Effects of uncertainty

As already stated, all the data used to calculate the NPV or DCF (capital estimate, operating costs, annual sales, selling price, etc.) are subject to 

In order to quantify the uncertainties in a project it is necessary to indicate the relative chances that a variable (e.g. selling price) will have different values. This can be done subjectively on the basis of, say, a 10% chance that the price will be as low as x, a 10% chance that the price will be as high as z against an expected mid-value of y. If it is assumed that the variables lie in a normal distribution in the range considered then the subjective probability estimates can be used to define the total distribution. Having made estimates of subjective probability distribution for each of the major variables we need a method of combining the various inputs to the project cash flows to obtain the resulting distribution of NPV or DCF, One such method is the Monte Carlo simulation. If there are a number of independent inputs to the project (capital, materials costs, etc) each represented by a probability distribution of values, then there is an infinite number of possible outcomes. Representatives of these 

The aim of project evaluation is to use the available data to provide information which will assist decision making on the future of the project. Use of sensitivity analysis and risk analysis techniques point up areas where uncertainty in the input data has greatest effect and indicates the effects of these uncertainties on the project outcome. Such evaluation does not eliminate the need for skilled judgement in the management team nor does it necessarily make the decision process any easier. However, it does ensure that a complete view of the project is available and makes clear the need for definitive company policy on risk and profitability criteria. 

Cash flow comparison of benzene and n-butane routes to maleic anhydride Consider a 25 kilotonnes/year plant. 

Sales forecasts 10 kilotonnes in first year of operation, 20 kilotonnes in second year 

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Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

Whiting, W.B., TM. Tong, and M.E. Reed, 1993. Effect of Uncertainties in Thermodynamic Data and Model Parameters on Calculated Process Performance, Industiial and Engineeiing Chemistiy Reseaieh, 32, 1993, 1367-1371. (Relational model development)... 

Thermal design methods, for heat exchangers, 13 248-263 Thermal design parameters, effect of uncertainties in, 13 257-258 Thermal desorption... 

Investigate the influence of incorrect parameter values in the feedforward control model. Vary the parameters by 10% effects in the control model only to see the effects of uncertainties. This will involve renaming parameters used in the control algorithm, such that the main process parameters still remain the same. 

The sensitivity analysis of a system of chemical reactions consist of the problem of determining the effect of uncertainties in parameters and initial conditions on the solution of a set of ordinary differential equations [22, 23], Sensitivity analysis procedures may be classified as deterministic or stochastic in nature. The interpretation of system sensitivities in terms of first-order elementary sensitivity coefficients is called a local sensitivity analysis and typifies the deterministic approach to sensitivity analysis. Here, the first-order elementary sensitivity coefficient is defined as the gradient... 

Fish, D. J., and M. R. Burton, The Effect of Uncertainties in Kinetic and Photochemical Data on Model Predictions of Stratospheric Ozone Depletion, J. Geophys. Res., 102, 25537-25542 (1997). 

Sistla, G N. Zhou, W. Hao, J.-Y. Ku, S. T. Rao, R. Bornstein, F. Freedman, and P. Thunis, Effects of Uncertainties in Meteorological Inputs on Urban Airshed Model Predictions and Ozone Control Strategies, Atmos. Environ., 30, 2011-2025 (1996). 

Kraiczi, H., Frisen, M. Effect of uncertainty about population parameters on pharmacodynamics-based prediction of clinical trial power. Contemp Clin Trials 2005, 26 118-130. 

How precise are the exposure estimates This question focuses on the simultaneous, combined effect of uncertainties in all exposure factors with respect to overall uncertainty in the exposure assessment. This question can be answered by propagating uncertainty estimates for exposure model inputs through the exposure model. Typically, this question could be answered in terms of absolute or relative ranges (e.g. a 95% probability range of 25% of the exposure for a particular percentile of interindividual variability), based upon estimates of uncertainty for a particular percentile of the exposed population. 

Walsh et al. (1995) examined the effect of uncertain parameters on the optimal operation of BREAD processes and the use of control to reduce the effect of uncertainties. The study provided an important step towards the implementation of optimal operating policies on real (uncertain) processes. 

At this point, it is useful to examine the effect of uncertainty in data by sensitivity analysis. Some physical properties are essential for design, such as for example the vapor pressure of the fatty ester, VLE for binaries involving the lauric acid, alcohol and water, as well as the Gibbs free energy of formation of the fatty ester. 

In the final section, VII, the effects of uncertainties in reaction rate and absorption coefficients on the numerical predictions are examined, important areas for further theoretical and experimental research are recommended, and the results of Sections IV, V, and VI are summarized. 

Perform probabilistic sensitivity analyses for all of the key inputs represented by a distribution in the Monte Carlo analysis in such a way as to distinguish the effects of variability from the effects of uncertainty in the inputs. 

Schecher W. D. and Driscoll C. T. (1988) An evaluation of the equilibrium calculations within acidification models the effect of uncertainty in measured chemical components. Water Resour. Res. 24, 533-540. 

Uncertainty and disturbances can be described in terms of mathematical constraints defining a finite set of hounded regions for the allowable values of the uncertain parameters of the model and the parameters defining the disturbances. If uncertainty or disturbances were unbounded, it would not make sense to try to ensure satisfaction of performance requirements for all possible plant parameters and disturbances. If the uncertainty cannot be related mathematically to model parameters, the model cannot adequately predict the effect of uncertainty on performance. The simplest form of description arises when the model is developed so that the uncertainty and disturbances can be mapped to independent, bounded variations on model parameters. This last stage is not essential to the method, but it does fit many process engineering problems and allows particularly efficient optimization methods to be deployed. Some parameter variations are naturally bounded e.g.. feed properties and measurement errors should be bounded by the quality specification of the supplier. Other parameter variations require a mixture of judgment and experiment to define, e.g., kinetic parameters. 

Figure 3 The effect of uncertainty in combinations of indicator values with a sequentially forward selection.

In the framework of real-time optimization, measurements are used to compensate for effects of uncertainty. The main approach uses measurements to update the parameters of a process model. In contrast, the constraint-adaptation scheme uses the measurements to bias the constraints in the optimization problem. In this paper, an algorithm combining constraint adaptation with a constraint controller is presented. The former detects shifts in the set of active constraints and passes the set points of the active constraints to the latter. In order to avoid constraint violation, the set points are moved gradually during the iterative process. Moreover, the constraint controller manipulates linear combinations of the original input variables. The approach is illustrated for a simple case study. 

The main objective of this work is to estimate the effect of uncertainty of each of the fitted parameters to the prediction of the equilibrium pressure given by the used VDWP model. For this purpose a sensitivity analysis for each one of the parameters of interest was carried out. In addition, a literature survey was conducted to obtain the reported values for the parameters together with the corresponding approach used for the calculation of those values ... 

To determine the effect of uncertainties of the various parameters on the calculated interfacial tension, a set of sensitivity calculations was carried out. It was found that a 1 % uncertainty in the capillary diameter, the capillary depression, or the density of the aluminum, causes a 1.0-1.1% uncertainty in the calculated interfacial tension. The 1% uncertainty in the density of the melt or in the temperature, leads to an uncertainty in the interfacial tension of less than 0.1%. 

Separate simulations were performed with no, low, moderate, or high degrees of uncertainty to explore the effect of uncertainty on the probability of trial success using a global SA. Uncertainty, expressed as %CV for each parameter, was set for the fixed model effects at 0% (none), 10% (low), 35% (moderate), or 50% (high). 

TABLE 35.2 Effect of Uncertainty Level on the Estimate of Trial Power Using a Global Sensitivity Analysis for the Zidovndine Analog Efficacy Trial Simnlation... 

Brown RG, Jahanshahi M, Marsden CD (1993) Response choice in Parkinson s disease. The effects of uncertainty and stimulus-response compatibility. Brain, 116, 869-885. 

The condition number is a measure of input-output controllability. If the condition number is small, then the multivariable effects of uncertainties are not likely to be... 

To investigate the effect of fracture geometry on the scale effect of the permeability, some parametric study is carried out. Table 1 shows the parameters examined for this aim. Case 1 is the reference case in which the original measured data at Sella-field are used. Case2 is the case to examine the effect of uncertainty on the fracture density, in which the density is defined by Eq. (6). Thus the number of fracture in this case is about 4 times that in Case 1. Case 3 is related to the uncertainty on the... 

Thermal and hydraulic coupling analysis is carried out to examine the effect of uncertainty related to the up-scaling method on the performance assessment. The hypothetical region is shown in Figure 7. At the depth of 530m, the high level... 

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