequency content of seismic motions. The Bayesian framework also facilitates the calculatirais of various statistics by using limited amounts of data. 

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