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Sensitivity analysis example

A Monte Carlo simulation is fast to perform on a computer, and the presentation of the results is attractive. However, one cannot guarantee that the outcome of a Monte Carlo simulation run twice with the same input variables will yield exactly the same output, making the result less auditable. The more simulation runs performed, the less of a problem this becomes. The simulation as described does not indicate which of the input variables the result is most sensitive to, but one of the routines in Crystal Ball and Risk does allow a sensitivity analysis to be performed as the simulation is run.This is done by calculating the correlation coefficient of each input variable with the outcome (for example between area and UR). The higher the coefficient, the stronger the dependence between the input variable and the outcome. [Pg.167]

In order to test the economic performance of the project to variations in the base case estimates for the input data, sensitivity analysis is performed. This shows how robust the project is to variations in one or more parameters, and also highlights which of the inputs the project economics is more sensitive to. These inputs can then be addressed more specifically. For example if the project economics is highly sensitive to a delay in first production, then the scheduling should be more critically reviewed. [Pg.325]

A major advantage of this hydride approach lies in the separation of the remaining elements of the analyte solution from the element to be determined. Because the volatile hydrides are swept out of the analyte solution, the latter can be simply diverted to waste and not sent through the plasma flame Itself. Consequently potential interference from. sample-preparation constituents and by-products is reduced to very low levels. For example, a major interference for arsenic analysis arises from ions ArCE having m/z 75,77, which have the same integral m/z value as that of As+ ions themselves. Thus, any chlorides in the analyte solution (for example, from sea water) could produce serious interference in the accurate analysis of arsenic. The option of diverting the used analyte solution away from the plasma flame facilitates accurate, sensitive analysis of isotope concentrations. Inlet systems for generation of volatile hydrides can operate continuously or batchwise. [Pg.99]

Example 3 Sensitivity Analysis The following data describe a project. Revenue from annual sales and total annual expense over a 10-year period are given in the first three columns of Table 9-5. The fixed-capital investment Cfc is 1 million. Plant items have a zero salvage value. Working capital C c is 90,000, and the cost of land Ci is 10,000. There are no tax allowances other than depreciation i.e., is zero. The fractional tax rate t is 0.50. For this project, the net present value for a 10 percent discount factor and straight-line depreciation was shown to be 276,210 and the discoiinted-cash-flow rate of return to be 16.4 percent per year. [Pg.818]

The varianee equation provides a valuable tool with whieh to draw sensitivity inferenees to give the eontribution of eaeh variable to the overall variability of the problem. Through its use, probabilistie methods provide a more effeetive way to determine key design parameters for an optimal solution (Comer and Kjerengtroen, 1996). From this and other information in Pareto Chart form, the designer ean quiekly foeus on the dominant variables. See Appendix XI for a worked example of sensitivity analysis in determining the varianee eontribution of eaeh of the design variables in a stress analysis problem. [Pg.152]

Life cycle cost (LCC) calculations are made to make sure that both the purchase price and the operating costs for life cycle are considered in investment decisions. In the chapter the basic calculation methods and sensitivity analysis are introduced. Examples of calculation results and references to LCC information sources are given. [Pg.7]

The modeling of steady-state problems in combustion and heat and mass transfer can often be reduced to the solution of a system of ordinary or partial differential equations. In many of these systems the governing equations are highly nonlinear and one must employ numerical methods to obtain approximate solutions. The solutions of these problems can also depend upon one or more physical/chemical parameters. For example, the parameters may include the strain rate or the equivalence ratio in a counterflow premixed laminar flame (1-2). In some cases the combustion scientist is interested in knowing how the system mil behave if one or more of these parameters is varied. This information can be obtained by applying a first-order sensitivity analysis to the physical system (3). In other cases, the researcher may want to know how the system actually behaves as the parameters are adjusted. As an example, in the counterflow premixed laminar flame problem, a solution could be obtained for a specified value of the strain... [Pg.404]

In all analyses, there is uncertainty about the accuracy of the results that may be dealt with via sensitivity analyses [1, 2]. In these analyses, one essentially asks the question What if These allow one to vary key values over clinically feasible ranges to determine whether the decision remains the same, that is, if the strategy initially found to be cost-effective remains the dominant strategy. By performing sensitivity analyses, one can increase the level of confidence in the conclusions. Sensitivity analyses also allow one to determine threshold values for these key parameters at which the decision would change. For example, in the previous example of a Bayesian evaluation embedded in a decision-analytic model of pancreatic cancer, a sensitivity analysis (Fig. 24.6) was conducted to evaluate the relationship... [Pg.583]

In fact, reaction 4.105 also represents an example of a condensation reaction. A prior redox reaction in non-aqueous medium also often occurs, e.g., in the highly sensitive analysis of peroxides with HI in acetic acid, both under absolutely water-free conditions, where iodine is quantitatively liberated and is subsequently titrated. For much work on non-aqueous redox titrations by Tomicek s school published mainly in the Czech literature, see ref. 17. [Pg.303]

In this example with only three components, the optimum could have been determined by simply overlaying the individual response contour plots. This approach would be difficult, if not impossible, if the formulation would have many responses or contain four or more components. By contrast, the combination of the desirability function and the Complex algorithm permits an optimization of a multiresponse formulation having many constrained components in addition to providing the basis for sensitivity analysis. [Pg.70]

Rate constants and turnover calculations are sensitive to the initial data. For example, sensitivity analysis showed that mixing the NHC into a larger amount of soil impacts the calculated rate constants. For example, if only the SOC in the 0-15 cm zone was considered (SOC = 26,750 kg C ha-1) for data from Larson et al. (1972), then kSU( was 0.14 g (g SOC year)-1. However, if the 0-30 cm soil zone was considered (SOC = 53,500 kg C ha-1), then NHC was 0.28 g C (g SOC year)-1. In these calculations, increasing the soil depth did not impact ksoc... [Pg.199]

Carbon turnover in production fields can be determined, using non-isotopic techniques, by combining historical soil samples, current soil samples, and whole field yield monitor data. Sensitivity analysis of such data shows that the amount of above-ground biomass that could be harvested decreases with root to shoot ratio (Table 8.1). For example, if root biomass is ignored, analysis suggests that only 20-30% of the above-ground biomass can be harvested, whereas if the root to shoot ratio is 1.0, then between 40% and 70% of the residue could be harvested. [Pg.210]

The last entry in Table 1.1 involves checking the candidate solution to determine that it is indeed optimal. In some problems you can check that the sufficient conditions for an optimum are satisfied. More often, an optimal solution may exist, yet you cannot demonstrate that the sufficient conditions are satisfied. All you can do is show by repetitive numerical calculations that the value of the objective function is superior to all known alternatives. A second consideration is the sensitivity of the optimum to changes in parameters in the problem statement. A sensitivity analysis for the objective function value is important and is illustrated as part of the next example. [Pg.20]

Part I comprises three chapters that motivate the study of optimization by giving examples of different types of problems that may be encountered in chemical engineering. After discussing the three components in the previous list, we describe six steps that must be used in solving an optimization problem. A potential user of optimization must be able to translate a verbal description of the problem into the appropriate mathematical description. He or she should also understand how the problem formulation influences its solvability. We show how problem simplification, sensitivity analysis, and estimating the unknown parameters in models are important steps in model building. Chapter 3 discusses how the objective function should be developed. We focus on economic factors in this chapter and present several alternative methods of evaluating profitability. [Pg.663]

In this example, using marginal cost rather than AWP would make a difference for an important population subgroup. More importantly, there is no discussion in the article of why AWP was used for the reference case, or why a factor of 50% (which seems to have been too low) was used in the sensitivity analysis. [Pg.204]

The first two sections of Chapter 5 give a practical introduction to dynamic models and their numerical solution. In addition to some classical methods, an efficient procedure is presented for solving systems of stiff differential equations frequently encountered in chemistry and biology. Sensitivity analysis of dynamic models and their reduction based on quasy-steady-state approximation are discussed. The second central problem of this chapter is estimating parameters in ordinary differential equations. An efficient short-cut method designed specifically for PC s is presented and applied to parameter estimation, numerical deconvolution and input determination. Application examples concern enzyme kinetics and pharmacokinetic compartmental modelling. [Pg.12]

Existence and uniqueness of the particular solution of (5.1) for an initial value y° can be shown under very mild assumptions. For example, it is sufficient to assume that the function f is differentiable and its derivatives are bounded. Except for a few simple equations, however, the general solution cannot be obtained by analytical methods and we must seek numerical alternatives. Starting with the known point (tD,y°), all numerical methods generate a sequence (tj y1), (t2,y2),. .., (t. y1), approximating the points of the particular solution through (tQ,y°). The choice of the method is large and we shall be content to outline a few popular types. One of them will deal with stiff differential equations that are very difficult to solve by classical methods. Related topics we discuss are sensitivity analysis and quasi steady state approximation. [Pg.262]

The formulation and solution procedure just described is originally due to Stewart and Sorenson [378] in 1976, and has since been used extensively. For example, Glarborg, et al. [151] use sensitivity analysis in the development of combustion reaction mechanisms. [Pg.637]

Figure 17.12 shows some aspects of flame behavior that are revealed through sensitivity analysis (sensitivity analysis is discussed Section 15.5.4). For example, the maximum temperature is relatively insensitive to reaction rates, except very near the extinction point. At the extinction point, all sensitivities become unbounded because at the turning point the Jacobian of the system is singular. Near extinction, the hydrogen-atom concentration is... [Pg.708]


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