Case Studies and White Papers
Employing Power to "Right-Size" Design of Experiments
This article provides insights on how many runs are required to make it very likely that a test will reveal any important effects. Due to the mathematical complexities of multifactor design of experiments (DOE) matrices, the calculations for adequate power and precision are not practical to do by 'hand' so the focus is kept at a high level--scoping out the forest rather than detailing all the trees. By example, reader will learn the price that must be paid for an adequately-sized experiment and the penalty incurred by conveniently grouping hard-to-change factors.
Due to operational or physical considerations, standard factorial and response surface method (RSM) design of experiments (DOE) often prove to be unsuitable. In such cases a computer-generated statistically-optimal design fills the breech. This article explores vital mathematical properties for evaluating alternative designs with a focus on what is really important for industrial experimenters. To assess “goodness of design” such evaluations must consider the model choice, specific optimality criteria (in particular D and I), precision of estimation based on the fraction of design space (FDS), the number of runs to achieve required precision, lack-of-fit testing, and so forth. With a focus on RSM, all these issues are considered at a practical level, keeping engineers and scientists in mind. This brings to the forefront such considerations as subject-matter knowledge from first principles and experience, factor choice and the feasibility of the experiment design.
Improved Copper and Gold Recovery at KGHM International’s Robinson Mine
In an effort to recover additional copper and gold at KGHM International's Robinson Mine located near Ruth, Nevada, an in-plant study was undertaken to quantify potential flotation recoveries from the concentrator's final tailings stream. Tests were conducted by passing a small continuous sample of final tailings through a single 1.5 m3 FLSmidth XCELL™ demonstration flotation machine. This paper reviews the results obtained from the in-plant testing with the single 1.5 m3 flotation cell and provides a comparison to the subsequent operational performance of multiple 160 m3 flotation machines. The DOE test campaign produced a highly reliable Copper Tailings Grade Model. Actual operational data validated the performance of the predictive model and pilot cell testing. The full-scale flotation plant achieved a 27.1% recovery over a three-year period. The added recovery has increased copper production by 5.95 million kg annually and gold by a significant amount. (Proceedings from 2013 Copper International Conference, Santiago, Chile, Dec 1-4, Session MP44.)
DOE Improves Throughput in Manufacturing of Key Intermediate
Researchers at Codexis , a California-based, worldwide leader in protein engineering, used Design-Expert software to improve the performance of an enzyme. Their DOE rapidly developed an efficient catalytic manufacturing process for manufacturing, resulting in high throughput yield of product with excellent selectivity and purity.
Design of experiments (DoE) incorporates statistical methods and multivariate analysis into microscale chemistry. Controlled experiments help analysts evaluate processes with that involve several variables, such as temperature and osmolality in cell culture processes. Often three variables are studied together, with the results expressed in a three-dimensional response-surface graphs.
Resin manufacturer Interplastic rapidly developed a new gel coat via design of experiments using Design-Expert software. “Stat-Ease helped us to achieve an exceptionally high level of quality with this product, which has been very well received by our customers and is a resounding success in the market.”
Optimal Experimental Design with R
BOOK REVIEW: This book provides guidance on the construction of experiments, including sample size calculations, hypothesis testing, and confidence estimation.
Framing a QbD Design Space with Tolerance Intervals
Given the push for Quality by Design (QbD) by FDA and drug agencies worldwide, statistical methods are becoming increasingly vital for pharmaceutical manufacturers. Response surface methods for DOE provide powerful tools to manage the impact of multiple factors and their interactions.
Researchers at Codexis Laboratories Singapore performed a full-factorial designed experiment with 20 runs to determine the impact of four independent variables on product selectivity during a silylation reaction. The result was a process that delivered 95% selectivity along with an 88% yield.
Given the push for Quality by Design (QbD) by the US FDA and equivalent agencies worldwide, statistical methods are becoming increasingly vital for pharmaceutical manufacturers. Design of experiments (DOE) is a primary tool because “it provides structured, organized method for determining the relationship between factors affecting a process and the response of that process." Tolerance intervals (TI) verify that the design space will be robust for meeting the manufacturing specifications on every individual unit, not just on average.