Frequency Estimation

Frequency Estimation References Guidelines for Process Equipment... 

Frequency Estimation There are two primary sources for estimates of incident frequencies. These are historical records and the apphcation of fault tree analysis and related techniques, and they are not necessarily applied independently. Specific historical data can sometimes be usehiUy applied as a check on frequency estimates of various subevents of a fault tree, for example. 

The use of historical data provides the most straightforward approach to the generation of incident frequency estimates but is subject to the apphcability and the adequacy of the records. Care should be exercised in extrac ting data from long periods of the historical record over which design or operating standards or measurement criteria may have changed. 

There are a variety of ways to express absolute QRA results. Absolute frequency results are estimates of the statistical likelihood of an accident occurring. Table 3 contains examples of typical statements of absolute frequency estimates. These estimates for complex system failures are usually synthesized using basic equipment failure and operator error data. Depending upon the availability, specificity, and quality of failure data, the estimates may have considerable statistical uncertainty (e.g., factors of 10 or more because of uncertainties in the input data alone). When reporting single-point estimates or best estimates of the expected frequency of rare events (i.e., events not expected to occur within the operating life of a plant), analysts sometimes provide a measure of the sensitivity of the results arising from data uncertainties. 

Sometimes the expected consequences of an accident alone may provide you with sufficient information for decision-making purposes. Conventionally, the form of these estimates will be dictated by the purpose (concern) of the study (safety, economics, etc.). Absolute consequence estimates are best estimates of the impacts of an accident and, like frequency estimates, may have considerable uncertainty. Table 4 contains examples of typical consequence estimates obtained from QRA. These examples point to the difficulty in comparing various safety and economic results on a common basis—there is no common denominator. 

Like frequency estimates, consequence estimates can have very large uncertainties. Estimates that vary by orders of magnitude can result from (1) basic uncertainties in chemical/physical properties, (2) differences in average vs. time-dependent meteorological conditions, and/or (3) uncertainties in the release, dispersion, and effects models. Some... 

The frequency analysis step involves estimating the likelihood of occurrence of each of the undesired situations defined in the hazard identification step. Sometimes you can do this through direct comparison with experience or extrapolation from historical accident data. While this method may be of great assistance in determining accident frequencies, most accidents analyzed by QRA are so rare that the frequencies must be synthesized using frequency estimation methods and models. 

If there is a lack of specific, appropriate data for a process facility, there can be considerable uncertainty in a frequency estimate like the one above. When study objectives require absolute risk estimates, it is customary for engineers to want to express their lack of confidence in an estimate by reporting a range estimate (e.g., 90% confidence limits of 8 X 10 per year to 1 X 10 per year) rather than a single-point estimate (e.g., 2 X 10per year). For this reason alone it may be necessary for you to require that an uncertainty analysis be performed. 

Determine Risk Potential. The objective is to determine the possibility of significant risk of injury to svcrkers or the public, or risk to the company s good name. It is done by bounding, consequence analyses and approximate frequency estimates, primarily for company protection. ... 

Flood Event Frequency Estimates were developed from flooding events in nuclear power plants with adjustments for plant-specific features and data. The data were from the IPE Surry flood analysis, industry sources, and licensing event reports (LERs). Some plant specific models were developed for the circulating water (CW) and service water (SW) lines... 

Event frequencies estimated from historical data failure rates from System Reliability Service... 

NUMBER AND TYPE OF RECORDS Event frequencies estimated from historical... 

Pipe Break Frequency Estimation for Nuclear Power Plants Nuclear 19 occunences of pipe failures (breaks), supplemented by expert-opinion estimates Leaks of 1 gpm for 2 inches in diameter pipe 50 gpm tor all pipe for 81 nuclear plants 101. 

Pipe Break Frequency Estimation for Nuclear Power Plants... 

Likelihood estimation, sometimes called frequency estimation, cluuactcrizes the probability of occurrence for each potential incident considered in tlie iiiuilysis. The major tools used for likelihood estimation are listed below. ... 

Cause-consequence analysis serx es to characterize tlie physical effects resulting from a specific incident and the impact of these physical effects on people, the environment, and property. Some consequence models or equations used to estimate tlie potential for damage or injury are as follows Source Models, Dispersion Models, Fire Explosion Models, and Effect Models. Likelihood estimation (frequency estimation), cliaractcrizcs the probability of occurrence for each potential incident considered in tlie analysis. The major tools used for likelihood estimation are as follows Historical Data, Failure sequence modeling techniques, and Expert Judgment. 

Each occupied building was qualitatively ranked according to frequency and consequence per Table 5.2 and Table 5.4. Consequence ratings were based upon the results of the previously conducted consequence assessments. Frequency estimates were based upon consensus estimates of the HAZOP team. Risk rankings were then determined per Figure 5.1. 

Fallin D, Schork NJ. Accuracy of haplotype frequency estimation for biallelic loci via the expectation-maximization algorithm for unphased diploid genotype data. Am J Hum Genet 2000 67 947-959. 

With proper safety precautions and operating procedures the occurrence of explosions in the vapor space of fixed roof storage tanks are a very rare event. A frequency estimate of an explosion once in every 1,000 years, per tank, has been stated. Explosive mixtures may exist in the vapor space of a tank unless precautions are taken. Any vapor will seek an ignition source, so prevention of ignition cannot be guaranteed. This is especially true with liquids that have low conductivity that... 

Because males have only one X chromosome, gene frequency estimation for X-Hnked traits differs from that of autosomal traits. Consider hemophilia A (Chapter 1), which is an X-linked recessive disease. If a male s X chromosome has a factor VIII mutation, he will have hemophilia A. If his X chromosome does not have the mutation, he will not develop the disease. Thus, the gene frequency for hemophilia A is obtained simply by counting the proportion of affected males in the population (i.e., the proportion of X chromosomes containing the mutation). Approximately one in 10,000 males has hemophilia A. Thus, the gene frequency for this disease, q, is 1/10,000. 

Females have two X chromosomes, so they must inherit two copies of the mutated chromosome to develop hemophilia A. Gene frequencies are similar in males and females, so we can use the gene frequency estimated in males to predict the genotype frequencies in females. Assuming Hardy-Weinberg equilibrium, the frequency of affected females is given by... 

The initiating frequency estimate is derived from the cause of the fire scenario. This may initially be obtained from historical data (or more specific data if available) and modified where necessary to take account of any site-specific considerations that may affect the frequency. See Section 6.2.4.6 for additional... 

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