Technical Reports, Statistics

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Browsing Technical Reports, Statistics by Author "Anderson-Cook, Christine M."

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    Cost Penalized Estimation and Prediction Evaluation for Split-Plot Designs
    Liang, Li; Anderson-Cook, Christine M.; Robinson, Timothy J. (Virginia Tech, 2005-02-02)
    The use of response surface methods generally begins with a process or system involving a response y that depends on a set of k controllable input variables (factors) x₁, x₂,…,xk. To assess the effects of these factors on the response, an experiment is conducted in which the levels of the factors are varied and changes in the response are noted. The size of the experimental design (number of distinct level combinations of the factors as well as number of runs) depends on the complexity of the model the user wishes to fit. Limited resources due to time and/or cost constraints are inherent to most experiments, and hence, the user typically approaches experimentation with a desire to minimize the number of experimental trials while still being able to adequately estimate the underlying model.
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    A Model to Predict the Impact of Specification Changes on Chloride-Induced Corrosion Service Life of Virginia Bridge Decks
    Trevor J. Kirkpatrick; Richard E. Weyers; Anderson-Cook, Christine M.; Michael M. Sprinkel; Michael C. Brown (Virginia Center for Transportation Innovation and Research, 2002-10)
    A model to determine the time to first repair and subsequent rehabilitation of concrete bridge decks exposed to chloride deicer salts that recognizes and incorporates the statistical nature of factors affecting the corrosion process is developed. The model expands on an existing deterministic model by using statistical computing techniques, including resampling techniques such as the parametric and simple bootstrap. Emphasis was placed on the diffusion portion of the diffusion-cracking model, but advances can be readily included for the time for corrosion deterioration after corrosion initiation. Data collected from ten bridge decks built in Virginia between 1981 and 1994 were used to model the surface chloride concentration, apparent diffusion coefficient, and clear cover depth. Several ranges of the chloride corrosion initiation concentration, as determined from the available literature, were investigated. The time to first repair and subsequent rehabilitation predicted by the stochastic model is shorter than the time to first repair and subsequent rehabilitation predicted by the deterministic model. The stochastic model is believed to more accurately reflect the true nature of bridge deck deterioration because it takes into account the fact that data for each of the parameters affecting chloride diffusion and corrosion initiation are not necessarily normally distributed. The model was validated by comparison of projected service lives of bridge decks built from 1981 to 1994 derived from the model to historical service life data for 129 bridge decks built in Virginia between 1968 and 1972. The time to rehabilitation predicted for the set of bridge decks built between 1981 and 1994 by the stochastic model was approximately 13 years longer than the normalized time to rehabilitation projected for the bridge decks built between 1968 and 1972 using historical data. The time to first repair and rehabilitation predicted by the probabilistic method more closely matches that of historical data than the time to first repair and rehabilitation predicted by the average value solution. The additional service life expected for the set of bridges built between 1981 and 1994 over those constructed from 1968 to 1972 can be attributed to the decrease in w/c ratio from 0.47 to 0.45 and slight increase in as-built cover depth from approximately 50 mm (2 in.) to 63.5 to 76 mm (2.5 to 3.0 in.).
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    Robust Parameter Design: A Semi-Parametric Approach
    Pickle, Stephanie M.; Robinson, Timothy J.; Birch, Jeffrey B.; Anderson-Cook, Christine M. (Virginia Tech, 2005)
    Parameter design or robust parameter design (RPD) is an engineering methodology intended as a cost-effective approach for improving the quality of products and processes. The goal of parameter design is to choose the levels of the control variables that optimize a defined quality characteristic. An essential component of robust parameter design involves the assumption of well estimated models for the process mean and variance. Traditionally, the modeling of the mean and variance has been done parametrically. It is often the case, particularly when modeling the variance, that nonparametric techniques are more appropriate due to the nature of the curvature in the underlying function. Most response surface experiments involve sparse data. In sparse data situations with unusual curvature in the underlying function, nonparametric techniques often result in estimates with problematic variation whereas their parametric counterparts may result in estimates with problematic bias. We propose the use of semi-parametric modeling within the robust design setting, combining parametric and nonparametric functions to improve the quality of both mean and variance model estimation. The proposed method will be illustrated with an example and simulations.