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Browsing by Author "Ye, Keying"

Now showing 1 - 20 of 55
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    Accounting for Business Combinations: A Test for Long-Term Market Memory
    Chatraphorn, Pongprot (Virginia Tech, 2001-12-19)
    The purpose of this research is to examine whether accounting methods for business combinations (purchase and pooling-of-interests accounting) have a different effect on firms' market value of equity in the combination year and thereafter. In particular, after the accounting method is no longer disclosed in the financial statements, does it have an impact on market value of equity of the combined firms because the accounting figures are different? A five-year period subsequent to a particular business combination is used because public companies are not required to disclose the details of the combination for more than three years after the effective date of the combination. This research, thus, tests whether market participants still take into consideration the accounting method of past business combinations when this information is no longer disclosed in the financial statements. In addition to the testing of the impact of the accounting methods, the value-relevance of goodwill amortization is investigated. The sample consisted of 100 U.S. business combination transactions during the period 1985–1995 (77 pooling firms and 23 purchase firms). The results do not indicate that market participants price pooling firms and purchase firms differently at the time of business combinations. The results, in addition, do not confirm that when the details of a particular business combinations do not appear in the financial statements, pooling firms' accounting figures have a more positive effect on security prices than those of purchase firms. It seems that market participant are able, even in the long term, to account for the accounting difference between purchase and pooling-of-interests. Also, goodwill amortization does not appear to be value relevant.
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    An Alternative Estimate of Preferred Direction for Circular Data
    Otieno, Bennett Sango (Virginia Tech, 2002-07-25)
    Circular or Angular data occur in many fields of applied statistics. A common problem of interest in circular data is estimating a preferred direction and its corresponding distribution. This problem is complicated by the so-called wrap-around effect, which exists because there is no minimum or maximum on the circle. The usual statistics employed for linear data are inappropriate for directional data, as they do not account for the circular nature of directional data. Common choices for summarizing the preferred direction are the sample circular mean, and sample circular median. A newly proposed circular analog of the Hodges-Lehmann estimator is proposed, as an alternative estimate of preferred direction. The new measure of preferred direction is a robust compromise between circular mean and circular median. Theoretical results show that the new measure of preferred direction is asymptotically more efficient than the circular median and that its asymptotic efficiency relative to the circular mean is quite comparable. Descriptions of how to use the methods for constructing confidence intervals and testing hypotheses are provided. Simulation results demonstrate the relative strengths and weaknesses of the new approach for a variety of distributions.
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    Analysis of Zero-Heavy Data Using a Mixture Model Approach
    Wang, Shin Cheng (Virginia Tech, 1998-03-18)
    The problem of high proportion of zeroes has long been an interest in data analysis and modeling, however, there are no unique solutions to this problem. The solution to the individual problem really depends on its particular situation and the design of the experiment. For example, different biological, chemical, or physical processes may follow different distributions and behave differently. Different mechanisms may generate the zeroes and require different modeling approaches. So it would be quite impossible and inflexible to come up with a unique or a general solution. In this dissertation, I focus on cases where zeroes are produced by mechanisms that create distinct sub-populations of zeroes. The dissertation is motivated from problems of chronic toxicity testing which has a data set that contains a high proportion of zeroes. The analysis of chronic test data is complicated because there are two different sources of zeroes: mortality and non-reproduction in the data. So researchers have to separate zeroes from mortality and fecundity. The use of mixture model approach which combines the two mechanisms to model the data here is appropriate because it can incorporate the mortality kind of extra zeroes. A zero inflated Poisson (ZIP) model is used for modeling the fecundity in Ceriodaphnia dubia toxicity test. A generalized estimating equation (GEE) based ZIP model is developed to handle longitudinal data with zeroes due to mortality. A joint estimate of inhibition concentration (ICx) is also developed as potency estimation based on the mixture model approach. It is found that the ZIP model would perform better than the regular Poisson model if the mortality is high. This kind of toxicity testing also involves longitudinal data where the same subject is measured for a period of seven days. The GEE model allows the flexibility to incorporate the extra zeroes and a correlation structure among the repeated measures. The problem of zero-heavy data also exists in environmental studies in which the growth or reproduction rates of multi-species are measured. This gives rise to multivariate data. Since the inter-relationships between different species are imbedded in the correlation structure, the study of the information in the correlation of the variables, which is often accessed through principal component analysis, is one of the major interests in multi-variate data. In the case where mortality influences the variables of interests, but mortality is not the subject of interests, the use of the mixture approach can be applied to recover the information of the correlation structure. In order to investigate the effect of zeroes on multi-variate data, simulation studies on principal component analysis are performed. A method that recovers the information of the correlation structure is also presented.
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    Availability Analysis for the Quasi-Renewal Process
    Rehmert, Ian Jon (Virginia Tech, 2000-10-09)
    The behavior of repairable equipment is often modeled under assumptions such as perfect repair, minimal repair, or negligible repair. However the majority of equipment behavior does not fall into any of these categories. Rather, repair actions do take time and the condition of equipment following repair is not strictly "as good as new" or "as bad as it was" prior to repair. Non-homogeneous processes that reflect this type of behavior are not studied nearly as much as the minimal repair case, but they far more realistic in many situations. For this reason, the quasi-renewal process provides an appealing alternative to many existing models for describing a non-homogeneous process. A quasi-renewal process is characterized by a parameter that indicates process deterioration or improvement by falling in the interval [0,1) or (1,Infinity) respectively. This parameter is the amount by which subsequent operation or repair intervals are scaled in terms of the immediately previous operation or repair interval. Two equivalent expressions for the point availability of a system with operation intervals and repair intervals that deteriorate according to a quasi-renewal process are constructed. In addition to general expressions for the point availability, several theoretical distributions on the operation and repair intervals are considered and specific forms of the quasi-renewal and point availability functions are developed. The two point availability expressions are used to provide upper and lower bounds on the approximated point availability. Numerical results and general behavior of the point availability and quasi-renewal functions are examined. The framework provided here allows for the description and prediction of the time-dependent behavior of a non-homogeneous process without the assumption of limiting behavior, a specific cost structure, or minimal repair.
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    Bayesian D-Optimal Design for Generalized Linear Models
    Zhang, Ying (Virginia Tech, 2006-12-07)
    Bayesian optimal designs have received increasing attention in recent years, especially in biomedical and clinical trials. Bayesian design procedures can utilize the available prior information of the unknown parameters so that a better design can be achieved. However, a difficulty in dealing with the Bayesian design is the lack of efficient computational methods. In this research, a hybrid computational method, which consists of the combination of a rough global optima search and a more precise local optima search, is proposed to efficiently search for the Bayesian D-optimal designs for multi-variable generalized linear models. Particularly, Poisson regression models and logistic regression models are investigated. Designs are examined for a range of prior distributions and the equivalence theorem is used to verify the design optimality. Design efficiency for various models are examined and compared with non-Bayesian designs. Bayesian D-optimal designs are found to be more efficient and robust than non-Bayesian D-optimal designs. Furthermore, the idea of the Bayesian sequential design is introduced and the Bayesian two-stage D-optimal design approach is developed for generalized linear models. With the incorporation of the first stage data information into the second stage, the two-stage design procedure can improve the design efficiency and produce more accurate and robust designs. The Bayesian two-stage D-optimal designs for Poisson and logistic regression models are evaluated based on simulation studies. The Bayesian two-stage optimal design approach is superior to the one-stage approach in terms of a design efficiency criterion.
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    A Bayesian Hierarchical Approach to Dual Response Surface Modeling
    Chen, Younan; Ye, Keying (Virginia Tech, 2005)
    In modern quality engineering, dual response surface methodology is a powerful tool to monitor an industrial process by using both the mean and the standard deviation of the measurements as the responses. The least squares method in regression is often used to estimate the coefficients in the mean and standard deviation models, and various decision criteria are proposed by researchers to find the optimal conditions. Based on the inherent hierarchical structure of the dual response problems, we propose a hierarchical Bayesian approach to model dual response surfaces. Such an approach is compared with two frequentist least squares methods by using two real data sets and simulated data.
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    Bayesian Hierarchical Methods and the Use of Ecological Thresholds and Changepoints for Habitat Selection Models
    Pooler, Penelope S. (Virginia Tech, 2005-12-02)
    Modeling the complex relationships between habitat characteristics and a species' habitat preferences pose many difficult problems for ecological researchers. These problems are complicated further when information is collected over a range of time or space. Additionally, the variety of factors affecting these choices is difficult to understand and even more difficult to accurately collect information about. In light of these concerns, we evaluate the performance of current standard habitat preference models that are based on Bayesian methods and then present some extensions and supplements to those methods that prove to be very useful. More specifically, we demonstrate the value of extending the standard Bayesian hierarchical model using finite mixture model methods. Additionally, we demonstrate that an extension of the Bayesian hierarchical changepoint model to allow for estimating multiple changepoints simultaneously can be very informative when applied to data about multiple habitat locations or species. These models allow the researcher to compare the sites or species with respect to a very specific ecological question and consequently provide definitive answers that are often not available with more commonly used models containing many explanatory factors. Throughout our work we use a complex data set containing information about horseshoe crab spawning habitat preferences in the Delaware Bay over a five-year period. These data epitomize some of the difficult issues inherent to studying habitat preferences. The data are collected over time at many sites, have missing observations, and include explanatory variables that, at best, only provide surrogate information for what researchers feel is important in explaining spawning preferences throughout the bay. We also looked at a smaller data set of freshwater mussel habitat selection preferences in relation to bridge construction on the Kennerdell River in Western Pennsylvania. Together, these two data sets provided us with insight in developing and refining the methods we present. They also help illustrate the strengths and weaknesses of the methods we discuss by assessing their performance in real situations where data are inevitably complex and relationships are difficult to discern.
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    Bayesian hierarchical modelling of dual response surfaces
    Chen, Younan (Virginia Tech, 2005-11-29)
    Dual response surface methodology (Vining and Myers (1990)) has been successfully used as a cost-effective approach to improve the quality of products and processes since Taguchi (Tauchi (1985)) introduced the idea of robust parameter design on the quality improvement in the United States in mid-1980s. The original procedure is to use the mean and the standard deviation of the characteristic to form a dual response system in linear model structure, and to estimate the model coefficients using least squares methods. In this dissertation, a Bayesian hierarchical approach is proposed to model the dual response system so that the inherent hierarchical variance structure of the response can be modeled naturally. The Bayesian model is developed for both univariate and multivariate dual response surfaces, and for both fully replicated and partially replicated dual response surface designs. To evaluate its performance, the Bayesian method has been compared with the original method under a wide range of scenarios, and it shows higher efficiency and more robustness. In applications, the Bayesian approach retains all the advantages provided by the original dual response surface modelling method. Moreover, the Bayesian analysis allows inference on the uncertainty of the model parameters, and thus can give practitioners complete information on the distribution of the characteristic of interest.
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    Bayesian Methodology for Missing Data, Model Selection and Hierarchical Spatial Models with Application to Ecological Data
    Boone, Edward L. (Virginia Tech, 2003-01-31)
    Ecological data is often fraught with many problems such as Missing Data and Spatial Correlation. In this dissertation we use a data set collected by the Ohio EPA as motivation for studying techniques to address these problems. The data set is concerned with the benthic health of Ohio's waterways. A new method for incorporating covariate structure and missing data mechanisms into missing data analysis is considered. This method allows us to detect relationships other popular methods do not allow. We then further extend this method into model selection. In the special case where the unobserved covariates are assumed normally distributed we use the Bayesian Model Averaging method to average the models, select the highest probability model and do variable assessment. Accuracy in calculating the posterior model probabilities using the Laplace approximation and an approximation based on the Bayesian Information Criterion (BIC) are explored. It is shown that the Laplace approximation is superior to the BIC based approximation using simulation. Finally, Hierarchical Spatial Linear Models are considered for the data and we show how to combine analysis which have spatial correlation within and between clusters.
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    Bayesian Model Averaging and Variable Selection in Multivariate Ecological Models
    Lipkovich, Ilya A. (Virginia Tech, 2002-04-09)
    Bayesian Model Averaging (BMA) is a new area in modern applied statistics that provides data analysts with an efficient tool for discovering promising models and obtaining esti-mates of their posterior probabilities via Markov chain Monte Carlo (MCMC). These probabilities can be further used as weights for model averaged predictions and estimates of the parameters of interest. As a result, variance components due to model selection are estimated and accounted for, contrary to the practice of conventional data analysis (such as, for example, stepwise model selection). In addition, variable activation probabilities can be obtained for each variable of interest. This dissertation is aimed at connecting BMA and various ramifications of the multivari-ate technique called Reduced-Rank Regression (RRR). In particular, we are concerned with Canonical Correspondence Analysis (CCA) in ecological applications where the data are represented by a site by species abundance matrix with site-specific covariates. Our goal is to incorporate the multivariate techniques, such as Redundancy Analysis and Ca-nonical Correspondence Analysis into the general machinery of BMA, taking into account such complicating phenomena as outliers and clustering of observations within a single data-analysis strategy. Traditional implementations of model averaging are concerned with selection of variables. We extend the methodology of BMA to selection of subgroups of observations and im-plement several approaches to cluster and outlier analysis in the context of the multivari-ate regression model. The proposed algorithm of cluster analysis can accommodate re-strictions on the resulting partition of observations when some of them form sub-clusters that have to be preserved when larger clusters are formed.
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    Bayesian Two Stage Design Under Model Uncertainty
    Neff, Angela R. (Virginia Tech, 1997-01-16)
    Traditional single stage design optimality procedures can be used to efficiently generate data for an assumed model y = f(x(m),b) + ε. The model assumptions include the form of f, the set of regressors, x(m) , and the distribution of ε. The nature of the response, y, often provides information about the model form (f) and the error distribution. It is more difficult to know, apriori, the specific set of regressors which will best explain the relationship between the response and a set of design (control) variables x. Misspecification of x(m) will result in a design which is efficient, but for the wrong model. A Bayesian two stage design approach makes it possible to efficiently design experiments when initial knowledge of x(m) is poor. This is accomplished by using a Bayesian optimality criterion in the first stage which is robust to model uncertainty. Bayesian analysis of first stage data reduces uncertainty associated with x(m), enabling the remaining design points (second stage design) to be chosen with greater efficiency. The second stage design is then generated from an optimality procedure which incorporates the improved model knowledge. Using this approach, numerous two stage design procedures have been developed for the normal linear model. Extending this concept, a Bayesian design augmentation procedure has been developed for the purpose of efficiently obtaining data for variance modeling, when initial knowledge of the variance model is poor.
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    A Bivariate Renewal Process and Its Applications in Maintenance Policies
    Yang, Sang-Chin (Virginia Tech, 1999-12-13)
    Same types of systems with the same age usually have different amounts of cumulated usage. These systems when in operation usually have different performance and effectiveness. In this case the existing models of the univariate measures of system effectiveness are inadequate and incomplete. For example, the univariate availability measures for these same-aged systems are all the same even though with different amounts of usage. This is the motivation for this research to pursue a bivariate approach in reliability and maintenance modeling. This research presents a framework for bivariate modeling of a single-unit system. Five key efforts are identified and organized as: (i) bivariate failure modeling, (ii) bivariate renewal modeling, (iii) bivariate corrective maintenance (CM) modeling, (iv) bivariate preventive maintenance (PM) modeling, and (v) bivariate availability modeling. The results provide a foundation for further study of bivariate and multivariate models. For bivariate failure modeling, several bivariate failure models are constructed to represent the possible correlation structures of the two system aging variables, time and usage. The behavior of these models is examined under various correlation structures. The developed models are used to analyze example maintenance problems. Models for bivariate renewal, bivariate CM, and bivariate PM are derived based on the constructed bivariate failure models and the developed bivariate renewal theory. For bivariate CM modeling, corrective maintenance is modeled as an alternating bivariate renewal process or simply an ordinary bivariate renewal process. For bivariate PM modeling, PM models are examined under a bivariate age replacement preventive maintenance policy. The Laplace transforms of the renewal functions (and densities) for these models are obtained. Definitions for bivariate availability functions are developed. Based on the derived CM and PM models, the Laplace transforms for their corresponding bivariate availability models are constructed. The idea of the quality of availability measure is also defined in terms of bivariate availability models. The most significant observation is that this framework provides a new way to study the reliability and maintenance of equipment for which univariate measures are incomplete. Therefore, a new area of reliability research is identified. The definitions offered may be modified and the approach to model formulation presented may be used to define other models.
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    Canonical Variate Analysis and Related Methods with Longitudinal Data
    Beaghen, Michael Jr. (Virginia Tech, 1997-11-13)
    Canonical variate analysis (CVA) is a widely used method for analyzing group structure in multivariate data. It is mathematically equivalent to a one-way multivariate analysis of variance and often goes by the name of canonical discriminant analysis. Change over time is a central feature of many phenomena of interest to researchers. This dissertation extends CVA to longitudinal data. It develops models whose purpose is to determine what is changing and what is not changing in the group structure. Three approaches are taken: a maximum likelihood approach, a least squares approach, and a covariance structure analysis approach. All methods have in common that they hypothesize canonical variates which are stable over time. The maximum likelihood approach models the positions of the group means in the subspace of the canonical variates. It also requires modeling the structure of the within-groups covariance matrix, which is assumed to be constant or proportional over time. In addition to hypothesizing stable variates over time, one can also hypothesize canonical variates that change over time. Hypothesis tests and confidence intervals are developed. The least squares methods are exploratory. They are based on three-mode PCA methods such as the Tucker2 and parallel factor analysis. Graphical methods are developed to display the relationships between the variables over time. Stable variates over time imply a particular structure for the between-groups covariance matrix. This structure is modeled using covariance structure analysis, which is available in the SAS package Proc Calis. Methods related to CVA are also discussed. First, the least squares methods are extended to canonical correlation analysis, redundancy analysis, Procrustes rotation and correspondence analysis with longitudinal data. These least squares methods lend themselves equally well to data from multiple datasets. Lastly, a least squares method for the common principal components model is developed.
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    Causal Gene Network Inference from Genetical Genomics Experiments via Structural Equation Modeling
    Liu, Bing (Virginia Tech, 2006-09-11)
    The goal of this research is to construct causal gene networks for genetical genomics experiments using expression Quantitative Trait Loci (eQTL) mapping and Structural Equation Modeling (SEM). Unlike Bayesian Networks, this approach is able to construct cyclic networks, while cyclic relationships are expected to be common in gene networks. Reconstruction of gene networks provides important knowledge about the molecular basis of complex human diseases and generally about living systems. In genetical genomics, a segregating population is expression profiled and DNA marker genotyped. An Encompassing Directed Network (EDN) of causal regulatory relationships among genes can be constructed with eQTL mapping and selection of candidate causal regulators. Several eQTL mapping approaches and local structural models were evaluated in their ability to construct an EDN. The edges in an EDN correspond to either direct or indirect causal relationships, and the EDN is likely to contain cycles or feedback loops. We implemented SEM with genetics algorithms to produce sub-models of the EDN containing fewer edges and being well supported by the data. The EDN construction and sparsification methods were tested on a yeast genetical genomics data set, as well as the simulated data. For the simulated networks, the SEM approach has an average detection power of around ninety percent, and an average false discovery rate of around ten percent.
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    Children's Religious Coping Following Residential Fires: An Exploratory Study
    Wang, Yanping (Virginia Tech, 2004-04-22)
    Recent advancements in the general child disaster literature underscore the important role of coping in children's postdisaster adjustment. Religious coping in children, a potentially important category of coping strategies, has received little attention until recent years. Moreover, its role in the context of post fire adjustment has not been studied. The present study examined the psychometric soundness of the Religious Coping Activities Scale (RCAS; Pargament et al., 1990) in children and adolescents and explored its utility in predicting children's religious coping over time: moreover, the study evaluated its role in predicting PTSD symptomatology over an extended period of time. This investigation included 140 children and adolescents (ages 8-18). Factor analyses of the RCAS revealed a 6-factor solution very similar to the factor structure in the original study. This finding suggests that the RCAS is a promising instrument to measure children's religious coping efforts. Hypotheses concerning the prediction of children's religious coping were only partially supported. Regression analyses indicated mixed findings in terms of the contributions of selected variables to the prediction of children's Spiritually Based Coping and Religious Discontent. Overall, the regression model predicted Religious Discontent better than Spiritually Based Coping. A mixed-effects regression model and hierarchical regression analyses were both employed to examine the role of children's religious coping in predicting short-term and long-term PTSD symptomatology following the residential fires. Results from the mixed-effects regression indicated that loss, time since the fire, child's age, race, and race by age interaction significantly predicted children's PTSD symptoms over time. However, time specific regression analyses revealed different predictive power of the variables across the three assessment waves. Specifically, analyses with Time 1 data revealed the same findings as did the mixed-effects model, except that time since the fire was not a significant predictor in this analysis. General coping strategies appeared to be the only salient predictors for PTSD at Time 2. Finally, Religious Discontent appeared to be negatively related to PTSD at a later time.
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    Classification Analysis for Environmental Monitoring: Combining Information across Multiple Studies
    Zhang, Huizi (Virginia Tech, 2006-08-14)
    Environmental studies often employ data collected over large spatial regions. Although it is convenient, the conventional single model approach may fail to accurately describe the relationships between variables. Two alternative modeling approaches are available: one applies separate models for different regions; the other applies hierarchical models. The separate modeling approach has two major difficulties: first, we often do not know the underlying clustering structure of the entire data; second, it usually ignores possible dependence among clusters. To deal with the first problem, we propose a model-based clustering method to partition the entire data into subgroups according to the empirical relationships between the response and the predictors. To deal with the second, we propose Bayesian hierarchical models. We illustrate the use of the Bayesian hierarchical model under two situations. First, we apply the hierarchical model based on the empirical clustering structure. Second, we integrate the model-based clustering result to help determine the clustering structure used in the hierarchical model. The nature of the problem is classification since the response is categorical rather than continuous and logistic regression models are used to model the relationship between variables.
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    Cluster-Based Bounded Influence Regression
    Lawrence, David E. (Virginia Tech, 2003-07-17)
    In the field of linear regression analysis, a single outlier can dramatically influence ordinary least squares estimation while low-breakdown procedures such as M regression and bounded influence regression may be unable to combat a small percentage of outliers. A high-breakdown procedure such as least trimmed squares (LTS) regression can accommodate up to 50% of the data (in the limit) being outlying with respect to the general trend. Two available one-step improvement procedures based on LTS are Mallows 1-step (M1S) regression and Schweppe 1-step (S1S) regression (the current state-of-the-art method). Issues with these methods include (1) computational approximations and sub-sampling variability, (2) dramatic coefficient sensitivity with respect to very slight differences in initial values, (3) internal instability when determining the general trend and (4) performance in low-breakdown scenarios. A new high-breakdown regression procedure is introduced that addresses these issues, plus offers an insightful summary regarding the presence and structure of multivariate outliers. This proposed method blends a cluster analysis phase with a controlled bounded influence regression phase, thereby referred to as cluster-based bounded influence regression, or CBI. Representing the data space via a special set of anchor points, a collection of point-addition OLS regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster "halfset" of observations, with the remaining observations becoming one or more minor clusters. An initial regression estimator arises from the main cluster, with a multiple point addition DFFITS argument used to carefully activate the minor clusters through a bounded influence regression framework. CBI achieves a 50% breakdown point, is regression equivariant, scale equivariant and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo studies demonstrate the performance advantage of CBI over S1S and the other high breakdown methods regarding coefficient stability, scale estimation and standard errors. A dendrogram of the clustering process is one graphical display available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical viewpoint towards data analysis and the marriage of estimation with diagnostic summary.
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    Construction and Analysis of Linear Trend-Free Factorial Designs Under a General Cost Structure
    Kim, Kiho (Virginia Tech, 1997-07-28)
    When experimental units exhibit a smooth trend over time or in space, random allocation of treatments may no longer be appropriate. Instead, systematic run orders may have to be used to reduce or eliminate the effects of such a trend. The resulting designs are referred to as trend-free designs. We consider here, in particular, linear trend-free designs for factorial treatment structures such that estimates of main effects and two-factor interactions are trend-free. In addition to trend-freeness we incorporate a general cost structure and propose methods of constructing optimal or near-optimal full or fractional factorial designs. Building upon the generalized foldover scheme (GFS) introduced by Coster and Cheng (1988) we develop a procedure of selection of foldover vectors (SFV) which is a construction method for an appropriate generator matrix. The final optimal or near-optimal design can then be developed from this generator matrix. To achieve a reduction in the amount of work, i.e., a reduction of the large number of possible generator matrices, and to make this whole process easier to use by a practitioner, we introduce the systematic selection of foldover vectors (SSFV). This method does not always produce optimal designs but in all cases practical compromise designs. The cost structure for factorial designs can be modeled according to the number of level changes for the various factors. In general, if cost needs to be kept to a minimum, factor level changes will have to be kept at a minimum. This introduces a covariance structure for the observations from such an experiment. We consider the consequences of this covariance structure with respect to the analysis of trend-free factorial designs. We formulate an appropriate underlying mixed linear model and propose an AIC-based method using simulation studies, which leads to a useful practical linear model as compared to the theoretical model, because the theoretical model is not always feasible. Overall, we show that estimation of main effects and two-factor interactions, trend-freeness, and minimum cost cannot always be achieved simultaneously. As a consequence, compromise designs have to be considered, which satisfy requirements as much as possible and are practical at the same time. The proposed methods achieve this aim.
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    Control charts applying a sequential test at fixed sampling intervals with optional sampling at fixed times
    Stoumbos, Zachary G. (Virginia Tech, 1993)
    In recent years, variable sampling interval (VSI) control charts have been intensively investigated. In contrast to traditional fixed sampling interval (FSI) control charts, VSI charts vary the sampling interval as a function of the data. VSI charts detect many process changes faster than their FSI counterparts. A disadvantage, however, of VSI charts as recently formulated is that the advance prediction of sampling times is impossible for more than the next sample. A control chart is proposed which applies a sequential probability ratio test (SPRT) at fixed sampling intervals, the SPRT chart, to monitor the mean of a process with a normal distribution. A natural modification of the SPRT chart, the SPRT chart with sampling at fired times (SFT), is also proposed in which samples are always taken at pre-specified, equally spaced fixed times, with additional samples taken between these times as indicated by the data. A third control chart is introduced as a generalization of the VSI cumulative sum (CUSUM) chart that uses two sampling intervals, called the universal CUSUM (UC) chart, in order to address the need for a general framework for the study of control charts that are equivalent to a sequence of SPRT’s. The UC chart can also be viewed as a generalization of the SPRT chart. The integral equation approach is adapted for the evaluation of properties of both the unmodified and modified with SFT versions of the SPRT chart, such as average time to signal (ATS), steady state ATS (SSATS), and average number of observations to signal (ANOS). After comparisons are performed within the general framework of the UC chart, the unmodified SPRT chart is found to be more efficient than both the FSI and VSI X charts and the FSI CUSUM chart, though very similar in efficiency to the VSI CUSUM chart. The modified SPRT chart with SFT is found to be more efficient than all five of the other control charts, including its unmodified version and the VSI CUSUM chart. General guidelines are provided for the design of both versions of the SPRT chart.
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    Control charts based on residuals for monitoring processes with correlated observations
    Lu, Chao-Wen (Virginia Tech, 1993-08-05)
    In statistical process control, it is usually assumed that observations on the process output at different times are lID. However, for many processes the observations are correlated and control charts for monitoring these processes have recently received much attention. For monitoring the process level, this study evaluates the properties of control charts, such as the EWMA chart and the CUSUM chart, based on the residuals from the forecast values of an ARMA model. It is assumed that the process mean is a ftrst order autoregressive (AR(l)) model and the observations are the mean plus a random error. Properties of these charts are evaluated using a Markov chain approach or an integral equation approach. The performance of control charts based on the residuals is compared to the performance of control charts based on the original observations. A combined chart using forecasts and residuals as the control statistics as well as a combined chart using the EWMA of observations and the EWMA of residuals as the control statistics are also studied by simulation. It is found that no universally "good" chart exists among all the charts investigated in this study. In addition, for monitoring the process variance, two kinds of EWMA chart based on residuals are studied and compared.