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No-confounding designs of 20 and 24 runs for screening experiments and a design selection methodology

Description

Nonregular screening designs can be an economical alternative to traditional resolution IV 2^(k-p) fractional factorials. Recently 16-run nonregular designs, referred to as no-confounding designs, were introduced in the literature. These designs have the property that no pair of main effect (ME) and two-factor interaction (2FI) estimates are completely confounded. In this dissertation, orthogonal arrays were evaluated with many popular design-ranking criteria in order to identify optimal 20-run and 24-run no-confounding designs. Monte Carlo simulation was used to empirically assess the model fitting effectiveness of the recommended no-confounding designs. The results of the simulation demonstrated that these new designs, particularly the 24-run designs, are successful at detecting active effects over 95% of the time given sufficient model effect sparsity. The final chapter presents a screening design selection methodology, based on decision trees, to aid in the selection of a screening design from a list of published options. The methodology determines which of a candidate set of screening designs has the lowest expected experimental cost.

ContributorsStone, Brian (Author) / Montgomery, Douglas C. (Thesis advisor) / Silvestrini, Rachel T. (Committee member) / Fowler, John W (Committee member) / Borror, Connie M. (Committee member) / Arizona State University (Publisher)

Created2013

Bridging the gap between space-filling and optimal designs

Description

This dissertation explores different methodologies for combining two popular design paradigms in the field of computer experiments. Space-filling designs are commonly used in order to ensure that there is good coverage of the design space, but they may not result in good properties when it comes to model fitting. Optimal designs traditionally perform very well in terms of model fitting, particularly when a polynomial is intended, but can result in problematic replication in the case of insignificant factors. By bringing these two design types together, positive properties of each can be retained while mitigating potential weaknesses. Hybrid space-filling designs, generated as Latin hypercubes augmented with I-optimal points, are compared to designs of each contributing component. A second design type called a bridge design is also evaluated, which further integrates the disparate design types. Bridge designs are the result of a Latin hypercube undergoing coordinate exchange to reach constrained D-optimality, ensuring that there is zero replication of factors in any one-dimensional projection. Lastly, bridge designs were augmented with I-optimal points with two goals in mind. Augmentation with candidate points generated assuming the same underlying analysis model serves to reduce the prediction variance without greatly compromising the space-filling property of the design, while augmentation with candidate points generated assuming a different underlying analysis model can greatly reduce the impact of model misspecification during the design phase. Each of these composite designs are compared to pure space-filling and optimal designs. They typically out-perform pure space-filling designs in terms of prediction variance and alphabetic efficiency, while maintaining comparability with pure optimal designs at small sample size. This justifies them as excellent candidates for initial experimentation.

ContributorsKennedy, Kathryn (Author) / Montgomery, Douglas C. (Thesis advisor) / Johnson, Rachel T. (Thesis advisor) / Fowler, John W (Committee member) / Borror, Connie M. (Committee member) / Arizona State University (Publisher)

Created2013

Statistical Analysis of Power Differences between Experimental Design Software Packages

Description

Based on findings of previous studies, there was speculation that two well-known experimental design software packages, JMP and Design Expert, produced varying power outputs given the same design and user inputs. For context and scope, another popular experimental design software package, Minitab® Statistical Software version 17, was added to the comparison. The study compared multiple test cases run on the three software packages with a focus on 2k and 3K factorial design and adjusting the standard deviation effect size, number of categorical factors, levels, number of factors, and replicates. All six cases were run on all three programs and were attempted to be run at one, two, and three replicates each. There was an issue at the one replicate stage, however—Minitab does not allow for only one replicate full factorial designs and Design Expert will not provide power outputs for only one replicate unless there are three or more factors. From the analysis of these results, it was concluded that the differences between JMP 13 and Design Expert 10 were well within the margin of error and likely caused by rounding. The differences between JMP 13, Design Expert 10, and Minitab 17 on the other hand indicated a fundamental difference in the way Minitab addressed power calculation compared to the latest versions of JMP and Design Expert. This was found to be likely a cause of Minitab’s dummy variable coding as its default instead of the orthogonal coding default of the other two. Although dummy variable and orthogonal coding for factorial designs do not show a difference in results, the methods affect the overall power calculations. All three programs can be adjusted to use either method of coding, but the exact instructions for how are difficult to find and thus a follow-up guide on changing the coding for factorial variables would improve this issue.

ContributorsArmstrong, Julia Robin (Author) / McCarville, Daniel R. (Thesis director) / Montgomery, Douglas (Committee member) / Industrial, Systems (Contributor, Contributor) / Barrett, The Honors College (Contributor)

Created2017-05