Multiplicative uncertainty

So what is the total uncertainty when using this pipet to deliver two successive volumes of solution from the previous discussion we know that the total uncertainty is greater than 0.000 mL and less than 0.012 mL. To estimate the cumulative effect of multiple uncertainties, we use a mathematical technique known as the propagation of uncertainty. Our treatment of the propagation of uncertainty is based on a few simple rules that we will not derive. A more thorough treatment can be found elsewhere. ... 

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. 

As described in equation (6.59), longitudinal dispersion coefficient has a 67% confidence interval that is a factor of 1.7 times the best estimate. If the distribution of multiplicative uncertainty is normal, the 95% confidence interval would be at a factor of 3.4 times the best estimate. The reaeration coefficient has are MME of 1.8 for the Thackston and Krenkel equation (equation (9.7)). Again, if the multiplicative distribution is normal, the MME is 0.4 times the 95% confidence interval. Then the 95% confidence interval is a multiplicative factor of 4.5. 

The European system for regulating synthetic chemicals, described in Chapter 5, is predominantly risk-based . This means that restrictions on the manufacture or use of chemicals must be justified by reference to evidence that there is a risk of the chemical causing a specified type of harm. REACH (Registration, Evaluation, Authorization and restriction of Chemicals) does not define the term risk , but the directive on risk assessment of new substances defined it as the incidence and severity of the adverse effects likely to occur [...] due to actual or predicted exposure to a substance (Article 2 of Directive 93/67/EEC). In the first part of this chapter I look at how risks from chemicals are assessed. What does chemicals risk assessment in practice aim to achieve Can it provide the reliable evidence needed for agreement by all parties on whether or not a chemical poses a risk My answer to this second question is no there are multiple uncertainties in chemicals risk assessment which lead to protracted debates as to whether a chemical poses a risk or not. 

Hoel, M., Karp, L., 2001. Taxes and quotas for a stock pollutant with multiplicative uncertainty. Journal of Public Economics 82, 91-114. 

Another source of uncertainty arises from actuators, mainly due to the time delay and spatial distribution from injection to complete combustion of the secondary fuel. A nonrational transfer function of time delay e lWs is used to treat the multiplicative uncertainty by embedding it in the family... 

Nair, R.S., J.H. Sherman, M.W. Stevens, and F.R. Johannsen. 1995. Selecting a more realistic uncertainty factor Reducing compounding effects of multiple uncertainties. Hum. Ecol. Risk Assess. 1 576-589. 

The bond graph model of the system in integral causality is given in Fig. 3.9b, and the bond graph model in LFT form of the system is given in Fig. 3.10 [15]. The model represents the movements around the static equilibrium with respect to gravity, neglecting initial conditions. Multiplicative uncertainties are introduced in elements Csph, Ba, M s and Mg, and Sp. 

J. Shao et al., Optimization of Integrated Supply Chain Planning under Multiple Uncertainty, DOI 10.1007/978-3-662-47250-7 l... 

Optunizatioi of Integrated Supply Chain Planning under Multiple Uncertainty... 

An important feature of Merrifield s method of sequential synthesis on the polymer support is that the synthesis goes unchecked. Unless the coupling reaction proceeds to completion in every step, the final product obtained after cleavage is bound to be contaminated with peptides differing from the desire sequence by one or more amino acid residues. Thus, because of the multiple uncertainties associated with solid-phase synthesis, it is highly desirable to have rapid analytical control of the two major synthetic operations, i.e., coupling and deprotection, in order to achieve unambiguous synthesis of the desired peptide. 

Secondly, although there had been plenty of studies in the literature that focused on two or three level SCs while considering a number of uncertain factors (e.g., customer demand) or a single SCP indicator (e.g., cost), the research on multiple stage SC systems with multiple uncertainties and multiple objectives based on real industrial cases had been sparse and deserved more attention. One reason was due to the lack of reliable industrial data and the impact of data confidentiality which remains important to the industry. 

Fourteen SMEs in China were contacted. The research involved the collection of primary data and required a considerable effort from the case companies, whilst companies were often very sensitive to data confidentiality and had limited human resources and relevant technologies to support data collection. Consequently, the choice was limited. However, two agreed to give their full support to the data collection. These companies are reasonably representative because their SCs include multiple functions and parties (e.g., many suppliers, manufacturing, private warehouse, transport companies, and many customers) in different markets. More importantly, the SC structure in the two case companies is similar in terms of information and material flows and their associated characteristics, for example, multiple uncertainties, although the scale of some uncertainties may be different. Additionally, these two manufacturers are located in the north and south of China, respectively, which represent alternative local economic and societal influences. The two companies are in different industries, and therefore, the investigation of their differences and similarities can contribute to the process of model generalisation. 

In this chapter, based upon two case studies, a generalised model will be developed including both the DSC and ISC, and then the multiple uncertainties will be categorised and explained. Finally the SCP will be presented in the DSC and ISC. 

The NOAEL has been criticized because it places excessive weight on a single point on the dose-response curve. An alternative approach to estimating the reference dose is called the benchmark dose (BMD). A low incidence of toxicity is chosen, for example, manifestation of the specified toxic effect in 5% of the test popniation, and the upper and lower 95% confidence limits are determined by statistical modeling. The upper 95% confidence limit corresponds to a lower dose triggering the toxic effect in 5% of the population, while the lower 95% confidence limit corresponds to a higher dose causing the same incidence of morbidity. The benchmark dose corresponds to the upper 95% confidence limit, i.e., the more conservative estimate of risk. Similarly to the NOAEL, the benchmark dose, is divided by multiple uncertainty factors to estimate the reference dose ... 

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