The use of airplanes for Mars exploration is a new and attractive approach because it provides high resolution power and large spatial coverage. However, it is also a challenging approach in engineering viewpoint. Mars airplanes are required to fly in lower Reynolds number and higher subsonic Mach number conditions due to thinner atmosphere and smaller speed of sound on the Mars, compared to typical commercial Earth airplanes. Some studies of Mars exploratory airplanes have been already reported by many researchers. However, these airplanes were designed only by utilizing and modifying existing design approaches for conventional Earth airplanes. Therefore, the use of a design optimization approach is desirable to realize more effective and global search for better design of Mars airplane and establish a new design concept for Mars airplanes. In addition, it is well known that there exist large wind variations on the Mars. Such wind variations may lead to drastic deterioration in performance, and thus failure in expected Mars exploratory mission. Therefore, it is desirable to consider not only the performance at design point but also robustness of performance against wind variations for more realistic and reliable design of Mars airplane. One of solutions to realize such design is use of a robust design optimization approach. However, traditional robust optimization approaches had lack of capability to reveal trade-off information between optimality and robustness which is useful for real-world robust designs. In this dissertation, a new robust design optimization approach “design for multiobjective six sigma (DFMOSS)” has been developed to solve the drawbacks of a conventional robust optimization approach “design for six sigma (DFSS)” for more efficient and more useful robust design optimizations, and applied to simple robust optimization problems to investigate efficiency and usefulness of the DFMOSS. This study showed that the DFMOSS has some advantages over the DFSS. First, the DFMOSS does not require the advance specification of input parameters such as weighting factors and sigma level. Second, the DFMOSS obtains multiple robust optimal solutions effectively by only one optimization run and reveals trade-off information between optimality and robustness. Third, satisfied sigma level of each robust optimal solution can be evaluated easily and flexibly in post-processing of the robust optimizations. Then, aerodynamic design optimizations of Mars exploratory airplane wing considering the effects of wind variations were realized by using the DFMOSS and the computational fluid dynamics (CFD) simulation. Realistic design information about the trade-off relation between the optimality and the robustness of aerodynamic performance of Mars exploratory airplane has been discussed based on the numerical results. First, three robust aerodynamic design optimizations of airfoil configuration for Mars exploratory airplane considering the effects of wind variations were carried out. In all cases, the robust aerodynamic design optimization using the DFMOSS revealed the trade-off relation between the optimality and the robustness in aerodynamic performance. In the first case considering the robustness of lift to drag ratio against the variation of flight Mach number, it was shown that an airfoil configuration with smaller maximum camber can improve the robustness in lift to drag ratio against the variation of flight Mach number. This is because such airfoil can suppress the growth of shock wave, i.e., realize smaller increment in pressure drag (wave drag) against increment in flight Mach number. In the second case considering the robustness of pitching moment coefficient against the variation of flight Mach number, it was shown that an airfoil configuration with larger curvature in the front part can improve the robustness of pitching moment coefficient against the variation of flight Mach number. This is because such airfoil can suppress the backward movement of shock wave occurred over the upper surface of airfoil against increment in flight Mach number, and eventually it results in smaller change in pitching-down moment produced in the rear part of airfoil against increment in flight Mach number. In the third case considering the robustness of lift to drag ration against the variation of angle of attack, it was shown that an airfoil configuration with blunter leading edge can improve the robustness of lift to drag ratio against the variation of angle of attack. This is because such airfoil configuration can suppress the growth of the separation bubble generated near the leading edge against increment in angle of attack. It leads to gentler change of negative pressure level in the front part near the leading edge, i.e., smaller change of drag against increment in angle of attack, and eventually it results in smaller change of lift to drag ratio against the variation of angle of attack. Second, robust aerodynamic design optimization of airfoil and wing planform configurations for Mars exploratory airplane considering effects of wind variations was carried out. The present robust aerodynamic design optimization found the solutions with robust characteristic in aerodynamic performance parameters against wind variations, and revealed qualitative trade-off information between the optimality and the robustness in aerodynamic performance parameters. This result showed that the DFMOSS is an effective approach even in large-scale robust design optimizations with many design variables and objective functions. Among the robust optimal solutions obtained in the present study, the solution with robust characteristic of lift against wind variations had the wing configuration with supercritical-like airfoil and larger twist-up angle locally at the mid-span section. Such wing configuration involved the leading-edge separation, which leaded to small local lift and large local drag, at the twisted-up section at the design point. Such extreme solution with leading-edge separation seems to be undesirable and unrealistic to be used in real-world design. Therefore, more detailed investigation of the obtained trade-off information without such extreme solutions may be useful for more realistic designs of Mars exploratory airplane. In addition, the present CFD simulation approach based on the Favre-averaged Navier-Stokes equations with the Baldwin-Lomax algebraic turbulence model did not have accuracy enough to simulate the flowfields involving large-scale separation phenomena. Therefore, further investigation of the CFD simulation approach for large-scale separation phenomena may lead to more realistic and more reliable future designs of Mars exploratory airplane.