Adaptive charting techniques for multivariate and dynamic processes

In the modern business environment, quality is one of the decisive fac-tors for the success and sustained development of an enterprise. The root cause of poor quality is the large variability result from certain assignable causes. In practice, Statistical Process Control (SPC) techniques have been widely utilized in a variety of industries for the purpose of assignable cause identification and variability reduction. Even though most SPC charts are designed to detect process shifts with constant magnitudes, time-varying shift patterns are frequently encountered in industrial practice. Among oth-ers, feedback-controlled processes and inertial processes are rather repre-sentative and popular in industries. However, the application of convention-al charts to such dynamic processes usually results in an unsatisfactory per-formance. Therefore, it is important to investigate the dynamic nature of these processes and introduce new schemes to detect such time-varying shift patterns more efficiently. In this thesis, an adaptive T2 chart is first proposed as a solution to the detection of dynamic shifts in a multivariate process. The adaptive T2 chart features monitoring a directionally variant statistic and updating its refer-ence vector repeatedly via exponentially weighted moving average (EWMA) forecasting. Therefore, its detection power is maximized at each step with respect to the predicted shifts. It is shown that the average run length (ARL) performance of the adaptive T2 chart depends on the process mean and co-variance matrix only through the value of the noncentrality parameter of the charting statistic. In addition, the adaptive T2 chart is flexible in design; its smoothing parameter can be tuned so that its performance over a desired shift range can be improved. Design guidelines for the adaptive T2 chart are also provided in this work. By noting all the features the adaptive T2 chart possesses, the research is carried on to implement the proposed chart to feedback-controlled processes and inertial processes. As oscillations are important features of feedback-controlled processes, an Oscillated EWMA (OEWMA) forecast-ing algorithm is developed to assist the estimation of the process mean shifts. The adaptive T2 chart based on OEWMA forecasting is shown to be robust even if the oscillation in a process is not obvious. One of the main features of an inertial process is its slow response to a sudden process change. In this thesis, the strategy of encapsulating historical observations for monitoring inertial processes is adopted; both model-based and model-free forecasting algorithms are studied. Simulation results show that the adaptive T2 chart based on EWMA is superior to other charts in detecting the dynamic shifts. As little is known about the performance of the adaptive T2 when parameters are estimated from samples, simulation experiments are conducted to investigate the effect of parameter estimation uncertainties. A guideline for choosing sample sizes is provided to practitioners. In multivariate process monitoring, including insignificant variables in-to charting statistics is both statistically inefficient and harmful to the chart-ing performance. The conventional dimension reduction techniques that are conducted statically during Phase I of chart design cannot satisfy the de-mand of processes with dynamic shifts. In this work, an adaptive dimension reduction framework is proposed. Specifically, several collections of pro-jection matrices are introduced. The original high-dimensional vectors are projected into a low dimensional space by the matrices. A multivariate sig-nal-to-noise ratio is introduced to evaluate the contribution of each variable to the charting performance dynamically. Only the variables that are in-structive to fault detection are being monitored. The chart that incorporates the adaptive dimension reduction technique is proved to be more efficient in detecting dynamic process shifts than conventional methods. The thesis finally presents a unified view of control charts. It is found that, including the newly proposed adaptive T2 chart, a lot of control charts can be fitted into this framework. The unified view provides a better under-standing of control charts and initializes opportunities for extending them to specfic applications