The Development of Statistical Monitoring Scheme and Simulation Model for the Autocorrelated Process

Abstract

The 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.