Sun-Kyoung Park

Bootstrap-Based T2 Multivariate Control Charts

Control charts have been used effectively for years to monitor processes and detect abnormal behaviors. However, most control charts require a specific distribution to establish their control limits. The bootstrap method is a nonparametric technique that does not rely on the assumption of a parametric distribution of the observed data. Although the bootstrap technique has been used to develop univariate control charts to monitor a single process, no effort has been made to integrate the effectiveness of the bootstrap technique with multivariate control charts. In the present study, we propose a bootstrap-based multivariate T 2 control chart that can efficiently monitor a process when the distribution of observed data is nonnormal or unknown. A simulation study was conducted to evaluate the performance of the proposed control chart and compare it with a traditional Hotellings T 2 control chart and the kernel density estimation (KDE)-based T 2 control chart. The results showed that the proposed chart performed better than the traditional T 2 control chart and performed comparably with the KDE-based T 2 control chart. Furthermore, we present a case study to demonstrate the applicability of the proposed control chart to real situations.

A nonparametric fault isolation approach through one-class classification algorithms

Multivariate control charts provide control limits for the monitoring of processes and detection of abnormal events so that processes can be improved. However, these multivariate control charts provide limited information about the contribution of any specific variable to the out-of-control alarm. Although many fault isolation methods have been developed to address this deficiency, most of these methods require a parametric distributional assumption that restricts their applicability to specific problems of process control and thus limits their broader usefulness. This study proposes a nonparametric fault isolation method based on a one-class classification algorithm that overcomes the limitation posed by the parametric assumption in existing fault isolation methods. The proposed approach decomposes the monitoring statistics obtained from a one-class classification algorithm into components that reflect the contribution of each variable to the out-of-control signal. A bootstrap approach is used to determine the significance of each variable. A simulation study is presented that examines the performance of the proposed method under various scenarios and to results are compared with those obtained using the T 2 decomposition method. The simulation results reveal that the proposed method outperforms the T 2 decomposition method in non-normal distribution cases.

Characterization of spatially homogeneous regions based on temporal patterns of fine particulate matter in the continental United States.

Abstract Statistical analyses of time-series or spatial data have been widely used to investigate the behavior of ambient air pollutants. Because air pollution data are generally collected in a wide area of interest over a relatively long period, such analyses should take into account both spatial and temporal characteristics. The objective of this study is 2-fold: (1) to identify an efficient way to characterize the spatial variations of fine particulate matter (PM2.5) concentrations based solely upon their temporal patterns, and (2) to analyze the temporal and seasonal patterns of PM2.5 concentrations in spatially homogenous regions. This study used 24-hr average PM2.5 concentrations measured every third day during a period between 2001 and 2005 at 522 monitoring sites in the continental United States. A k-means clustering algorithm using the correlation distance was used to investigate the similarity in patterns between temporal profiles observed at the monitoring sites. A k-means clustering analysis produced six clusters of sites with distinct temporal patterns that were able to identify and characterize spatially homogeneous regions of the United States. The study also presents a rotated principal component analysis (RPCA) that has been used for characterizing spatial patterns of air pollution and discusses the difference between the clustering algorithm and RPCA.

Data mining model-based control charts for multivariate and autocorrelated processes

Process monitoring and diagnosis have been widely recognized as important and critical tools in system monitoring for detection of abnormal behavior and quality improvement. Although traditional statistical process control (SPC) tools are effective in simple manufacturing processes that generate a small volume of independent data, these tools are not capable of handling the large streams of multivariate and autocorrelated data found in modern systems. As the limitations of SPC methodology become increasingly obvious in the face of ever more complex processes, data mining algorithms, because of their proven capabilities to effectively analyze and manage large amounts of data, have the potential to resolve the challenging problems that are stretching SPC to its limits. In the present study we attempted to integrate state-of-the-art data mining algorithms with SPC techniques to achieve efficient monitoring in multivariate and autocorrelated processes. The data mining algorithms include artificial neural networks, support vector regression, and multivariate adaptive regression splines. The residuals of data mining models were utilized to construct multivariate cumulative sum control charts to monitor the process mean. Simulation results from various scenarios indicated that data mining model-based control charts performs better than traditional time-series model-based control charts.

Integration of support vector machines and control charts for multivariate process monitoring

Statistical process control tools have been used routinely to improve process capabilities through reliable on-line monitoring and diagnostic processes. In the present paper, we propose a novel multivariate control chart that integrates a support vector machine (SVM) algorithm, a bootstrap method, and a control chart technique to improve multivariate process monitoring. The proposed chart uses as the monitoring statistic the predicted probability of class (PoC) values from an SVM algorithm. The control limits of SVM-PoC charts are obtained by a bootstrap approach. A simulation study was conducted to evaluate the performance of the proposed SVM–PoC chart and to compare it with other data mining-based control charts and Hotellings T 2 control charts under various scenarios. The results showed that the proposed SVM–PoC charts outperformed other multivariate control charts in nonnormal situations. Further, we developed an exponential weighed moving average version of the SVM–PoC charts for increasing sensitivity to small shifts.

Evaluation of Fine Particle Number Concentrations in CMAQ

The Community Multiscale Air Quality (CMAQ) model is widely used in air quality management and scientific investigation. Numerous studies have been conducted investigating how well CMAQ simulates fine particle mass concentrations, but relatively few studies have addressed how well CMAQ simulates fine particle number distribution. Accurate simulation of particle number concentrations is important because particle number and surface area concentrations may be directly related to human health and visibility. Simulated fine particle number concentrations derived using CMAQ are compared to measurements to identify problems and to improve model performance. Evaluation is done using measured particle number concentrations in Atlanta, Georgia, from 1/1/1999 to 8/31/2000. While homogeneous binary nucleation mechanism used in CMAQ needs to be modified for better prediction of particle number concentrations, there are also other factors that affect the predicted particle level. Assumed particle size of the primary emissions in CMAQ causes number concentrations to be significantly underestimated, while particle density has a small impact. Assuming particle size distributions by three lognormal modes cannot accurately simulate particles with size less than 0.01 μ m, particularly during nucleation events. An additional mode that accounts for particles smaller than 0.01 μ m can improve the accuracy of the number concentration simulations. Though, the use of the Expectation-Maximization (EM) algorithm to estimate size distribution parameters of measured particles suggests that assumed parameters for the lognormal modes in CMAQ are generally reasonable.

Spatial prediction of ozone concentration profiles

Ground level ozone is one of the major air pollutants in many urban areas. Ozone formation affects ecosystems and is known to be associated with many adverse health issues in humans. Effective modeling of ozone is a necessary step to develop a system to warn residents of high ozone levels. In the present study we propose a statistical procedure that uses multiscale and functional data analysis to improve the spatial prediction of ozone concentration profiles in the Dallas Fort Worth (DFW) area of Texas. This study uses daily eight-hour ozone concentrations and meteorological predictors during a period between 2003 and 2006 at 14 monitoring sites in the DFW area. Wavelet transformation was used as a means of multiscale data analysis, followed by functional modeling to reduce model complexity. Kriging was then used for spatial prediction. The experimental results with real data demonstrated that the proposed procedures achieved acceptable accuracy of spatial prediction.

Environmental Risk Assessment: Comparison of Receptor and Air Quality Models for Source Apportionment

ABSTRACT Source apportionment of particulate matter has been commonly performed using receptor models, but studies suggest that the assumptions in receptor models limit the accuracy of results. An alternative approach is the use of three-dimensional source-oriented air quality models. Here, a comparison is conducted between the PM2.5 apportioned from the Chemical Mass Balance (CMB) receptor model using organic tracers as molecular markers with those from the source-based Community Multiscale Air Quality (CMAQ) model. Source apportionment was conducted at sites in the southeastern United States for July 2001 and January 2002. PM2.5 source apportionment results had moderate discrepancies, which originate from different spatial scales, fundamental limitations, and uncertainties of the two models. Results from CMB fluctuated temporally more than real variation due to measurement and source profile errors and uncertainties, whereas those from CMAQ could not capture daily variation well. In addition, results from CMB are mass contributions for the monitoring location, whereas those from CMAQ represent the average mass contributions of the models grid. It is difficult to assess which approach is “better.” Indeed, both models have strengths and limitations, and each models strengths can be utilized to help overcome the other models limitations.

Regional Adjustment of Emission Strengths Via Four Dimensional Data Assimilation

The Four-Dimensional Data Assimilation was performed to evaluate source emission strengths over the United States. The USEPA Models-3 system (CMAQ/MM5/SMOKE) and ridge regression are used as the forward and inverse models, respectively. The continental US is divided into six regions, and data assimilation is performed for each region in July 2001 and January 2002. In addition, two separate scaling factors are calculated for weekdays and weekends. Results show that base emissions for CO and SO2 sources are relatively accurate. Base emissions for PEC source are overestimated 100%, but those for POA source are underestimated up to 70% when compared with the adjusted emissions. Emissions for NH3, NOx, and PMFINE sources are relatively accurate in July 2001, but those in January 2002 are around 100% higher than the adjusted emissions. Base VOC emissions in July 2001 are similar to the adjusted emissions but those in January 2002 are underestimated up to 70% when compared with the adjusted emissions. Though the emission adjustment itself improves the overall air quality model performance, a better improvement is expected with the modification of speciation profiles and temporal allocations in the Models-3 system, as well.

Data mining model adjustment control charts for cascade processes

Control charts have been widely recognised as important tools in system monitoring of abnormal behaviour and quality improvement. Traditional control charts have a major assumption that successive observations are uncorrelated and normally distributed. When this assumption is violated, the traditional control charts do not perform well, but instead show increased false alarm rates. In this study, we propose a data mining model adjustment control chart to address autocorrelation problems for cascade processes. The basic idea of the proposed control chart is to monitor the residuals obtained by data mining models. The data mining models used in this study include support vector regression and artificial neural networks. A simulation study was conducted to evaluate the performance of the proposed control chart and compare it with the standard regression adjustment control chart and the observations-based control chart in terms of average run length performance. The results showed that the proposed data mining model adjustment control charts yielded better performance than the two other methods considered in this study. [Received 8 December 2010; Revised 19 June 2011; Revised 9 September 2011; Accepted 29 November 2011]