Comparison of Two Probabilistic Techniques for the Assessment of Economic Uncertainty

Several approaches to probabilistic design have been proposed in the past. Only few acknowledged the paradigm shift from performance based design to design for cost. The incorporation of economics in the design process, however, makes a probabilistic approach to design necessary, due to the inherent uncertainty of assumptions and the circumstances of operating environments of the future aircraft. The approach previously proposed by the authors, linking Response Surface Methodology with Monte Carlo Simulations, has revealed itself to be inadequate for multi-constraint, multi-objective problems. In addition accuracy problems were observed that could not be resolved with the methodology. Hence, this paper proposes an alternate approach to probabilistic design, which is based on a Fast Probability Integration (FPI) technique. The paper critically reviews the combined Response Surface Equation/ Monte Carlo Simulation methodology and compares it against the Advanced Mean Value (AMV) method, one of several Fast Probability Integration techniques. The Advanced Mean Value method is a probability estimation method based on a Most Probable Point (MPP) analysis. The paper describes the method employed to identify the Most Probable Point and obtain a cumulative probability distribution. The resulting distribution function is compared to the one generated by the Response Surface Equation/Monte Carlo Simulation method. For this comparison a case study is formulated, employing a High Speed Civil Transport concept. Based on the outcome of this study an assessment and comparison of the analysis effort and time necessary for both methods is performed. If the Most Probable Point can be found efficiently, the Advanced Mean Value method shows significant time savings over the Response Surface Equation/Monte Carlo Simulation method, and generally yields more accurate CDF distributions.