This study is concerned with the design of cumulative sum charts based on a minimum cost criterion when there are multiple assignable causes occurring randomly, but with known effect. A cost model is developed that relates the design parameters (i.e. sampling interval, decision limit, reference value and sample size) of a cusum chart and the cost and risk factors of the process to the long run average loss cost per hour for the process. Optimum designs for various sets of cost and risk factors are found by minimizing the long run average loss-cost per hour of the process with respect to the design parameters of a cusum chart. Optimization is accomplished by use of Brown's method. A modified Brownian motion approximation is used for calculating ARLs in the cost model. The nature of the loss-cost function is investigated numerically. The effects of changes in the design parameters and in the cost and risk factors are also studied. An investigation of the limiting behavior of the loss-cost function as the decision limit approaches infinity reveals that in some cases there exist some points that yield a lower loss-cost than that of the local minimum obtained by Brown's method. It is conjectured that if the model is extended to include more realistic assumption about the occurrence of assignable causes then only the local minimum solutions will remain. This paper also shows that the multiple assignable cause model can be well approximated by a matched single cause model. Then in practice it may be sufficient to find the optimum design for the matched. single cause model. / Ph. D.

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. / Ph. D.

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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. / Ph. D.

Injury risk reduction is an ever-evolving topic within an athletic environment. Consequences from an injury include participation time loss, financial, social, and personal costs. Coaching and medical staff strive to reduce the risk through various manners. Training load monitoring is one method that is utilized in injury risk reduction through global positioning systems (GPS) with statistical modeling. The purpose of this study was to investigate the external loads for training sessions and competition in starters versus non-starters; to determine if there were control chart violations associated with sustained injuries; and to determine whether in-season injuries were associate with one or more control chart violations. NCAA Division I female soccer players were recruited during the fall 2019 season. Participants were provided a STATSports GPS unit to wear during all practice and competition sessions to analyze the following variables: total distance, high metabolic load distance, sprints, accelerations, decelerations, and dynamic stress load (DSL). These variables were analyzed using statistical process control charts (SPC Charts) and Nelson Rules. Overall, there were 1,235 violations for the team, with the highest amount coming from DSL. Throughout the season, there were 16 time-loss injuries. Within the 3- and 7-day periods prior to injury, there were only two cases in which the injured athlete had more violations when compared to the team average. Therefore, SPC Charts were not a good indicator of injury risk prediction within this population. Future research includes reassessing these methods within a larger population and for a longer duration (i.e. several seasons). / Master of Science / Reducing the risk of injury in athletes is a focal point for many coaches, training, and medical staffs in collegiate athletics. The consequences of injury range from loss of playing time to financial and long-term health costs. Being able to reduce the risk of injuries not only has personal implications for the athlete but also relates to overall team success. Using global positioning systems (GPS) to track the amount of work done in training can possibly reduce injury risk. This study planned to investigate the workload in NCAA Division 1 collegiate female soccer athletes and if any injuries were sustained during both training and competition settings. The results suggest that statistical process control (SPC) charts and the Nelson Rules did not predict injury risk within this population. There is limited research that has used these tools. Future work can reassess these methods within larger collegiate athletic populations, over a longer period of time.

A control chart that simultaneously tracks the mean and variance of a normally distributed variable with no compensation effect is defined in this work. This joint control chart is compared to five other charts: an Χ chart, an s² chart, a Reynolds and Ghosh chart, a Repko process capability plot, and a t-statistic chart. The criterion for comparison is the probability of a Type II sampling error. Several out-of-control cases are examined. In the case of Repko, an equation is defined to compute the Type II error probability. The results indicate that the Reynolds and Ghosh statistic is powerful for cases when the variance shifts out of control. The Χ chart is powerful when the mean shifts with moderate changes in the variance. The joint chart is powerful for moderate changes in the mean and variance. / Master of Science

Visualization plays an important role in epidemic time series analysis and forecasting. Viewing time series data plotted on a graph can help researchers identify anomalies and unexpected trends that could be overlooked if the data were reviewed in tabular form. However,there are challenges in reviewing data sets from multiple data sources (data can be aggregated in different ways and measure different criteria which can make a direct comparison between time series difficult. In the face of an emerging epidemic, the ability to visualize time series from various sources and organizations and to reconcile these datasets based on different criteria could be key in developing accurate forecasts and identifying effective interventions. Many tools have been developed for visualizing temporal data; however, none yet supports all the functionality needed for easy collaborative visualization and analysis of epidemic data. In this thesis, we develop EpiViewer, a time series exploration dashboard where users can upload epidemiological time series data from a variety of sources and compare, organize, and track how data evolves as an epidemic progresses. EpiViewer provides an easy-to-use web interface for visualizing temporal datasets either as line charts or bar charts. The application provides enhanced features for visual analysis, such as hierarchical categorization, zooming, and filtering, to enable detailed inspection and comparison of multiple time series on a single canvas. Finally, EpiViewer provides a built-in statistical Epi-features module to help users interpret the epidemiological curves. / Master of Science / We present EpiViewer, a time series exploration dashboard where users can upload epidemiological time series data from a variety of sources and compare, organize, and track how data evolves as an epidemic progresses. EpiViewer is a single page web application that provides a framework for exploring, comparing, and organizing temporal datasets. It offers a variety of features for convenient filtering and analysis of epicurves based on meta-attribute tagging. EpiViewer also provides a platform for sharing data between groups for better comparison and analysis.