A probabilistic multi-criteria decision making technique for conceptual and preliminary aerospace systems design

It has always been the intention of systems engineering to invent or produce the best product possible. Many design techniques have been introduced over the course of decades that try to fulfill this intention. Unfortunately, no technique has succeeded in combining multi-criteria decision making with probabilistic design. The design technique developed in this thesis, the Joint Probabilistic Decision Making (JPDM) technique, successfully overcomes this deficiency by generating a multivariate probability distribution that serves in conjunction with a criterion value range of interest as a universally applicable objective function for multi-criteria optimization and product selection. This new objective function constitutes a meaningful Xnetric, called Probability of Success (POS), that allows the customer or designer to make a decision based on the chance of satisfying the customer's goals. In order to incorporate a joint probabilistic formulation into the systems design process, two algorithms are created that allow for an easy implementation into a numerical design framework: the (multivariate) Empirical Distribution Function and the Joint Probability Model. The Empirical Distribution Function estimates the probability that an event occurred by counting how many times it occurred in a given sample. The Joint Probability Model on the other hand is an analytical parametric model for the multivariate joint probability. It is comprised of the product of the univariate criterion distributions, generated by the traditional probabilistic design process, multiplied with a correlation function that is based on available correlation information between pairs of random variables.; JPDM is an excellent tool for multi-objective optimization and product selection, because of its ability to transform disparate objectives into a single figure of merit, the likelihood of successfully meeting all goals or POS. The advantage of JPDM over other multi-criteria decision making techniques is that POS constitutes a single optimizable function or metric that enables a comparison of all alternative solutions on an equal basis. Hence, POS allows for the use of any standard single-objective optimization technique available and simplifies a complex multi-criteria selection problem into a simple ordering problem, where the solution with the highest POS is best. By distinguishing between controllable and uncontrollable variables in the design process, JPDM can account for the uncertain values of the uncontrollable variables that are inherent to the design problem, while facilitating an easy adjustment of the controllable ones to achieve the highest possible POS. Finally, JPDM's superiority over current multi-criteria decision making techniques is demonstrated with an optimization of a supersonic transport concept and ten contrived equations as well as a product selection example, determining an airline's best choice among Boeing's B-747, B-777, Airbus' A340, and a Supersonic Transport. The optimization examples demonstrate JPDM's ability to produce a better solution with a higher POS than an Overall Evaluation Criterion or Goal Programming approach. Similarly, the product selection example demonstrates JPDM's ability to produce a better solution with a higher POS and different ranking than the Overall Evaluation Criterion or Technique for Order Preferences by Similarity to the Ideal Solution (TOPSIS) approach.