Browsing by Author "Woodall, William H."
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- Adaptive Threshold Method for Monitoring Rates in Public Health SurveillanceGan, Linmin (Virginia Tech, 2010-04-30)We examine some of the methodologies implemented by the Centers for Disease Control and Prevention's (CDC) BioSense program. The program uses data from hospitals and public health departments to detect outbreaks using the Early Aberration Reporting System (EARS). The EARS method W2 allows one to monitor syndrome counts (W2count) from each source and the proportion of counts of a particular syndrome relative to the total number of visits (W2rate). We investigate the performance of the W2r method designed using an empiric recurrence interval (RI) in this dissertation research. An adaptive threshold monitoring method is introduced based on fitting sample data to the underlying distributions, then converting the current value to a Z-score through a p-value. We compare the upper thresholds on the Z-scores required to obtain given values of the recurrence interval for different sets of parameter values. We then simulate one-week outbreaks in our data and calculate the proportion of times these methods correctly signal an outbreak using Shewhart and exponentially weighted moving average (EWMA) charts. Our results indicate the adaptive threshold method gives more consistent statistical performance across different parameter sets and amounts of baseline historical data used for computing the statistics. For the power analysis, the EWMA chart is superior to its Shewhart counterpart in nearly all cases, and the adaptive threshold method tends to outperform the W2 rate method. Two modified W2r methods proposed in the dissertation also tend to outperform the W2r method in terms of the RI threshold functions and in the power analysis.
- Advancements in Degradation Modeling, Uncertainty Quantification and Spatial Variable SelectionXie, Yimeng (Virginia Tech, 2016-06-30)This dissertation focuses on three research projects: 1) construction of simultaneous prediction intervals/bounds for at least k out of m future observations; 2) semi-parametric degradation model for accelerated destructive degradation test (ADDT) data; and 3) spatial variable selection and application to Lyme disease data in Virginia. Followed by the general introduction in Chapter 1, the rest of the dissertation consists of three main chapters. Chapter 2 presents the construction of two-sided simultaneous prediction intervals (SPIs) or one-sided simultaneous prediction bounds (SPBs) to contain at least k out of m future observations, based on complete or right censored data from (log)-location-scale family of distributions. SPI/SPB calculated by the proposed procedure has exact coverage probability for complete and Type II censored data. In Type I censoring case, it has asymptotically correct coverage probability and reasonably good results for small samples. The proposed procedures can be extended to multiply-censored data or randomly censored data. Chapter 3 focuses on the analysis of ADDT data. We use a general degradation path model with correlated covariance structure to describe ADDT data. Monotone B-splines are used to modeling the underlying degradation process. A likelihood based iterative procedure for parameter estimation is developed. The confidence intervals of parameters are calculated using the nonparametric bootstrap procedure. Both simulated data and real datasets are used to compare the semi-parametric model with the existing parametric models. Chapter 4 studies the Lyme disease emergence in Virginia. The objective is to find important environmental and demographical covariates that are associated with Lyme disease emergence. To address the high-dimentional integral problem in the loglikelihood function, we consider the penalized quasi loglikelihood and the approximated loglikelihood based on Laplace approximation. We impose the adaptive elastic net penalty to obtain sparse estimation of parameters and thus to achieve variable selection of important variables. The proposed methods are investigated in simulation studies. We also apply the proposed methods to Lyme disease data in Virginia. Finally, Chapter 5 contains general conclusions and discussions for future work.
- Advancing the Utility of Manufacturing Data for Modeling, Monitoring, and Securing Machining ProcessesShafae, Mohammed Saeed Abuelmakarm (Virginia Tech, 2018-08-23)The growing adoption of smart manufacturing systems and its related technologies (e.g., embedded sensing, internet-of-things, cyber-physical systems, big data analytics, and cloud computing) is promising a paradigm shift in the manufacturing industry. Such systems enable extracting and exchanging actionable knowledge across the different entities of the manufacturing cyber-physical system and beyond. From a quality control perspective, this allows for more opportunities to realize proactive product design; real-time process monitoring, diagnosis, prognosis, and control; and better product quality characterization. However, a multitude of challenges are arising, with the growing adoption of smart manufacturing, including industrial data characterized by increasing volume, velocity, variety, and veracity, as well as the security of the manufacturing system in the presence of growing connectivity. Taking advantage of these emerging opportunities and tackling the upcoming challenges require creating novel quality control and data analytics methods, which not only push the boundaries of the current state-of-the-art research, but discover new ways to analyze the data and utilize it. One of the key pillars of smart manufacturing systems is real-time automated process monitoring, diagnosis, and control methods for process/product anomalies. For machining applications, traditionally, deterioration in quality measures may occur due to a variety of assignable causes of variation such as poor cutting tool replacement decisions and inappropriate choice cutting parameters. Additionally, due to increased connectivity in modern manufacturing systems, process/product anomalies intentionally induced through malicious cyber-attacks -- aiming at degrading the process performance and/or the part quality -- is becoming a growing concern in the manufacturing industry. Current methods for detecting and diagnosing traditional causes of anomalies are primarily lab-based and require experts to perform initial set-ups and continual fine-tuning, reducing the applicability in industrial shop-floor applications. As for efforts accounting for process/product anomalies due cyber-attacks, these efforts are in early stages. Therefore, more foundational research is needed to develop a clear understanding of this new type of cyber-attacks and their effects on machining processes, to ensure smart manufacturing security both on the cyber and the physical levels. With primary focus on machining processes, the overarching goal of this dissertation work is to explore new ways to expand the use and value of manufacturing data-driven methods for better applicability in industrial shop-floors and increased security of smart manufacturing systems. As a first step toward achieving this goal, the work in this dissertation focuses on adopting this goal in three distinct areas of interest: (1) Statistical Process Monitoring of Time-Between-Events Data (e.g., failure-time data); (2) Defending against Product-Oriented Cyber-Physical Attacks on Intelligent Machining Systems; and (3) Modeling Machining Process Data: Time Series vs. Spatial Point Cloud Data Structures.
- An Analog/Mixed Signal FFT Processor for Ultra-Wideband OFDM Wireless TransceiversLehne, Mark (Virginia Tech, 2008-07-28)As Orthogonal Frequency Division Multiplexing (OFDM) becomes more prevalent in new leading-edge data rate systems processing spectral bandwidths beyond 1 GHz, the required operating speed of the baseband signal processing, specifically the Analog- to-Digital Converter (ADC) and Fast Fourier Transform (FFT) processor, presents significant circuit design challenges and consumes considerable power. Additionally, since Ultra-WideBand (UWB) systems operate in an increasingly crowded wireless environment at low power levels, the ability to tolerate large blocking signals is critical. The goals of this work are to reduce the disproportionately high power consumption found in UWB OFDM receivers while increasing the receiver linearity to better handle blockers. To achieve these goals, an alternate receiver architecture utilizing a new FFT processor is proposed. The new architecture reduces the volume of information passed through the ADC by moving the FFT processor from the digital signal processing (DSP) domain to the discrete time signal processing domain. Doing so offers a reduction in the required ADC bit resolution and increases the overall dynamic range of the UWB OFDM receiver. To explore design trade-offs for the new discrete time (DT) FFT processor, system simulations based on behavioral models of the key functions required for the processor are presented. A new behavioral model of the linear transconductor is introduced to better capture non-idealities and mismatches. The non-idealities of the linear transconductor, the largest contributor of distortion in the processor, are individually varied to determine their sensitivity upon the overall dynamic range of the DT FFT processor. Using these behavioral models, the proposed architecture is validated and guidelines for the circuit design of individual signal processing functions are presented. These results indicate that the DT FFT does not require a high degree of linearity from the linear transconductors or other signal processing functions used in its design. Based on the results of the system simulations, a prototype 8-point DT FFT processor is designed in 130 nm CMOS. The circuit design and layout of each of the circuit functions; serial-to-parallel converter, FFT signal flow graph, and clock generation circuitry is presented. Subsequently, measured results from the first proof-of-concept IC are presented. The measured results show that the architecture performs the FFT required for OFDM demodulation with increased linearity, dynamic range and blocker handling capability while simultaneously reducing overall receiver power consumption. The results demonstrate a dynamic range of 49 dB versus 36 dB for the equivalent all-digital signal processing approach. This improvement in dynamic range increases receiver performance by allowing detection of weak sub-channels attenuated by multipath. The measurements also demonstrate that the processor rejects large narrow-band blockers, while maintaining greater than 40 dB of dynamic range. The processor enables a 10x reduction in power consumption compared to the equivalent all digital processor, as it consumes only 25 mWatts and reduces the required ADC bit depth by four bits, enabling application in hand-held devices. Following the success of the first proof-of-concept IC, a second prototype is designed to incorporate additional functionality and further demonstrate the concept. The second proof-of-concept contains an improved version of the serial-to-parallel converter and clock generation circuitry with the additional function of an equalizer and parallel- to-serial converter. Based on the success of system level behavioral simulations, and improved power consumption and dynamic range measurements from the proof-of-concept IC, this work represents a contribution in the architectural development and circuit design of UWB OFDM receivers. Furthermore, because this work demonstrates the feasibility of discrete time signal processing techniques at 1 GSps, it serves as a foundation that can be used for reducing power consumption and improving performance in a variety of future RF/mixed-signal systems.
- Analysis and Evaluation of Social Network Anomaly DetectionZhao, Meng John (Virginia Tech, 2017-10-27)As social networks become more prevalent, there is significant interest in studying these network data, the focus often being on detecting anomalous events. This area of research is referred to as social network surveillance or social network change detection. While there are a variety of proposed methods suitable for different monitoring situations, two important issues have yet to be completely addressed in network surveillance literature. First, performance assessments using simulated data to evaluate the statistical performance of a particular method. Second, the study of aggregated data in social network surveillance. The research presented tackle these issues in two parts, evaluation of a popular anomaly detection method and investigation of the effects of different aggregation levels on network anomaly detection.
- Analysis of Reliability Experiments with Random Blocks and SubsamplingKensler, Jennifer Lin Karam (Virginia Tech, 2012-07-20)Reliability experiments provide important information regarding the life of a product, including how various factors may affect product life. Current analyses of reliability data usually assume a completely randomized design. However, reliability experiments frequently contain subsampling which is a restriction on randomization. A typical experiment involves applying treatments to test stands, with several items placed on each test stand. In addition, raw materials used in experiments are often produced in batches. In some cases one batch may not be large enough to provide materials for the entire experiment and more than one batch must be used. These batches lead to a design involving blocks. This dissertation proposes two methods for analyzing reliability experiments with random blocks and subsampling. The first method is a two-stage method which can be implemented in software used by most practitioners, but has some limitations. Therefore, a more rigorous nonlinear mixed model method is proposed.
- Applications of Control Charts in Medicine and EpidemiologySego, Landon Hugh (Virginia Tech, 2006-04-05)We consider two applications of control charts in health care. The first involves the comparison of four methods designed to detect an increase in the incidence rate of a rare health event, such as a congenital malformation. A number of methods have been proposed: among these are the Sets method, two modifications of the Sets method, and the CUSUM method based on the Poisson distribution. Many of the previously published comparisons of these methods used unrealistic assumptions or ignored implicit assumptions which led to misleading conclusions. We consider the situation where data are observed as a sequence of Bernoulli trials and propose the Bernoulli CUSUM chart as a desirable method for the surveillance of rare health events. We compare the steady-state average run length performance of the Sets methods and its modifications to the Bernoulli CUSUM chart under a wide variety of circumstances. Except in a very few instances we find that the Bernoulli CUSUM chart performs better than the Sets method and its modifications for the extensive number of cases considered. The second application area involves monitoring clinical outcomes, which requires accounting for the fact that each patient has a different risk of death prior to undergoing a health care procedure. We propose a risk-adjusted survival time CUSUM chart (RAST CUSUM) for monitoring clinical outcomes where the primary endpoint is a continuous, time-to-event variable that is right censored. Risk adjustment is accomplished using accelerated failure time regression models. We compare the average run length performance of the RAST CUSUM chart to the risk-adjusted Bernoulli CUSUM chart, using data from cardiac surgeries to motivate the details of the comparison. The comparisons show that the RAST CUSUM chart is more efficient at detecting deterioration in the quality of a clinical procedure than the risk-adjusted Bernoulli CUSUM chart, especially when the fraction of censored observations is not too high. We address details regarding the implementation of a prospective monitoring scheme using the RAST CUSUM chart.
- Can long-term historical data from electronic medical records improve surveillance for epidemics of acute respiratory infections? A systematic evaluationZheng, Hongzhang; Woodall, William H.; Carlson, Abigail L.; DeLisle, Sylvain (PLOS, 2018-01-31)Background As the deployment of electronic medical records (EMR) expands, so is the availability of long-term datasets that could serve to enhance public health surveillance. We hypothesized that EMR-based surveillance systems that incorporate seasonality and other long-term trends would discover outbreaks of acute respiratory infections (ARI) sooner than systems that only consider the recent past. Methods We simulated surveillance systems aimed at discovering modeled influenza outbreaks injected into backgrounds of patients with ARI. Backgrounds of daily case counts were either synthesized or obtained by applying one of three previously validated ARI case-detection algorithms to authentic EMR entries. From the time of outbreak injection, detection statistics were applied daily on paired background+injection and background-only time series. The relationship between the detection delay (the time from injection to the first alarm uniquely found in the background+injection data) and the false-alarm rate (FAR) was determined by systematically varying the statistical alarm threshold. We compared this relationship for outbreak detection methods that utilized either 7 days (early aberrancy reporting system (EARS)) or 2 +/- 4 years of past data (seasonal autoregressive integrated moving average (SARIMA) time series modeling). Results In otherwise identical surveillance systems, SARIMA detected epidemics sooner than EARS at any FAR below 10%. The algorithms used to detect single ARI cases impacted both the feasibility and marginal benefits of SARIMA modeling. Under plausible real-world conditions, SARIMA could reduce detection delay by 5 +/- 16 days. It also was more sensitive at detecting the summer wave of the 2009 influenza pandemic. Conclusion Time series modeling of long-term historical EMR data can reduce the time it takes to discover epidemics of ARI. Realistic surveillance simulations may prove invaluable to optimize system design and tuning.
- Cluster_Based Profile Monitoring in Phase I AnalysisChen, Yajuan (Virginia Tech, 2014-03-26)Profile monitoring is a well-known approach used in statistical process control where the quality of the product or process is characterized by a profile or a relationship between a response variable and one or more explanatory variables. Profile monitoring is conducted over two phases, labeled as Phase I and Phase II. In Phase I profile monitoring, regression methods are used to model each profile and to detect the possible presence of out-of-control profiles in the historical data set (HDS). The out-of-control profiles can be detected by using the statis-tic. However, previous methods of calculating the statistic are based on using all the data in the HDS including the data from the out-of-control process. Consequently, the ability of using this method can be distorted if the HDS contains data from the out-of-control process. This work provides a new profile monitoring methodology for Phase I analysis. The proposed method, referred to as the cluster-based profile monitoring method, incorporates a cluster analysis phase before calculating the statistic. Before introducing our proposed cluster-based method in profile monitoring, this cluster-based method is demonstrated to work efficiently in robust regression, referred to as cluster-based bounded influence regression or CBI. It will be demonstrated that the CBI method provides a robust, efficient and high breakdown regression parameter estimator. The CBI method first represents the data space via a special set of points, referred to as anchor points. Then a collection of single-point-added ordinary least squares regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster containing at least half the 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 stabil-ity, scale estimation and standard errors. The cluster-based method in Phase I profile monitoring first replaces the data from each sampled unit with an estimated profile, using some appropriate regression method. The estimated parameters for the parametric profiles are obtained from parametric models while the estimated parameters for the nonparametric profiles are obtained from the p-spline model. The cluster phase clusters the profiles based on their estimated parameters and this yields an initial main cluster which contains at least half the profiles. The initial estimated parameters for the population average (PA) profile are obtained by fitting a mixed model (parametric or nonparametric) to those profiles in the main cluster. Profiles that are not contained in the initial main cluster are iteratively added to the main cluster provided their statistics are "small" and the mixed model (parametric or nonparametric) is used to update the estimated parameters for the PA profile. Those profiles contained in the final main cluster are considered as resulting from the in-control process while those not included are considered as resulting from an out-of-control process. This cluster-based method has been applied to monitor both parametric and nonparametric profiles. A simulated example, a Monte Carlo study and an application to a real data set demonstrates the detail of the algorithm and the performance advantage of this proposed method over a non-cluster-based method is demonstrated with respect to more accurate estimates of the PA parameters and improved classification performance criteria. When the profiles can be represented by vectors, the profile monitoring process is equivalent to the detection of multivariate outliers. For this reason, we also compared our proposed method to a popular method used to identify outliers when dealing with a multivariate response. Our study demonstrated that when the out-of-control process corresponds to a sustained shift, the cluster-based method using the successive difference estimator is clearly the superior method, among those methods we considered, based on all performance criteria. In addition, the influence of accurate Phase I estimates on the performance of Phase II control charts is presented to show the further advantage of the proposed method. A simple example and Monte Carlo results show that more accurate estimates from Phase I would provide more efficient Phase II control charts.
- Contributions to Profile Monitoring and Multivariate Statistical Process ControlWilliams, James Dickson (Virginia Tech, 2004-12-01)The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. Part 2: Approximate Distribution of T² Although the T² statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T² chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use.
- Control Charts with Missing ObservationsWilson, Sara R. (Virginia Tech, 2009-04-03)Traditional control charts for process monitoring are based on taking samples from the process at regular time intervals. However, it is often possible in practice for observations, and even entire samples, to be missing. This dissertation investigates missing observations in Exponentially Weighted Moving Average (EWMA) and Multivariate EWMA (MEWMA) control charts. The standardized sample mean is used since this adjusts the sample mean for the fact that part of the sample may be missing. It also allows for constant control limits even though the sample size varies randomly. When complete samples are missing, the weights between samples should also be adjusted. In the univariate case, three approaches for adjusting the weights of the EWMA control statistic are investigated: (1) ignoring missing samples; (2) adding the weights from previous consecutive missing samples to the current sample; and (3) increasing the weights of non-missing samples in proportion, so that the weights sum to one. Integral equation and Markov chain methods are developed to find and compare the statistical properties of these charts. The EI chart, which adjusts the weights by ignoring the missing samples, has the best overall performance. The multivariate case in which information on some of the variables is missing is also examined using MEWMA charts. Two methods for adjusting the weights of the MEWMA control statistic are investigated and compared using simulation: (1) ignoring all the data at a sampling point if the data for at least one variable is missing; and (2) using the previous EWMA value for any variable for which all the data are missing. Both of these methods are examined when the in-control covariance matrix is adjusted at each sampling point to account for missing observations, and when it is not adjusted. The MS control chart, which uses the previous value of the EWMA statistic for a variable if all of the data for that variable is missing at a sampling point, provides the best overall performance. The in-control covariance matrix needs to be adjusted at each sampling point, unless the variables are independent or only weakly correlated.
- Cumulative Sum Control Charts for Censored Reliability DataOlteanu, Denisa Anca (Virginia Tech, 2010-04-01)Companies routinely perform life tests for their products. Typically, these tests involve running a set of products until the units fail. Most often, the data are censored according to different censoring schemes, depending on the particulars of the test. On occasion, tests are stopped at a predetermined time and the units that are yet to fail are suspended. In other instances, the data are collected through periodic inspection and only upper and lower bounds on the lifetimes are recorded. Reliability professionals use a number of non-normal distributions to model the resulting lifetime data with the Weibull distribution being the most frequently used. If one is interested in monitoring the quality and reliability characteristics of such processes, one needs to account for the challenges imposed by the nature of the data. We propose likelihood ratio based cumulative sum (CUSUM) control charts for censored lifetime data with non-normal distributions. We illustrate the development and implementation of the charts, and we evaluate their properties through simulation studies. We address the problem of interval censoring, and we construct a CUSUM chart for censored ordered categorical data, which we illustrate by a case study at Becton Dickinson (BD). We also address the problem of monitoring both of the parameters of the Weibull distribution for processes with right-censored data.
- Debate: what is the best method to monitor surgical performance?Steiner, Stefan H.; Woodall, William H. (Biomed Central, 2016-04-05)Background There is considerable recent interest in the monitoring of individual surgeon or hospital surgical outcomes. If one aggregates data over time and assesses performance with a funnel plot, then the detection of any process deterioration or improvement could be delayed. The variable life adjusted display (VLAD) is widely used for monitoring on a case-by-case basis, but we show that use of the risk-adjusted Bernoulli cumulative sum (RA-CUSUM) chart leads to much better performance. Discussion We use simulation to illustrate that the RA-CUSUM chart has better performance than the VLAD in detecting changes in the rates of adverse events. Summary We recommend the RA-CUSUM approach over the VLAD approach for monitoring surgical performance. If the VLAD is used, we recommend running the RA-CUSUM chart in the background to generate signals that the process performance has changed.
- Design of adaptive EWMA control charts using the conditional false alarm rateAytaçoğlu, Burcu; Driscoll, Anne R.; Woodall, William H. (Wiley, 2023-04)Dynamic control limits can be useful in designing control charts, especially when sample sizes, risk scores, or other covariate values change over time. Computer simulation can be used to control the conditional false alarm rate and thus the in-control run length properties. We show that this approach can be useful in designing adaptive exponentially weighted moving average (AEWMA) control charts for which the control chart smoothing parameter at a given time point depends on the observed value at that time point. We use AEWMA charts as examples, but the approach can be applied to the adaptive cumulative sum (CUSUM) chart and other types of adaptive charts.
- The Design of GLR Control Charts for Process MonitoringXu, Liaosa (Virginia Tech, 2013-02-27)Generalized likelihood ratio (GLR) control charts are investigated for two types of statistical process monitoring (SPC) problems. The first part of this dissertation considers the problem of monitoring a normally distributed process variable when a special cause may produce a time varying linear drift in the mean. The design and application of a GLR control chart for drift detection is investigated. The GLR drift chart does not require specification of any tuning parameters by the practitioner, and has the advantage that, at the time of the signal, estimates of both the change point and the drift rate are immediately available. An equation is provided to accurately approximate the control limit. The performance of the GLR drift chart is compared to other control charts such as a standard CUSUM chart and a CUSCORE chart designed for drift detection. We also compare the GLR chart designed for drift detection to the GLR chart designed for sustained shift detection since both of them require only a control limit to be specified. In terms of the expected time for detection and in terms of the bias and mean squared error of the change-point estimators, the GLR drift chart has better performance for a wide range of drift rates relative to the GLR shift chart when the out-of-control process is truly a linear drift. The second part of the dissertation considers the problem of monitoring a linear functional relationship between a response variable and one or more explanatory variables (a linear profile). The design and application of GLR control charts for this problem are investigated. The likelihood ratio test of the GLR chart is generalized over the regression coefficients, the variance of the error term, and the possible change-point. The performance of the GLR chart is compared to various existing control charts. We show that the overall performance of the GLR chart is much better than other options in detecting a wide range of shift sizes. The existing control charts designed for certain shifts that may be of particular interest have several chart parameters that need to be specified by the user, which makes the design of such control charts more difficult. The GLR chart is very simple to design, as it is invariant to the choice of design matrix and the values of in-control parameters. Therefore there is only one design parameter (the control limit) that needs to be specified. Especially, the GLR chart can be constructed based on the sample size of n=1 at each sampling point, whereas other charts cannot be applied. Another advantage of the GLR chart is its built-in diagnostic aids that provide estimates of both the change-point and the values of linear profile parameters.
- Diagnostics after a Signal from Control Charts in a Normal ProcessLou, Jianying (Virginia Tech, 2008-09-04)Control charts are fundamental SPC tools for process monitoring. When a control chart or combination of charts signals, knowing the change point, which distributional parameter changed, and/or the change size helps to identify the cause of the change, remove it from the process or adjust the process back in control correctly and immediately. In this study, we proposed using maximum likelihood (ML) estimation of the current process parameters and their ML confidence intervals after a signal to identify and estimate the changed parameters. The performance of this ML diagnostic procedure is evaluated for several different charts or chart combinations for the cases of sample sizes and , and compared to the traditional approaches to diagnostics. None of the ML and the traditional estimators performs well for all patterns of shifts, but the ML estimator has the best overall performance. The ML confidence interval diagnostics are overall better at determining which parameter has shifted than the traditional diagnostics based on which chart signals. The performance of the generalized likelihood ratio (GLR) chart in shift detection and in ML diagnostics is comparable to the best EWMA chart combination. With the application of the ML diagnostics naturally following a GLR chart compared to the traditional control charts, the studies of a GLR chart during process monitoring can be further deepened in the future.
- Dynamic Probability Control Limits for Risk-Adjusted Bernoulli Cumulative Sum ChartsZhang, Xiang (Virginia Tech, 2015-12-12)The risk-adjusted Bernoulli cumulative sum (CUSUM) chart developed by Steiner et al. (2000) is an increasingly popular tool for monitoring clinical and surgical performance. In practice, however, use of a fixed control limit for the chart leads to quite variable in-control average run length (ARL) performance for patient populations with different risk score distributions. To overcome this problem, the simulation-based dynamic probability control limits (DPCLs) patient-by-patient for the risk-adjusted Bernoulli CUSUM charts is determined in this study. By maintaining the probability of a false alarm at a constant level conditional on no false alarm for previous observations, the risk-adjusted CUSUM charts with DPCLs have consistent in-control performance at the desired level with approximately geometrically distributed run lengths. Simulation results demonstrate that the proposed method does not rely on any information or assumptions about the patients' risk distributions. The use of DPCLs for risk-adjusted Bernoulli CUSUM charts allows each chart to be designed for the corresponding particular sequence of patients for a surgeon or hospital. The effect of estimation error on performance of risk-adjusted Bernoulli CUSUM chart with DPCLs is also examined. Our simulation results show that the in-control performance of risk-adjusted Bernoulli CUSUM chart with DPCLs is affected by the estimation error. The most influential factors are the specified desired in-control average run length, the Phase I sample size and the overall adverse event rate. However, the effect of estimation error is uniformly smaller for the risk-adjusted Bernoulli CUSUM chart with DPCLs than for the corresponding chart with a constant control limit under various realistic scenarios. In addition, there is a substantial reduction in the standard deviation of the in-control run length when DPCLs are used. Therefore, use of DPCLs has yet another advantage when designing a risk-adjusted Bernoulli CUSUM chart. These researches are results of joint work with Dr. William H. Woodall (Department of Statistics, Virginia Tech). Moreover, DPCLs are adapted to design the risk-adjusted CUSUM charts for multiresponses developed by Tang et al. (2015). It is shown that the in-control performance of the charts with DPCLs can be controlled for different patient populations because these limits are determined for each specific sequence of patients. Thus, the risk-adjusted CUSUM chart for multiresponses with DPCLs is more practical and should be applied to effectively monitor surgical performance by hospitals and healthcare practitioners. This research is a result of joint work with Dr. William H. Woodall (Department of Statistics, Virginia Tech) and Mr. Justin Loda (Department of Statistics, Virginia Tech).
- Effect of Phase I Estimation on Phase II Control Chart Performance with Profile DataChen, 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.
- The effect of temporal aggregation level in social network monitoringZhao, Meng J.; Driscoll, Anne R.; Sengupta, Srijan; Stevens, Nathaniel T.; Fricker, Ronald D. Jr.; Woodall, William H. (PLOS, 2018-12-19)Social networks have become ubiquitous in modern society, which makes social network monitoring a research area of significant practical importance. Social network data consist of social interactions between pairs of individuals that are temporally aggregated over a certain interval of time, and the level of such temporal aggregation can have substantial impact on social network monitoring. There have been several studies on the effect of temporal aggregation in the process monitoring literature, but no studies on the effect of temporal aggregation in social network monitoring. We use the degree corrected stochastic block model (DCSBM) to simulate social networks and network anomalies and analyze these networks in the context of both count and binary network data. In conjunction with this model, we use the Priebe scan method as the monitoring method. We demonstrate that temporal aggregation at high levels leads to a considerable decrease in the ability to detect an anomaly within a specified time period. Moreover, converting social network communication data from counts to binary indicators can result in a significant loss of information, hindering detection performance. Aggregation at an appropriate level with count data, however, can amplify the anomalous signal generated by network anomalies and improve detection performance. Our results provide both insights on the practical effects of temporal aggregation and a framework for the study of other combinations of network models, surveillance methods, and types of anomalies.
- Efficient Sampling Plans for Control Charts When Monitoring an Autocorrelated ProcessZhong, Xin (Virginia Tech, 2006-02-24)This dissertation investigates the effects of autocorrelation on the performances of various sampling plans for control charts in detecting special causes that may produce sustained or transient shifts in the process mean and/or variance. Observations from the process are modeled as a first-order autoregressive process plus a random error. Combinations of two Shewhart control charts and combinations of two exponentially weighted moving average (EWMA) control charts based on both the original observations and on the process residuals are considered. Three types of sampling plans are investigated: samples of n = 1, samples of n > 1 observations taken together at one sampling point, or samples of n > 1 observations taken at different times. In comparing these sampling plans it is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so taking samples of n = 1 allows more frequent plotting. The best overall performance of sampling plans for control charts in detecting both sustained and transient shifts in the process is obtained by taking samples of n = 1 and using an EWMA chart combination with a observations chart for mean and a residuals chart for variance. The Shewhart chart combination with the best overall performance, though inferior to the EWMA chart combination, is based on samples of n > 1 taken at different times and with a observations chart for mean and a residuals chart for variance.