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Unformatted text preview: all probability distribution for the output variable, either in terms of its probability density function (or mass function for discrete output variables) or its cumulative distribution function. (See sidebar on cost S-curves.) Some techniques for this are: The Cost S-Curve The cost S-curve gives the probability of a project's cost not exceeding a given cost estimate. This probability is sometimes called the budget confidence level. This curve aids in establishing the amount of contingency and Allowance for Program Adjustment (APA) funds to set aside as a reserve against risk. In the S-curve shown above, the project's cost commitment provides only a 40 percent level of confidence; with reserves, the level is increased to 50 percent. The steepness of the S-curve tells the project manager how much the level of confidence improves when a small amount of reserves are added. Note that an Estimate at Completion (EAC) S-curve could be used in conjunction with the risk management approach described for TPMs (see Section 4.9.2), as another method of cost status reporting and assessment meet. NASA Systems Engineering Handbook Systems Analysis and Modeling Issues • • • Analytic solution Decision analysis Monte Carlo simulation. Analytic Solution. When the structure of a model and its uncertainties permit, a closed-form analytic solution for the required probability density (or cumulative distribution) function is sometimes feasible. Examples can be found in simple reliability models (see Figure 29). Decision Analysis. This technique, which was discussed in Section 4.6, also can produce a cumulative distribution function, though it is necessary to descretize any continuous input probability distributions. The more probability intervals that are used, the greater the accuracy of the results, but the larger the decision tree. Furthermore, each uncertain model input adds more than linear computational complexity to that tree, making this technique less efficient in many situations than Monte Carlo simulation, described next. Monte Carlo Simulation. This technique is often used to calculate an approximate solution to a stochastic model that is too complicated to...
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