Technical Reports, Statistics

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Browsing Technical Reports, Statistics by Author "Chen, Yajuan"

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    Cluster-Based Bounded Influence Regression
    Lawrence, David E.; Birch, Jeffrey B.; Chen, Yajuan (Virginia Tech, 2012)
    A regression methodology is introduced that obtains competitive, robust, efficient, high breakdown regression parameter estimates as well as providing an informative summary regarding possible multiple outlier structure. The 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 “half-set” of observations, with the remaining observations comprising one or more minor clusters. An initial regression estimator arises from the main cluster, with a group-additive DFFITS argument used to carefully activate the minor clusters through a bounded influence regression frame work. CBI achieves a 50% breakdown point, is regression equivariant, scale and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo results demonstrate the performance advantage of CBI over other popular robust regression procedures regarding coefficient stability, scale estimation and standard errors. The dendrogram of the clustering process and the weight plot are graphical displays available for multivariate outlier detection. Overall, the proposed methodology represents advancement in the field of robust regression, offering a distinct philosophical view point towards data analysis and the marriage of estimation with diagnostic summary.
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    Cluster-Based Profile Monitoring in Phase I Analysis
    Chen, Yajuan; Birch, Jeffrey B. (Virginia Tech, 2012)
    An innovative profile monitoring methodology is introduced for Phase I analysis. The proposed technique, which is referred to as the cluster-based profile monitoring method, incorporates a cluster analysis phase to aid in determining if non conforming profiles are present in the historical data set (HDS). To cluster the profiles, the proposed method first replaces the data for each profile with an estimated profile curve, using some appropriate regression method, and clusters the profiles based on their estimated parameter vectors. This cluster phase then yields a main cluster which contains more than half of the profiles. The initial estimated population average (PA) parameters are obtained by fitting a linear mixed model to those profiles in the main cluster. In-control profiles, determined using the Hotelling’s T² statistic, that are not contained in the initial main cluster are iteratively added to the main cluster and the mixed model is used to update the estimated PA parameters. A simulated example and Monte Carlo results demonstrate the performance advantage of this proposed method over a current noncluster based method with respect to more accurate estimates of the PA parameters and better classification performance in determining those profiles from an in-control process from those from an out-of-control process in Phase I.
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    Effect of Phase I Estimation on Phase II Control Chart Performance with Profile Data
    Chen, Yajuan; Birch, Jeffrey B.; Woodall, William H. (Virginia Tech, 2014)
    This paper illustrates how Phase I estimators in statistical process control (SPC) can affect the performance of Phase II control charts. The deleterious impact of poor Phase I estimators on the performance of Phase II control charts is illustrated in the context of profile monitoring. Two types of Phase I estimators are discussed. One approach uses functional cluster analysis to initially distinguish between estimated profiles from an in-control process and those from an out-of-control process. The second approach does not use clustering to make the distinction. The Phase II control charts are established based on the two resulting types of estimates and compared across varying sizes of sustained shifts in Phase II. A simulated example and a Monte Carlo study show that the performance of the Phase II control charts can be severely distorted when constructed with poor Phase I estimators. The use of clustering leads to much better Phase II performance. We also illustrate that the performance of Phase II control charts based on the poor Phase I estimators not only have more false alarms than expected but can also take much longer than expected to detect potential changes to the process.
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    A Phase I Cluster-Based Method for Analyzing Nonparametric Profiles
    Chen, Yajuan; Birch, Jeffrey B.; Woodall, William H. (Virginia Tech, 2014)
    A cluster-based method was used by Chen et al.²⁴ to analyze parametric profiles in Phase I of the profile monitoring process. They showed performance advantages in using their cluster-based method of analyzing parametric profiles over a non-cluster-based method with respect to more accurate estimates of the parameters and improved classification performance criteria. However, it is known that, in many cases, profiles can be better represented using a nonparametric method. In this study, we use the clusterbased method to analyze profiles that cannot be easily represented by a parametric function. The similarity matrix used during the clustering phase is based on the fits of the individual profiles with pspline regression. The clustering phase will determine an initial main cluster set which contains greater than half of the total profiles in the historical data set. The profiles with in-control T² statistics are sequentially added to the initial main cluster set and upon completion of the algorithm, the profiles in the main cluster set are classified as the in-control profiles and the profiles not in the main cluster set are classified as out-of-control profiles. A Monte Carlo study demonstrates that the cluster-based method results in superior performance over a non-cluster-based method with respect to better classification and higher power in detecting out-of-control profiles. Also, our Monte Carlo study shows that the clusterbased method has better performance than a non-cluster-based method whether the model is correctly specified or not. We illustrate the use of our method with data from the automotive industry.