Addition, uncertainties

Nonparenthetical values are zero additional uncertainty. Parenthetical values are 0.5% additional uncertainty. AU. straight lengths are expressed as multiples of the pipe diameter D. They are measured from the upstream face of the primary device. 

Unstructured model uncertainty relates to unmodelled effects such as plant disturbances and are related to the nominal plant CmCv) as either additive uncertainty (s)... 

Consider a Nyquist contour for the nominal open-loop system Gm(iLu)C(iuj) with the model uncertainty given by equation (9.119). Let fa( ) be the bound of additive uncertainty and therefore be the radius of a disk superimposed upon the nominal Nyquist contour. This means that G(iuj) lies within a family of plants 7r(C(ja ) e tt) described by the disk, defined mathematically as... 

The NOAEL is selected based in part on the assumption that, if the critical toxic effect is prevented, then all toxic effects are prevented. The NOAEL for the critical toxic effect should not be confused with the "no-obscrx cd-cffcct-lcvel" (NOEL). In some studies, only LOAEL rather than a NOAEL is available. The use of a LOAEL. however, requires the use of an additional uncertainty factor (as seen below). 

In addition to the UFs listed above, a modifying factor (MF) is also applied. An MF ranging from >0 to 10 is included to reflect a qualitative professional assessment of additional uncertainties in the critical study and in the entire data base for the chemical not e.xplicitly addressed by the preceding uncertainty factors. The default value for the MF is 1.0. 

Although methods have been established to derive these levels (Barnes and Dourson 1988 EPA 1990c), uncertainties are associated with these techniques. Furthermore, ATSDR acknowledges additional uncertainties inherent in the application of the procedures to derive less than lifetime MRLs. As an example, acute inhalation MRLs may not be protective for health effects that are delayed in development or are acquired following repeated acute insults, such as h q)ersensitivity reactions, asthma, or chronic bronchitis. As these kinds of health effects data become available and methods to assess levels of significant human exposure improve, these MRLs will be revised. 

Risk assessors tend to build in additional uncertainty factors to avoid healthrelevant underestimates. This is partly done by using screening methods designed to look for worst case situations. Such worse case assumptions lead to intake estimates that exceed reality. For chemicals that present potential risks, more information is needed to allow more refined screening or even the most accurate estima-... 

The Environmental Protection Agency derived a reference dose (RfD) of 0.08 mg/kg/day based on the same NOAEL from the Hart (1980) study. The RfD, however, utilized an additional uncertainty factor of 10 to extrapolate to chronic exposure. 

In Table 8.1 three different analytical results are listed, the uncertainties of which are estimated in several ways (A) measurement uncertainty only, as sometimes can be done in analytical practice, (B) additionally uncertainty of calibration considered, and (C) uncertainty of sample preparation included (partially nonstatistically estimated). Whereas in cases (A) and (B) the results are judged to be significantly false, in case (C) the difference is statistically not significant. The situation is illustrated in Fig. 8.4a when a comparison is carried out on the basis of the f-test (Eq. 8.6). 

The connection between the multiplicative insensitivity of 12 and thermodynamics is actually rather intuitive classically, we are normally only concerned with entropy differences, not absolute entropy values. Along these lines, if we examine Boltzmann s equation, S = kB In 12, where kB is the Boltzmann constant, we see that a multiplicative uncertainty in the density of states translates to an additive uncertainty in the entropy. From a simulation perspective, this implies that we need not converge to an absolute density of states. Typically, however, one implements a heuristic rule which defines the minimum value of the working density of states to be one. 

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