Document Type

Dissertation - Open Access

Award Date


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics

First Advisor

Gemechis Djira


Response surface methodology (RSM) is a ubiquitous optimization approach used in a wide variety of scientific research studies. The philosophy behind a response surface method is to sequentially run relatively simple experiments or models in order to optimize a response variable of interest. In other words, we run a small number of experiments sequentially that can provide a large amount of information upon augmentation. In this dissertation, the RSM technique is utilized in order to find the optimum fabrication condition of a polymer solar cell that maximizes the cell efficiency. The optimal device performance was achieved using 10.25 mg/ml polymer concentration, 0.42 polymer-fullerene ratio, and 1624 rpm of active layer spinning speed. The cell efficiency at the optimum stationary point was found to be 5.23% for the Poly(diketopyrrolopyrrole-terthiophene) (PDPP3T)/PC60BM solar cells. Secondly, we explored methods for constructing a confidence region for the stationary point in RSM. In particular, we developed methods for constructing simultaneous confidence intervals for the coordinates of a stationary point in a quadratic response surface model. The methods include Bonferroni adjustment, a plug-in approach based on the asymptotic distribution of maximum likelihood estimators, and bootstrapping. The simultaneous coverage probabilities of the proposed methods are assessed via simulation. The coverage probabilities for the Bonferroni and plug-in approaches are pretty close to the nominal levels of 0.95 for large sample sizes. The metaheuristic method is also considered in order to search for an alternative solution to the design matrix that may be near to the optimal solution. Finally, we explored recent developments in RSM including generalized linear models and the case of multivariate response variables.

Library of Congress Subject Headings

Response surfaces (Statistics)
Solar cells.
Mathematical optimization.


Includes bibliographical references (123-130)



Number of Pages



South Dakota State University


In Copyright - Educational Use Permitted

Available for download on Thursday, August 23, 2018