Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

abstract: The emergence of new technologies as well as a fresh look at analyzing existing processes have given rise to a new type of response characteristic, known as a profile. Profiles are useful when a quality variable is functionally dependent on one or more explanatory, or independent, variables. So, instead of observing a single measurement on each unit or product a set of values is obtained over a range which, when plotted, takes the shape of a curve. Traditional multivariate monitoring schemes are inadequate for monitoring profiles due to high dimensionality and poor use of the information stored in functional form leading to very large variance-covariance matrices. Profile monitoring has become an important area of study in statistical process control and is being actively addressed by researchers across the globe. This research explores the understanding of the area in three parts. A comparative analysis is conducted of two linear profile-monitoring techniques based on probability of false alarm rate and average run length (ARL) under shifts in the model parameters. The two techniques studied are control chart based on classical calibration statistic and a control chart based on the parameters of a linear model. The research demonstrates that a profile characterized by a parametric model is more efficient monitoring scheme than one based on monitoring only the individual features of the profile. A likelihood ratio based changepoint control chart is proposed for detecting a sustained step shift in low order polynomial profiles. The test statistic is plotted on a Shewhart like chart with control limits derived from asymptotic distribution theory. The statistic is factored to reflect the variation due to the parameters in to aid in interpreting an out of control signal. The research also looks at the robust parameter design study of profiles, also referred to as signal response systems. Such experiments are often necessary for understanding and reducing the common cause variation in systems. A split-plot approach is proposed to analyze the profiles. It is demonstrated that an explicit modeling of variance components using generalized linear mixed models approach has more precise point estimates and tighter confidence intervals. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010

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Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Employing a split-plot design structure minimizes the number of required experimental settings for the hard-to-change factors. In this research, we propose classes of equivalent estimation second-order response surface split-plot designs for which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Designs that possess the equivalence property enjoy the advantages of best linear unbiased estimates and design selection that is robust to model misspecification and independent of the variance components. We present a generalized proof of the equivalence conditions that enables the development of several systematic design construction strategies and provides the ability to verify numerically that a design provides equivalent estimates, resulting in a broad catalog of designs. We explore the construction of balanced and unbalanced split-plot versions of the central composite and Box-Behnken designs. In addition, we illustrate the utility of numerical verification in generating D-optimal and minimal point designs, including split-plot versions of the Notz, Hoke, Box and Draper, and hybrid designs. Finally, we consider the practical implications of analyzing a near-equivalent design when a suitable equivalent design is not available. By simulation, we compare methods of estimation to provide a practitioner with guidance on analysis alternatives when a best linear unbiased estimator is not available. Our goal throughout this research is to develop practical experimentation strategies for restricted randomization that are consistent with the philosophy of traditional response surface methodology. / Ph. D.

When a reliability experiment is used, practitioners can understand better what lifetimes to expect of a product under different operating conditions and what factors are important to designing reliability into a product. Reliability experiments, however, can be very challenging to analyze because often the reliability or lifetime data tend to follow distinctly non-normal distributions and the experiments typically involve censoring. Time and cost constraints may also lead to reliability experiments with experimental protocols that are not completely randomized. In many industrial experiments, for example, the split-plot structure arises when the randomization of the experimental runs is restricted. Additionally, for many reliability experiments, it is often cost effective to apply a treatment combination to a stand with multiple units on it as opposed to each unit individually, which introduces subsampling. The analysis of lifetime data assuming a completely randomized design has been well studied, but until recently analysis methodologies for more complex experimental designs with multiple error terms have not been a focus of the reliability field. This dissertation provides two analysis methods for analyzing right-censored Weibull distributed lifetime data from a split-plot experiment with subsampling. We evaluate the proposed methods through a simulation study. Companies also routinely perform life tests on their products to ensure that products meet requirements. Each of these life tests typically involves testing several units simultaneously with interest in the times to failure. Again, the fact that lifetime data tend to be nonnormally distributed and censored make the development of a control charting procedure more demanding. In this dissertation, one-sided lower and upper likelihood ratio based cumulative sum (CUSUM) control charting procedures are developed for right-censored Weibull lifetime data to monitor changes in the scale parameter, also known as the characteristic life, for a fixed value of the Weibull shape parameter. Because a decrease in the characteristic life indicates a decrease in the mean lifetime of a product, a one-sided lower CUSUM chart is the main focus. We illustrate the development and implementation of the chart and evaluate the properties through a simulation study. / Ph. D.

abstract: In mixture-process variable experiments, it is common that the number of runs is greater than in mixture-only or process-variable experiments. These experiments have to estimate the parameters from the mixture components, process variables, and interactions of both variables. In some of these experiments there are variables that are hard to change or cannot be controlled under normal operating conditions. These situations often prohibit a complete randomization for the experimental runs due to practical and economical considerations. Furthermore, the process variables can be categorized into two types: variables that are controllable and directly affect the response, and variables that are uncontrollable and primarily affect the variability of the response. These uncontrollable variables are called noise factors and assumed controllable in a laboratory environment for the purpose of conducting experiments. The model containing both noise variables and control factors can be used to determine factor settings for the control factor that makes the response "robust" to the variability transmitted from the noise factors. These types of experiments can be analyzed in a model for the mean response and a model for the slope of the response within a split-plot structure. When considering the experimental designs, low prediction variances for the mean and slope model are desirable. The methods for the mixture-process variable designs with noise variables considering a restricted randomization are demonstrated and some mixture-process variable designs that are robust to the coefficients of interaction with noise variables are evaluated using fraction design space plots with the respect to the prediction variance properties. Finally, the G-optimal design that minimizes the maximum prediction variance over the entire design region is created using a genetic algorithm. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010

Freshwater mussels (Unionidae) in the United States have experienced dramatic declines, and 25% species are listed as federally endangered. Hence, recovery plans for endangered species proposed a strategy of propagation of young mussels for release to natal rivers to augment declining populations. In this study, I conducted laboratory experiments, assessed site suitability for mussel restoration, and evaluated survival and growth rates of released mussels to meet the requirements of recovery plan. I conducted multiple experiments to develop an improved protocol for juvenile mussel propagation and culture. Significantly greater survival and growth rates were found in newly metamorphosed juveniles of the rainbow mussel (Villosa iris) reared in a substrate of fine sediment and one-month-old juveniles of wavy-rayed lampmussel (Lampsilis fasciola) fed on natural food in pond water. Bio-filter media greatly increased water quality by reducing the concentration of ammonia and nitrite. The negative impacts of flatworm predation and filamentous algae in juvenile culture were controlled, and juvenile escapement was prevented. Juvenile mussels were successfully produced and cultured to stockable size (>15 mm) for release. I released laboratory-propagated mussels at three historically important sites in Clinch and Powell rivers for the assessment of site suitability. Use of cages was the most effective method to determine site suitability because the free-released mussels (untagged, tagged) had low catchability. Mussels released at Horton Ford, Clinch River, exhibited significantly faster growth. Horton Ford is the most suitable site, while environmental conditions at Fugate Ford, Powell River, are deemed unsuitable for mussel restoration and recovery. To facilitate the detection of released mussels, I applied Passive Integrated Transponder tags to laboratory-produced juveniles of the endangered Cumberlandian combshell (Epioblasma brevidens) and released them near Brooks Bridge, Powell River. The detection probability increased above 98%. I developed a set of hierarchical Bayesian models incorporating individual variations, seasonal variations, periodic growth stages and growth cessation to estimate survival, detection probability and growth of released mussels in a changing environment. Mussels of E. brevidens exhibited great survival (> 99% per month) and growth, indicating suitable conditions for recovery of this endangered species at this site. / Ph. D.