Uncertainty types

Hoffman and Hammonds (1994) Type A uncertainty Type B uncertainty Uncertainty... 

Aleatory uncertainty The kind of uncertainty resulting from randomness or unpredictability due to stochasticity. Aleatory uncertainty is also known as variability, stochastic uncertainty. Type I or Type A uncertainty, irreducible uncertainty, conflict, and objective uncertainty. 

Epistemic uncertainty The kind of uncertainty arising from imperfect knowledge. Epistemic uncertainty is also known as incertitnde, ignorance, subjective uncertainty. Type II or Type B uncertainty, redncible nncertainty, nonspeci-hcity and state-of-knowledge uncertainty. 

Source of uncertainty Type Relative uncertainty (%) Degrees of freedom... 

Measurement uncertainty Type A effects [repeatability and reproducibility precision] Type effects... 

The distinction between the two categories of uncertainties (types A and B) is based on the method of their evaluation. Those of type A, but not those of type B, can be evaluated by statistical methods [6], These categories do not correspond exactly to the former grouping of uncertainties into random and systematic. No distinction is made between types A and B for the combination of uncertainties... 

The second source of uncertainty (type 2 from our lack of basic knowledge) is typically much more troublesome, and tends to dominate because it is often much larger than that posed by type 1. Thus, it is incumbent on the risk assessor to understand and describe this unavoidable subjectivity in as much detail as possible to facilitate the understanding of those who rely on the work, allowing them to comprehend and appreciate its boundaries and limitations. 

Using the example assume that one has data on the source rate (G) which indicates that between residence values are normally distributed with a mean of 50mgh and a standard deviation of 5mgh for the particular source of interest. (This is an example of uncertainty type 1 above - a known and measured quantity with natural variability.)... 

The uncertainty due to varying instrument background can be significant. If the background varies, the assumption of pure Poisson counting statistics to evaluate the uncertainty of the net count rate for a sample may seriously underestimate the uncertainty. Options include replicate background measurements to determine its uncertainty (Type A evaluation), or to evaluate an additional component of uncertainty to be added to the Poisson counting uncertainty. 

A more rigorous definition of uncertainty (Type A) relies on the statistical notion of confidence intervals and the Central Limit Theorem. The confidence interval is based on the calculation of the standard error of the mean, Sx, which is derived from a random sample of the population. The entire population has a mean /x and a variance a. A sample with a random distribution has a sample mean and a sample standard deviation of x and s, respectively. The Central Limit Theorem holds that the standard error of the mean equals the sample standard deviation divided by the square root of the number of samples ... 

Uncertainty budget Parameter Typical (p,l value Standard uncertainty Type A/B n Description... 

In the next step, standard uncertainties are defined for each source of uncertainty. GUM defines two different methods for estimating uncertainty. Type A is a method of evaluation by the statistical analysis of series of observations. Standard deviations can be calculated through repeated observations. Type B is a method of evaluation of uncertainty by means other than the statistical analysis of series of observations. Calibration results or tolerances given in manuals can be used here. They are usually expressed in the form of limits or confidence intervals. Typical rules for converting such information to an estimated standard uncertainty u are introduced in [5] (p. 164). 

However, a new distinction has arisen - Type A and Type B uncertainties. Type A uncertainties are defined as those that have been determined by repeated measurements to assess the magnitude and distribution of the parameter. Type B uncertainties are those whose magnitude has been derived in any other manner. For example, the uncertainty on gamma-ray emission probability is... 

In general, there are two uncertainty types, namely, random uncertainty and nonrandom (inherent) uncertainty. For random uncertainty, the classical example is the question of What is the probability of observing a dry year from a sequence of say, 12-year record It is assumed that the probability of wet and dry year occurrences is equally likely, mutually exclusive and completely random (independent). Given the information that there are 4 dry and 8 wet years in sequence, the probabilities of random wet and dry year occurrences are 4/12 = 0.32 and 8/12 = 0.78, respectively. Hence, random uncertainty deals with events. Once the event occnrs, the uncertainty goes away for that particular event. 

There will be some uncertainty as to the well initials, since the exploration and appraisal wells may not have been completed optimally, and their locations may not be representative of the whole of the field. A range of well initials should therefore be used to generate a range of number of wells required. The individual well performance will depend upon the fluid flow near the wellbore, the type of well (vertical, deviated or horizontal), the completion type and any artificial lift techniques used. These factors will be considered in this section. 

The computation of mesopore size distribution is valid only if the isotherm is of Type IV. In view of the uncertainties inherent in the application of the Kelvin equation and the complexity of most pore systems, little is to be gained by recourse to an elaborate method of computation, and for most practical purposes the Roberts method (or an analogous procedure) is adequate—particularly in comparative studies. The decision as to which branch of the hysteresis loop to use in the calculation remains largely arbitrary. If the desorption branch is adopted (as appears to be favoured by most workers), it needs to be recognized that neither a Type B nor a Type E hysteresis loop is likely to yield a reliable estimate of pore size distribution, even for comparative purposes. 

I. 000 X 10- 1.000 X 10-k 1.000 X 10-k and 1.000 X 10- M from a 0.1000 M stock solution. Calculate the uncertainty for each solution using a propagation of uncertainty, and compare to the uncertainty if each solution was prepared by a single dilution of the stock solution. Tolerances for different types of volumetric glassware and digital pipets are found in Tables 4.2 and 4.4. Assume that the uncertainty in the molarity of the stock solution is 0.0002. 

Relationships Between Objects, Processes, and Events. Relationships can be causal, eg, if there is water in the reactor feed, then an explosion can take place. Relationships can also be stmctural, eg, a distiUation tower is a vessel containing trays that have sieves in them or relationships can be taxonomic, eg, a boiler is a type of heat exchanger. Knowledge in the form of relationships connects facts and descriptions that are already represented in some way in a system. Relational knowledge is also subject to uncertainty, especiaUy in the case of causal relationships. The representation scheme has to be able to express this uncertainty in some way. 

The accuracy of absolute risk results depends on (1) whether all the significant contributors to risk have been analyzed, (2) the realism of the mathematical models used to predict failure characteristics and accident phenomena, and (3) the statistical uncertainty associated with the various input data. The achievable accuracy of absolute risk results is very dependent on the type of hazard being analyzed. In studies where the dominant risk contributors can be calibrated with ample historical data (e.g., the risk of an engine failure causing an airplane crash), the uncertainty can be reduced to a few percent. However, many authors of published studies and other expert practitioners have recognized that uncertainties can be greater than 1 to 2 orders of magnitude in studies whose major contributors are rare, catastrophic events. 

Type of trim. Use equal percentage whenever there is a large design uncertainty or wide rangeability is desired. Use linear for small uncertainty cases. 

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