Engineering design often involves the determination of design variable settings to optimize competing performance requirements. In the early design stages we propose narrowing down the domain of design solutions using metamodels of principal components of the multiple performance levels that have been scaled by a multivariate quadratic loss function. The multivariate quadratic loss function is often used as the objective function in reaching optimal solutions because it utilizes the correlation structure of the design's performance metrics and penalizes off-target performance in a symmetrical manner. We also compare the computational performance of these loss-scaled principal components when used to solve for the design with minimal expected multivariate quadratic loss under three modeling approaches: response surface methodology, multivariate adaptive regression splines, and spatial point modeling. We demonstrate the technique on the design of the mechanical frame of an electric vehicle with six desired performance levels determined simultaneously by the dimensions of eight mechanical design elements. The method is the focus in this work.

In recent decades advances in radiation imaging and radiation therapy have led to a dramatic increase in the number of people exposed to radiation. Consequently, there is a clear need for personalized biodosimetry diagnostics in order to monitor the dose of radiation received and adapt it to each patient depending on their sensitivity to radiation exposure (Hall E.J. and Brenner D. J., 2008). Similarly, after a large-scale radiological event such as a dirty bomb attack, there will be a major need to assess, within a few days the radiation doses received by tens of thousands of individuals. Current high throughput devices can handle only a few hundred individuals per day. Hence there is a great need for a very fast self-contained non-invasive biodosimetric device based on a rapid blood test.This paper presents a case study where regression methods and designed experiments are used to arrive at the optimal settings for various factors that impact the kinetics in a biodosimetric device. We use ridge regression to initially identify a set of potentially important variables in the mixing process which is one of the critical sub systems of the device. This was followed by a series of designed experiments to arrive at the optimal setting of the significant microfluidic cartridge and piezoelectric disk (PZT) (D. Sadler, F. Zenhausern, U.S. Patent 6,986,601; Lee, S. Y., Ko, B., Yang, W., 2005) related factors. This statistical approach has been utilized to study the microfluidic mixing to mix water and dye mixtures of 70 μl volume. The outcome of the statistical design, experimentation and analysis was then exploited for optimizing the design, fabrication and assembly of the microfluidic devices. As a result of the experiments that were performed, the system was fine tuned and the mixing time was reduced from 5.5 minutes to 2 minutes.

Poisson regression is a commonly used tool for analyzing rate data; however, the assumption that the mean and variance of a process are equal rarely holds true in practice. When this assumption is violated, a quasi-Poisson distribution can be used to account for the existing over- or under-dispersion. This paper presents an analysis of a study conducted by NASA to assess the performance of a new airborne spacing algorithm. A deterministic computer simulation was conducted to examine the algorithm in various conditions designed to simulate real-life scenarios, and two measures of algorithm performance were modeled using both continuous and categorical factors. Due to the presence of under-dispersion, tests for significance of main effects and two-factor interactions required bias adjustment. This paper presents a comparison of tests of effects for the Poisson and quasi-Poisson models, details of fitting these models using common statistical software packages, and calculation of dispersion tests.