Department of Information Systems, Statistics & Management Science
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Browsing Department of Information Systems, Statistics & Management Science by Author "Barrett, Bruce"
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Item The Development of Statistical Monitoring Scheme and Simulation Model for the Autocorrelated Process(University of Alabama Libraries, 2020) Wang, Zhi; Perry, Marcus; University of Alabama TuscaloosaThe modern development in data acquisition and storage technologies have allowed for rapid data collection. One representative example is collecting data via high-sample-rate sensors developed with a rate of hundreds or more samples per second. The proximity between the observations can induce high autocorrelation into data sequences. Consequently, develop statistical tools for dealing with the autocorrelated process is of paramount value in modern data analysis. For this reason, the dissertation places primacy upon developing appropriate monitoring schemes and simulation models for the autocorrelated processes. In addition, the complexity of the modern process precludes the using of some conventional statistical approaches that has rigor distribution assumption. The wide practicality of the modern process motivates the work in the dissertation and award the great potential of the future investigation. Statistical process control (SPC) has wide applications in quality engineering, manufacturing industries, social science, disease surveillance, and many other areas. In this dissertation, a distribution-free jointly and independently monitoring scheme for location and scale using individual observations is developed based on the Bernoulli Cumulative Summation (CUSUM) control chart and the Bahadur model. The approach takes autocorrelation into consideration and circumvents the model-misspecification problem. The necessity of the method is appropriately motivated, simulation studies and real-world applications are used to evaluate the reliability and performance of the proposed scheme. Knowing when a process has deviated from the desired in-control status would simplify the control chart post-signal diagnostics. In the dissertation, we developed the maximum likelihood estimators (MLE) of time change point and introduced the built-in change point estimators for CUSUM and binomial exponentially weighted moving average (EWMA) charts. Relative mean index plots are provided and general conclusions are summarized to assist control charts users selecting change point and control chart design combination that guarantees robust change point estimation performance across a range of potential change magnitudes. Another aspect we studied is the simulation of the autocorrelated process. In this dissertation, we developed a simulation approach that permits users to simulate autocorrelated processes from both discrete and continuous distribution with a fully customizable order and structure of autocorrelation. Simulation studies and real-world applications are used to evaluate and illustrate the usefulness of the proposed simulation model.Item Statistical Process Monitoring for Some Nonstandard Situations in Estimated Parameters Case(University of Alabama Libraries, 2020) Yao, Yuhui; Chakraborti, Subha; University of Alabama TuscaloosaStatistical process control (SPC) and monitoring techniques are useful in practice in a variety of applications. Recent advancements in the literature have shown the need for distinguishing between Phase I (retrospective) and Phase II (prospective) process monitoring and the importance of taking proper account of the effects of parameter estimation. This work considers the retrospective and prospective process monitoring for the balanced random effects (variance components) model with Phases I and II Shewhart charts and Phase II EWMA chart with estimated parameters. In Phase I, Shewhart-type charts are recommended in this phase because of their broader shift detection ability. The proposed methodology takes proper account of the effects of parameter estimation and uses the false alarm probability (FAP) metric to design the chart. The proposed Phase I chart is shown to be easily adaptable to more general models, with more variance components and nested factors, and can accommodate various estimators of variance. Thus, it enables a broader Phase I process monitoring strategy, under normality, which can be applied within the ANOVA framework applicable for many DOE models. In Phase II, multiple control charts are dominating including the Shewhart-type charts and its generalization, the EWMA charts which is famous of detecting smaller shift. In order to not inflate the false alarm rate, the effect of parameter estimation is considered and the proposed Phase II charts are measured by the average run length (ARL). Two types of corrected limits are provided, following the recent literature, one based on the unconditional perspective and the other on the conditional perspective and the exceedance probability criterion (EPC). In the sequel, the corrected (adjusted) charting constants are calculated and tabulated. The tabulations can be found, on demand, from accompanying R packages. Simulation studies for the robustness and the out-of-control performance are conducted. Illustrations are shown using real-world data. R packages are provided to help deployment of the new methodology in practice.