Experimental design in the presence of an uncontrollable variable: Model characteristics and design augmentation in a front wheel alignment experiment.

An off-line experiment was performed to estimate a model for process control describing the empirical relationship between the design and production factors affecting the front wheel camber angle. During the experiment, an additional factor was identified which could not be manipulated. Labeled an uncontrollable variable, this factor had to be included in the experiment since it was shown to affect the camber angle. Motivated by this experiment, problems are identified in experimental designs which ignore an uncontrollable variable. It is shown how the uncontrollable variable affects the determinant of the information matrix and the variance of predictions generated from the model. Numerous examples are given. A methodology is developed for improving the original experimental design by augmenting the experiment with another observation of the uncontrollable variable modeled as a normally distributed random variable. Under the constraints of a cost model, four sampling options are evaluated for choosing a value of the uncontrollable variable for the augmented design. Augmented designs are evaluated using two criteria: the expected value of $\vert$X\sp\primeX$\vert$, and the expected center the information function (with respect to the uncontrollable variable). The methodology augments the experiment with either a 3\sp3, a 3 x 2 x 2, or a 2\sp3 factorial design. Expressions for the expected value of $\vert$X\sp\primeX$\vert$, the expected center of the information function, and the expected cost of the augmented design are derived. Depending upon the cost of measuring the uncontrollable variable, more than one sampling option results in an expected value of $\vert$X\sp\primeX$\vert$ which is greater than the value expected by merely selecting the next observation of the uncontrollable variable. More than one sampling option also results in an expected center of the information function closer to the mean of the uncontrollable variable distribution than the value expected by merely selecting the next observation. Strategies to center the information function can lead to a greater expected value of $\vert$X\sp\primeX$\vert$. Both desirable design criteria are expected depending upon the cost of measuring the uncontrollable variable. The methodology improves the process control model by allowing minimal variance predictions to be generated for vehicles representative of those produced in the assembly plant.Ph.D.Industrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105479/1/9023620.pdfDescription of 9023620.pdf : Restricted to UM users only

Analysing student evaluations of teaching: Comparing means and proportions

Student Evaluations of Teaching (SETs) play a central role in modern academia. They are used for tenure, promotion, teaching improvement and other important decisions. One would think that the data collected from a SET would be analysed correctly, but such is typically not the case, as can be seen in this study later. Therefore we propose a correct method for analysing SET data. The present paper compares the two methods on a large data-set of actual SETs. We show that the traditional method can misrepresent a teacher\u27s performance, and that the traditional method can be extremely sensitive to outliers; neither of these characteristics is desirable. In contrast, the proposed method appears to suffer from neither of these defects. © 2011 Taylor & Francis

Identification of factors affecting front end alignment : on-line and off-line analyses

http://deepblue.lib.umich.edu/bitstream/2027.42/7196/5/bam0384.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/7196/4/bam0384.0001.001.tx