ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.
In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.
Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.
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- Creators: Pan, Rong
Description
Bayesian networks are powerful tools in system reliability assessment due to their flexibility in modeling the reliability structure of complex systems. This dissertation develops Bayesian network models for system reliability analysis through the use of Bayesian inference techniques.
Bayesian networks generalize fault trees by allowing components and subsystems to be related by conditional probabilities instead of deterministic relationships; thus, they provide analytical advantages to the situation when the failure structure is not well understood, especially during the product design stage. In order to tackle this problem, one needs to utilize auxiliary information such as the reliability information from similar products and domain expertise. For this purpose, a Bayesian network approach is proposed to incorporate data from functional analysis and parent products. The functions with low reliability and their impact on other functions in the network are identified, so that design changes can be suggested for system reliability improvement.
A complex system does not necessarily have all components being monitored at the same time, causing another challenge in the reliability assessment problem. Sometimes there are a limited number of sensors deployed in the system to monitor the states of some components or subsystems, but not all of them. Data simultaneously collected from multiple sensors on the same system are analyzed using a Bayesian network approach, and the conditional probabilities of the network are estimated by combining failure information and expert opinions at both system and component levels. Several data scenarios with discrete, continuous and hybrid data (both discrete and continuous data) are analyzed. Posterior distributions of the reliability parameters of the system and components are assessed using simultaneous data.
Finally, a Bayesian framework is proposed to incorporate different sources of prior information and reconcile these different sources, including expert opinions and component information, in order to form a prior distribution for the system. Incorporating expert opinion in the form of pseudo-observations substantially simplifies statistical modeling, as opposed to the pooling techniques and supra Bayesian methods used for combining prior distributions in the literature.
The methods proposed are demonstrated with several case studies.
Bayesian networks generalize fault trees by allowing components and subsystems to be related by conditional probabilities instead of deterministic relationships; thus, they provide analytical advantages to the situation when the failure structure is not well understood, especially during the product design stage. In order to tackle this problem, one needs to utilize auxiliary information such as the reliability information from similar products and domain expertise. For this purpose, a Bayesian network approach is proposed to incorporate data from functional analysis and parent products. The functions with low reliability and their impact on other functions in the network are identified, so that design changes can be suggested for system reliability improvement.
A complex system does not necessarily have all components being monitored at the same time, causing another challenge in the reliability assessment problem. Sometimes there are a limited number of sensors deployed in the system to monitor the states of some components or subsystems, but not all of them. Data simultaneously collected from multiple sensors on the same system are analyzed using a Bayesian network approach, and the conditional probabilities of the network are estimated by combining failure information and expert opinions at both system and component levels. Several data scenarios with discrete, continuous and hybrid data (both discrete and continuous data) are analyzed. Posterior distributions of the reliability parameters of the system and components are assessed using simultaneous data.
Finally, a Bayesian framework is proposed to incorporate different sources of prior information and reconcile these different sources, including expert opinions and component information, in order to form a prior distribution for the system. Incorporating expert opinion in the form of pseudo-observations substantially simplifies statistical modeling, as opposed to the pooling techniques and supra Bayesian methods used for combining prior distributions in the literature.
The methods proposed are demonstrated with several case studies.
ContributorsYontay, Petek (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Shunk, Dan L. (Committee member) / Du, Xiaoping (Committee member) / Arizona State University (Publisher)
Created2016
Description
Mixture experiments are useful when the interest is in determining how changes in the proportion of an experimental component affects the response. This research focuses on the modeling and design of mixture experiments when the response is categorical namely, binary and ordinal. Data from mixture experiments is characterized by the perfect collinearity of the experimental components, resulting in model matrices that are singular and inestimable under likelihood estimation procedures. To alleviate problems with estimation, this research proposes the reparameterization of two nonlinear models for ordinal data -- the proportional-odds model with a logistic link and the stereotype model. A study involving subjective ordinal responses from a mixture experiment demonstrates that the stereotype model reveals useful information about the relationship between mixture components and the ordinality of the response, which the proportional-odds fails to detect.
The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions.
The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance.
The second half of this research deals with the construction of exact D-optimal designs for binary and ordinal responses. For both types, the base models fall under the class of Generalized Linear Models (GLMs) with a logistic link. First, the properties of the exact D-optimal mixture designs for binary responses are investigated. It will be shown that standard mixture designs and designs proposed for normal-theory responses are poor surrogates for the true D-optimal designs. In contrast with the D-optimal designs for normal-theory responses which locate support points at the boundaries of the mixture region, exact D-optimal designs for GLMs tend to locate support points at regions of uncertainties. Alternate D-optimal designs for binary responses with high D-efficiencies are proposed by utilizing information about these regions.
The Mixture Exchange Algorithm (MEA), a search heuristic tailored to the construction of efficient mixture designs with GLM-type responses, is proposed. MEA introduces a new and efficient updating formula that lessens the computational expense of calculating the D-criterion for multi-categorical response systems, such as ordinal response models. MEA computationally outperforms comparable search heuristics by several orders of magnitude. Further, its computational expense increases at a slower rate of growth with increasing problem size. Finally, local and robust D-optimal designs for ordinal-response mixture systems are constructed using MEA, investigated, and shown to have high D-efficiency performance.
ContributorsMancenido, Michelle V (Author) / Montgomery, Douglas C. (Thesis advisor) / Pan, Rong (Thesis advisor) / Borror, Connie M. (Committee member) / Shunk, Dan L. (Committee member) / Arizona State University (Publisher)
Created2016